designv11-0.json

[
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure1-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure1-1.png",
        "caption": "Fig. 1 Triggering instants and intervals of event generator using static ETM: t0 = 0, tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.0586xT(t)x(t) } . The rectangular window indicates that time intervals between two consecutive triggering events tk+1 \u2212 tk are positive, i.e., Zeno behavior does not happen",
        "texts": [],
        "surrounding_texts": [
            "where\n\u03a9\u030411 = AP\u22121 + P\u22121AT + BY + Y TBT + \u03b5 I .\nMoreover, the control u(t) is obtained as follows:\nu(t) = Y Px(tk), t \u2208 [tk, tk+1).\nRemark 2 Different from the traditional digital control techniques, the main difficulty of the event-triggered control is that it requires the designingof both ofZeno-free eventtriggered mechanisms and controllers. In this paper, in order to solve the problem of event-triggered control for uncertain systems, we have proposed the static ETM (7) and the dynamic ETM (14) and proved that both of these ETMs are Zeno-free. Then, by using the ETMs (7) and (14), we have proposed LMI conditions (34), (44), (45) and (48) for the design of stabilizing event-triggered feedback controller u(t) = Kx(tk), k \u2208 [tk, tk+1).\nLet us consider the system of the form (1)\u2013(2), where\nA = \u23a1 \u23a3 \u22120.1 0 1 0 \u22122 0\n\u22120.1 2 0.1\n\u23a4 \u23a6 , B = \u23a1 \u23a3 1 2 3 \u23a4 \u23a6 , G = \u23a1 \u23a3 1 0 \u22120.1 \u23a4 \u23a6 ,\nF(t) = | sin t |, H = \u23a1 \u23a3 0.1 0\n0.01\n\u23a4 \u23a6 T , f (x(t)) = \u23a1 \u23a3 0.5 sin(x1(t)) 0\n0.5 sin(x3(t)).\n\u23a4 \u23a6 .\nIt is not hard to check that f (x(t)) is Lipschitz with L f = 0.5 and system (1) with u(t) = 0 is unstable. In the following, we will use Theorems 1 and 2 to design controller u(t) to stabilize system (1).\nBy using Theorem 1, for given \u03c3 = 0.8, the LMI condition (34) is feasible with \u03b51 = 0.6951, \u03b52 = 0.8614,\nP = \u23a1 \u23a3 0.264 0.0405 \u22120.0567 0.0405 0.1921 \u22120.1177\n\u22120.0567 \u22120.1177 0.2651\n\u23a4 \u23a6 ,\nY = [\u22121.2481 \u22121.3843 \u22122.1687 ] ,",
            "the static ETM is\ntk+1 = inf { t > tk | eT(t)e(t) \u2265 0.0586xT(t)x(t) } (49)\nand the control law u(t) is obtained as\nu(t) = [\u22120.2624 \u22120.0612 \u22120.3411 ] x(tk),\nfor t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 1 and 2 show the triggering instants and intervals of the event generator using static ETM and the state responses of (5). It is clear from Fig. 2 that system (5) is asymptotically stable.",
            "By using Theorem 2, for given \u03c3 = 0.8 and \u03b1 = 0.18, the LMI condition (45) is feasible with \u03b51 = 0.1078, \u03b52 = 0.0391,\nP = \u23a1 \u23a3\n1.5169 \u22120.0038 \u22120.1657 \u22120.0038 0.0559 0.009 \u22120.1657 0.009 0.4244\n\u23a4 \u23a6 , Y = [\u22120.1813 \u22120.6678 \u22120.7928 ] ,\nthe dynamic ETM is\ntk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.18xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } ,\n(50)\nand the control law u(t) is obtained as\nu(t) = [\u22120.2179 \u22120.0555 \u22120.3854 ] x(tk), t \u2208 [tk, tk+1).\nFor simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 3 and 4 show the triggering instants and intervals of the event generator using dynamic ETM and the state responses of system (5). It is clear from Fig. 4 that the closed-loop system is asymptotically stable."
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure17-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure17-1.png",
        "caption": "Fig. 17. Performance of the sliding surface.",
        "texts": [
            " 15 and 16 show the fulfillment of the constraints proosed for the TEs (\u22061 and \u22062). Notice that as in the simulaion, the controllers that are not considering in its mathematical tructure the error constraints do not satisfy the mentioned contraints. Also, the faster converge of the TEs when the CNTSM as implemented has been demonstrated in Figs. 15 and 16, espectively. Taking into consideration the results presented in Figs. 13\u201316, he last stage to verify the fulfillment of the state constraints is o verify the performance obtained in each sliding surface. To this oal, Fig. 17 evidences the fulfillment of the constraints proposed t t b t p f t d l N 8 he constraints proposed to the SS. However, the main problem ackled with the proposed controller is to ensure the full-state m constraints in the robotic system. That means, both states x1 and x2 must fulfill the predefined set of constraints. The last Figure presented in the experimental results section (Fig. 18), corresponds to the control signals provided to each DC Motor of the RM. From these figures, notice that both controllers (CNTSM and NCNTSM) exhibit similar control energy consumption"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure1-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure1-1.png",
        "caption": "Fig. 1. FEA inductance profiles of 12/8 SRM.",
        "texts": [
            " Substituting (2) into (1), the phase voltage equations can be derived as follows:[ vk vk\u22121 ] = R [ ik ik\u22121 ] + [ Linc k Minc k,k\u22121 Minc k\u22121,k Linc k\u22121, ]\u23a1 \u23a3 dik dt dik \u22121 dt \u23a4 \u23a6 + \u03c9m \u23a1 \u23a3 \u2202Lk , k \u2202 \u03b8 \u2202Mk , k \u22121 \u2202\u03b8 \u2202Mk \u22121 , k \u2202 \u03b8 \u2202Lk \u22121 , k \u22121 \u2202\u03b8 \u23a4 \u23a6 [ ik ik\u22121 ] (3) where \u03b8 and \u03c9m are rotor position and angular speed, respectively; incremental inductance and incremental mutual inductance can be denoted as follows: Linc k = Lk,k + ik dLk,k dik ; Linc k\u22121 = Lk\u22121,k\u22121 + ik\u22121 dLk\u22121,k\u22121 dik\u22121 (4) Minc k,k\u22121 = Mk,k\u22121 + ik\u22121 dMk,k\u22121 dik\u22121 . (5) Finite-element analysis (FEA) of the studied motor was conducted using JMAG software [17]. The incremental inductance and mutual inductance are shown in Fig. 1. As shown in Fig. 1(a), incremental inductance is both phase current and rotor position dependent. Therefore, by estimating incremental inductance and measuring the phase current, the rotor position can be estimated by using incremental-inductance-rotor position-current characteristics. Phase current is controlled by a hysteresis controller. By considering the mutual flux effect and magnetic saturation, the kth phase voltage equation is derived as (6) and (7) when kth phase switches are ON and OFF, respectively Udc = Rik + Linc k dik (tk on) dt + \u2202Lk,k \u2202\u03b8 ik\u03c9m + Minc k,k\u22121 dik\u22121(tk on) dt + \u2202Mk,k\u22121 \u2202\u03b8 ik\u22121\u03c9m (6) \u2212Udc = Rik + Linc k dik (tk off ) dt + \u2202Lk,k \u2202\u03b8 ik\u03c9m + Minc k,k\u22121 dik\u22121(tk off ) dt + \u2202Mk,k\u22121 \u2202\u03b8 ik\u22121\u03c9m (7) where tk on and tk off are time instants when the kth phase switches are ON and OFF, respectively, dik(tk o n )/dt and dik (tk off )/dt are the kth phase current slopes at tk on and tk off , respectively, and Udc is the dc-link voltage",
            " By considering the magnetic saturation, the incrementalinductance estimation error due to the mutual flux can be derived as (11) and (12), shown at the bottom of the page, in Modes I and II, respectively [16]. In Mode III, at tk on(III) and tk off (III) , (k\u20131)th phase current slope has the same sign (either both negative or positive). Therefore, the mutual flux effect does not exist in Mode III Comparing (11) and (12), the absolute value of incrementalinductance estimation error in Mode I is slightly higher than that in Mode II. Based on the magnetic characteristics of the studied SRM shown in Fig. 1, the absolute value of incrementalinductance estimation error of phase A due to mutual flux from phase C in Mode I is shown in Fig. 3. Considering the magnetic saturation, incremental-inductance estimation error due to mutual flux is both rotor position and current dependent. As shown in Fig. 4, the mutual flux from phase C introduces around maximum 7% and minimum 1% error in phase A incrementalinductance estimation. Based on the error analysis in the last section, the mutual flux introduces a maximum\u00b17% incremental-inductance estimation error in Modes I and II, while the mutual flux effect does not exist in Mode III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure6-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure6-1.png",
        "caption": "Fig. 6 Responses of x1(t), x2(t) and x3(t) of the closed-loop system (5) using static ETM: t0 = 0, tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.1753xT(t)x(t) } . The rectangular window indicates that the stabilizability of the closed-loop system (42) using the above static ETM is guaranteed",
        "texts": [
            "9633, P = \u23a1 \u23a3 0.354 \u22120.0228 0.0017 \u22120.0228 0.4749 0.0032 0.0017 0.0032 0.4148 \u23a4 \u23a6 , Y = [\u22120.0125 \u22120.0272 \u22121.0269 ] , the static ETM is tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.1753xT(t)x(t) } (53) and the control law u(t) is obtained as u(t) = [\u22120.0056 \u22120.0159 \u22120.426 ] x(tk), for t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 5 and 6 show the triggering instants and intervals of the event generator using static ETM and the state responses of (42). It is clear from Fig. 6 that system (42) is asymptotically stable. By using Corollary 2, for given \u03c3 = 0.9 and \u03b1 = 0.25, the LMI condition (48) is feasible with \u03b5 = 1.0237, P = \u23a1 \u23a3 0.3222 0.0214 0.0022 0.0214 0.1458 0.0026 0.0022 0.0026 0.463 \u23a4 \u23a6 , Y = [ 0.0129 \u22120.0544 \u22120.9428 ] , the dynamic ETM is tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.25xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } , (54) and the control law u(t) is obtained as u(t) = [ 0.0009 \u22120.0101 \u22120.4366 ] x(tk), t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure5-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure5-1.png",
        "caption": "Fig. 5. Illustration of the proposed variable-hysteresis-band current controller.",
        "texts": [
            " Therefore, errk(I) = \u2212Minc k,k\u22121 Linc k\u22121 + Minc k,k\u22121 (L in c k \u22121 \u2212M in c k , k \u22121 ) (L in c k\u2212M in c k , k \u22121 ) \u2212 Minc k,k\u22121 (11) errk(II) = Minc k,k\u22121 Linc k\u22121 + Minc k,k\u22121 L in c k \u22121 +M in c k , k \u22121 L in c k \u2212M in c k , k \u22121 + Minc k,k\u22121 (12) the outgoing-phase incremental-inductance estimation is always operating in Mode III by using this scheme. Since the phase current slope of kth phase (incoming phase) is much higher than (k\u20131)th phase, the sign of (k\u20131)th phase current slope is changed only once or not changed at all. Therefore, the variable-sampling scheme cannot be applied to the incoming-phase incrementalinductance estimation. Fig. 5 illustrates the principle of the proposed variablehysteresis-band current control during the kth phase estimation. The basic concept of the variable-hysteresis-band current control method is to make sure that the switching state of (k\u20131)th phase is unchanged during the time intervals tk on(II)-tk off (II) and tk on(I)-tk off (I) . Therefore, the sign of (k\u20131)th phase current slope is unchanged in these intervals. When the incrementalinductance estimation of kth phase is completed at tko n ( I I ) and tko f f ( I ) , switches of (k\u20131)th phase are turned off or on according to the error between (k\u20131)th phase current and its reference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure3-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure3-1.png",
        "caption": "Fig. 3 The triggering instants and intervals of event generator using dynamic ETM: t0 = 0, tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.18xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } . The rectangular window indicates that the time intervals between two consecutive triggering events tk+1 \u2212 tk are positive, i.e., Zeno behavior does not happen. Clearly, the next execution time given by this dynamic ETM is larger than that given by the static ETM shown in Fig. 1",
        "texts": [],
        "surrounding_texts": [
            "By using Theorem 2, for given \u03c3 = 0.8 and \u03b1 = 0.18, the LMI condition (45) is feasible with \u03b51 = 0.1078, \u03b52 = 0.0391, P = \u23a1 \u23a3 1.5169 \u22120.0038 \u22120.1657 \u22120.0038 0.0559 0.009 \u22120.1657 0.009 0.4244 \u23a4 \u23a6 , Y = [\u22120.1813 \u22120.6678 \u22120.7928 ] , the dynamic ETM is tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.18xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } , (50) and the control law u(t) is obtained as u(t) = [\u22120.2179 \u22120.0555 \u22120.3854 ] x(tk), t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 3 and 4 show the triggering instants and intervals of the event generator using dynamic ETM and the state responses of system (5). It is clear from Fig. 4 that the closed-loop system is asymptotically stable."
        ]
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure2-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure2-1.png",
        "caption": "Fig. 2 Responses of x1(t), x2(t) and x3(t) of the closed-loop system (5) using static ETM: t0 = 0, tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.0586xT(t)x(t) } . The rectangular window indicates that the stabilizability of the closed-loop system (5) using the above static ETM is guaranteed",
        "texts": [
            "8614, P = \u23a1 \u23a3 0.264 0.0405 \u22120.0567 0.0405 0.1921 \u22120.1177 \u22120.0567 \u22120.1177 0.2651 \u23a4 \u23a6 , Y = [\u22121.2481 \u22121.3843 \u22122.1687 ] , the static ETM is tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.0586xT(t)x(t) } (49) and the control law u(t) is obtained as u(t) = [\u22120.2624 \u22120.0612 \u22120.3411 ] x(tk), for t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 1 and 2 show the triggering instants and intervals of the event generator using static ETM and the state responses of (5). It is clear from Fig. 2 that system (5) is asymptotically stable. By using Theorem 2, for given \u03c3 = 0.8 and \u03b1 = 0.18, the LMI condition (45) is feasible with \u03b51 = 0.1078, \u03b52 = 0.0391, P = \u23a1 \u23a3 1.5169 \u22120.0038 \u22120.1657 \u22120.0038 0.0559 0.009 \u22120.1657 0.009 0.4244 \u23a4 \u23a6 , Y = [\u22120.1813 \u22120.6678 \u22120.7928 ] , the dynamic ETM is tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.18xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } , (50) and the control law u(t) is obtained as u(t) = [\u22120.2179 \u22120.0555 \u22120.3854 ] x(tk), t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000027_d0an02029j-Figure4-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000027_d0an02029j-Figure4-1.png",
        "caption": "Fig. 4 (A) Fluorescence spectra and photograph of the CdZnTeS QDs (a) in ultrapure water, with (b) H2O2, (c) uric acid, (d) urate oxidase, and (e) uric acid + urate oxidase. (B) Grayscale response and photograph of the Alg@QDs-UOx MSs (f ) in ultrapure water, with (g) uric acid and (h) H2O2. Uric acid: 500 \u03bcM; urate oxidase: 0.25 units per ml; and H2O2: 500 \u03bcM. Excitation wavelength: 340 nm.",
        "texts": [
            " The amount of the 530 nm emission of CdZnTeS QDs was fixed as 15 nM, and the amount of urate oxidase was changed to optimize the feed ratio (Fig. S7\u2020), and the optimal feed ratio of CdZnTeS QDs to urate oxidase was 15 nM : 0.25 units per mL. The reaction time was optimized as shown in Fig. S8,\u2020 and with the increase of reaction time, the fluorescence intensity of the Alg@QDs-UOx MSs gradually decreased, and reached the minimum value at 10 minutes. So 10 minutes was chosen as the best reaction time. To investigate the feasibility of the proposed sensor for uric acid detection, as shown in Fig. 4A, addition of uric acid or urate oxidase to the CdZnTeS QD solution did not affect the fluorescence of the CdZnTeS QDs, while the fluorescence of the CdZnTeS QDs was quenched by the addition of H2O2 or the simultaneous addition of uric acid and urate oxidase. As shown in Fig. 4B, Alg@QDs-UOx MSs showed a good performance for visual detection of H2O2 and uric acid. The fluorescence response of the Alg@QDs-UOx MSs in different concentrations of uric acid (0\u2013900.0 \u03bcM) is shown in Fig. 5A and B, the Alg@QDs-UOx MSs had a good visual effect on uric acid detection under the self-made device. A good Analyst This journal is \u00a9 The Royal Society of Chemistry 2020 Pu bl is he d on 1 8 N ov em be r 20 20 . D ow nl oa de d by C ar le to n U ni ve rs ity o n 11 /3 0/ 20 20 2 :2 2: 53 P M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure18-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure18-1.png",
        "caption": "Fig. 18. Control signals.",
        "texts": [
            " 13\u201316, he last stage to verify the fulfillment of the state constraints is o verify the performance obtained in each sliding surface. To this oal, Fig. 17 evidences the fulfillment of the constraints proposed t t b t p f t d l N 8 he constraints proposed to the SS. However, the main problem ackled with the proposed controller is to ensure the full-state m constraints in the robotic system. That means, both states x1 and x2 must fulfill the predefined set of constraints. The last Figure presented in the experimental results section (Fig. 18), corresponds to the control signals provided to each DC Motor of the RM. From these figures, notice that both controllers (CNTSM and NCNTSM) exhibit similar control energy consumption. Therefore, one of the advantages of the CNTSM is to guarantee the fulfillment of the full state constraints in the RM without excessive consume of energy. With the aim of evidencing the obtained performance of the proposed controller, the least mean square error (LMSE) of the TE (\u2206) as well as the integral of the absolute value of the control signal (\u03c4 ) obtained with the NTSM, NCNTSM, and CNTSM have een summarized in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure4-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure4-1.png",
        "caption": "Fig. 4. Tracking error \u22061 of the two-link RM.",
        "texts": [],
        "surrounding_texts": [
            "l\n[\nt a F \u03b2\nN\nFig. 1. Control diagram of the trajectory tracking case.\nt s ( s t t t c\nf k 0\nThe simulations results were developed considering the folowing parameters m1 = 0.35 Kg, m2 = 0.35 Kg, l1 = 0.12 m, l2 = 0.12 m. Also, the value g = \u22129.8 m\ns2 was considered as the\ngravitational constant. Notice that these values match with the real plant parameters.\nThe initial state conditions were set to x1,1(0) = 0.1, x1,2(0) = \u22120.12, x\u03072,1(0) = 1.5 and x\u03072,2(0) = 0.95. The vector h that contains the reference trajectories proposed for each link of the RM were selected as h = [ sin (2t) sin (1.5t)\n]\u22a4. Consequently, the upper bounds for each reference trajectory and its derivatives are given by h+\n1,1 = 1, h+ 1,2 = 1, h+ 2,1 = 2 and h+ 2,2 = 1.5. To facilitate the application of the proposed controller in the numerical simulations, Fig. 1 shows a control diagram that illustrates the interaction of all the parameters involved in the proposed control design (given in Section 4C).\nFor the numerical simulations, it is also assumed that from t = 4 to t = 11, an external disturbance \u03b7(q) is affecting the RM. Then, the external perturbation is given by \u03b7(q) =\n0.2 sin(4t) 0.09 sin(10t) ]\u22a4. To validate the effectiveness of the control scheme (CNTSM) the performance obtained with the proposed controller is compared with the non-singular terminal sliding mode (NTSM) controller developed in [25]. In this work,\nthe sliding manifold is selected as \u03c3i = \u22061,i + 1 \u03b1+\ni \u2206\npi qi 2,i. On the\nother hand, the CNTSM controller is also compared with its non constraint counterpart. That means, the time varying gain (28) is changed by a constant. Notice that this change induces that the CNTSM actuates like a classical NTSM. The non constraint version of the CNTSM is named NCNTSM in the following results.\nThe numerical results consider that only the state x1 of the RM is available. Then, the ASTA proposed in the current manuscript is used to obtain the estimation of the state x2.\nThe considered values to adjust the ASTA algorithms for each link of the RM are: \u03b6i = 0.998, \u03b31,i = 0.8, \u03b32,i = 0.82, \u039b+\n1,i = 30, \u039b+\n2,i = 35, \u03bd+ 1,i = 20, \u03bd+ 2,i = 22 \u03bb+ 1,i = 18, \u03bb+ 2,i = 20 with i = 1, 2 describing the link number.\nOn the other hand, the values that adjust the proposed control are p1 = p2 = 7 and q1 = q2 = 5. The corresponding control gains \u03b11 and \u03b12 satisfy the structure give in (23) with \u03c81 = 100, \u03c82 = 100. The parameters \u03b91 and \u03b92 are proposed equal to zero o avoid the singularity problem. The upper value of each gain \u03b11 nd \u03b12 are given by \u03b1+ 1 = 0.95 and \u03b1+\n2 = 0.75, respectively. inally, for the controls \u03c42,1 and \u03c42,2, the gains \u03b21 = 48 and 2 = 64 are selected. To compare the performance of the control schemes NTSM and CNTSM with the proposed controller (CNTSM), the values for\nhe gains p1, p2, q1 and q2 as well as the gains \u03b1+ 1 and \u03b1+ 2 are elected similar to the CNTSM case. Consider that in both cases NTSM and NCNTSM) the gains for the control \u03c42,1 and \u03c42,2 are elected as a constants, that is, k1 = 92.5 and k2 = 122.5. Because hese control schemes do not consider the state constraints in heir structures. The mentioned values are selected considering he mean value of the gains k1 and k2 obtained with the CNTSM ontroller. The results presented below consider that the state constraints or the two-link RM are given by kb1,1 = 1.25, kb1,2 = 1.25, b2,1 = 2.15 and kb2,2 = 2.65. The TEs constraints satisfy k\u22061,1 =\n.2, k\u22061,2 = 0.2 aside from k\u22062,1 = 0.6, k\u22062,2 = 0.6, all of them satisfying the conditions given in (11).\nRemark 5. It should be noticed that in the simulation section, the set of predefined constraints has been selected to evidence the following scenarios. (1) The same position constraint for both links of the RM. (2) Different velocities constraints for each RM link. (3) Different TE constraints for each RM joint. Moreover, Figs. 1\u20136 evidence the effectiveness of the CNTSM to solve the RM trajectory tracking.\nThe mentioned scenarios (Remark 4) have been selected to evidence the effectiveness of the CNTSM despite of the constraints selection. Obviously, taking into account that the initial conditions of the sliding surface must begin inside the set of the predefined constraints.\nFigs. 2 and 3 show a comparison of the performance obtained with the selected three controllers. Notice that for the case of the first link, all controllers solve the trajectory tracking. Nevertheless, in the case of the second link, the NTSM and NCNTSM cannot satisfy the state constraint given by kb1,2.\nThe previous fact evidences the effectiveness of the CNTSM controller to guarantee the state constraints fulfillment. Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated.\nFigs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6.\nThe norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the",
            "p N\nroposed CNTSM performed better than the NTSM as well as the CNTSM.\nt\nIn addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained",
            "w 5 w o N\na w c s H e t t s c s\nith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM). The control signals obtained with the three controller schemes re compared in Fig. 9. The depicted control signals are obtained ith the implementation of a first order low-pass filter with a ut-off frequency of 100 Hz. This value was obtained using the uggestions obtained from the seminal study provided in [8]. ere, it is important to notice that all the controllers use a similar nergy (See Fig. 9). Therefore, from the energetic point of view, he proposed controller yields the better option to solve the rajectory tracking problem of a RM, as well as to satisfy the tate constraints but without an excess of energy consumption ompared to the other considered controllers. This condition is ignificant because the fulfillment of the state restrictions yields\nFig. 8. Histogram of \u2206 obtained with tested controllers.\nFig. 9. Control signals.\nto get the realization of a bounded controller as well. Hence, the benefits of the proposed controller include the finite-time accelerated converge to the origin of the TEs, the output feedback realization and the realization of a competitive bounded controller (in terms of the consumed energy).\n7. Practical implementation\nThis section presents the experimental setup (mechanical and electronic instrumentation) as well as the proposed control implementation. In addition, to evidence the effectiveness of the proposed control scheme a comparison between the proposed controller, a NTSM and, a NCNTSM controller has been added.\nThe proposed experimental setup considers a two-link RM that satisfies the dynamic model given in (6). The following subsection describes the mechanical structure of the RM as well as its electronic instrumentation."
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure3-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure3-1.png",
        "caption": "Fig. 3. Trajectory tracking of the state x2 .",
        "texts": [],
        "surrounding_texts": [
            "l\n[\nt a F \u03b2\nN\nFig. 1. Control diagram of the trajectory tracking case.\nt s ( s t t t c\nf k 0\nThe simulations results were developed considering the folowing parameters m1 = 0.35 Kg, m2 = 0.35 Kg, l1 = 0.12 m, l2 = 0.12 m. Also, the value g = \u22129.8 m\ns2 was considered as the\ngravitational constant. Notice that these values match with the real plant parameters.\nThe initial state conditions were set to x1,1(0) = 0.1, x1,2(0) = \u22120.12, x\u03072,1(0) = 1.5 and x\u03072,2(0) = 0.95. The vector h that contains the reference trajectories proposed for each link of the RM were selected as h = [ sin (2t) sin (1.5t)\n]\u22a4. Consequently, the upper bounds for each reference trajectory and its derivatives are given by h+\n1,1 = 1, h+ 1,2 = 1, h+ 2,1 = 2 and h+ 2,2 = 1.5. To facilitate the application of the proposed controller in the numerical simulations, Fig. 1 shows a control diagram that illustrates the interaction of all the parameters involved in the proposed control design (given in Section 4C).\nFor the numerical simulations, it is also assumed that from t = 4 to t = 11, an external disturbance \u03b7(q) is affecting the RM. Then, the external perturbation is given by \u03b7(q) =\n0.2 sin(4t) 0.09 sin(10t) ]\u22a4. To validate the effectiveness of the control scheme (CNTSM) the performance obtained with the proposed controller is compared with the non-singular terminal sliding mode (NTSM) controller developed in [25]. In this work,\nthe sliding manifold is selected as \u03c3i = \u22061,i + 1 \u03b1+\ni \u2206\npi qi 2,i. On the\nother hand, the CNTSM controller is also compared with its non constraint counterpart. That means, the time varying gain (28) is changed by a constant. Notice that this change induces that the CNTSM actuates like a classical NTSM. The non constraint version of the CNTSM is named NCNTSM in the following results.\nThe numerical results consider that only the state x1 of the RM is available. Then, the ASTA proposed in the current manuscript is used to obtain the estimation of the state x2.\nThe considered values to adjust the ASTA algorithms for each link of the RM are: \u03b6i = 0.998, \u03b31,i = 0.8, \u03b32,i = 0.82, \u039b+\n1,i = 30, \u039b+\n2,i = 35, \u03bd+ 1,i = 20, \u03bd+ 2,i = 22 \u03bb+ 1,i = 18, \u03bb+ 2,i = 20 with i = 1, 2 describing the link number.\nOn the other hand, the values that adjust the proposed control are p1 = p2 = 7 and q1 = q2 = 5. The corresponding control gains \u03b11 and \u03b12 satisfy the structure give in (23) with \u03c81 = 100, \u03c82 = 100. The parameters \u03b91 and \u03b92 are proposed equal to zero o avoid the singularity problem. The upper value of each gain \u03b11 nd \u03b12 are given by \u03b1+ 1 = 0.95 and \u03b1+\n2 = 0.75, respectively. inally, for the controls \u03c42,1 and \u03c42,2, the gains \u03b21 = 48 and 2 = 64 are selected. To compare the performance of the control schemes NTSM and CNTSM with the proposed controller (CNTSM), the values for\nhe gains p1, p2, q1 and q2 as well as the gains \u03b1+ 1 and \u03b1+ 2 are elected similar to the CNTSM case. Consider that in both cases NTSM and NCNTSM) the gains for the control \u03c42,1 and \u03c42,2 are elected as a constants, that is, k1 = 92.5 and k2 = 122.5. Because hese control schemes do not consider the state constraints in heir structures. The mentioned values are selected considering he mean value of the gains k1 and k2 obtained with the CNTSM ontroller. The results presented below consider that the state constraints or the two-link RM are given by kb1,1 = 1.25, kb1,2 = 1.25, b2,1 = 2.15 and kb2,2 = 2.65. The TEs constraints satisfy k\u22061,1 =\n.2, k\u22061,2 = 0.2 aside from k\u22062,1 = 0.6, k\u22062,2 = 0.6, all of them satisfying the conditions given in (11).\nRemark 5. It should be noticed that in the simulation section, the set of predefined constraints has been selected to evidence the following scenarios. (1) The same position constraint for both links of the RM. (2) Different velocities constraints for each RM link. (3) Different TE constraints for each RM joint. Moreover, Figs. 1\u20136 evidence the effectiveness of the CNTSM to solve the RM trajectory tracking.\nThe mentioned scenarios (Remark 4) have been selected to evidence the effectiveness of the CNTSM despite of the constraints selection. Obviously, taking into account that the initial conditions of the sliding surface must begin inside the set of the predefined constraints.\nFigs. 2 and 3 show a comparison of the performance obtained with the selected three controllers. Notice that for the case of the first link, all controllers solve the trajectory tracking. Nevertheless, in the case of the second link, the NTSM and NCNTSM cannot satisfy the state constraint given by kb1,2.\nThe previous fact evidences the effectiveness of the CNTSM controller to guarantee the state constraints fulfillment. Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated.\nFigs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6.\nThe norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the",
            "p N\nroposed CNTSM performed better than the NTSM as well as the CNTSM.\nt\nIn addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained",
            "w 5 w o N\na w c s H e t t s c s\nith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM). The control signals obtained with the three controller schemes re compared in Fig. 9. The depicted control signals are obtained ith the implementation of a first order low-pass filter with a ut-off frequency of 100 Hz. This value was obtained using the uggestions obtained from the seminal study provided in [8]. ere, it is important to notice that all the controllers use a similar nergy (See Fig. 9). Therefore, from the energetic point of view, he proposed controller yields the better option to solve the rajectory tracking problem of a RM, as well as to satisfy the tate constraints but without an excess of energy consumption ompared to the other considered controllers. This condition is ignificant because the fulfillment of the state restrictions yields\nFig. 8. Histogram of \u2206 obtained with tested controllers.\nFig. 9. Control signals.\nto get the realization of a bounded controller as well. Hence, the benefits of the proposed controller include the finite-time accelerated converge to the origin of the TEs, the output feedback realization and the realization of a competitive bounded controller (in terms of the consumed energy).\n7. Practical implementation\nThis section presents the experimental setup (mechanical and electronic instrumentation) as well as the proposed control implementation. In addition, to evidence the effectiveness of the proposed control scheme a comparison between the proposed controller, a NTSM and, a NCNTSM controller has been added.\nThe proposed experimental setup considers a two-link RM that satisfies the dynamic model given in (6). The following subsection describes the mechanical structure of the RM as well as its electronic instrumentation."
        ]
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure2-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure2-1.png",
        "caption": "Fig. 2. Illustration of three modes during kth phase inductance estimation.",
        "texts": [
            " (8) If the mutual inductance is neglected, incremental inductance can be estimated as follows: Linc k = 2Udc dik (tk o n ) dt \u2212 dik (tk o f f ) dt . (9) Therefore, incremental-inductance estimation error due to mutual flux can be derived as follows: errk = (Linc k m \u2212 Linc k )/Linc k m = \u2212Minc k,k\u22121 ( dik \u22121 (tk o n ) dt \u2212 dik \u22121 (tk o f f ) dt ) 2Udc \u2212 Minc k,k\u22121 ( dik \u22121 (tk o n ) dt \u2212 dik \u22121 (tk o f f ) dt ) . (10) In order to analyze the incremental-inductance estimation error due to the mutual flux, three modes are defined during kth phase incremental-inductance estimation as shown in Fig. 2: Modes I\u2013III. Since the incremental inductance of the incoming phase (kth phase) is much lower, kth phase current slope is much higher than (k\u20131)th phase. Upper and lower current references of kth phase are denoted as ik up and ik low , respectively, and upper and lower current references of (k\u20131)th phase are denoted as ik\u22121 u p and ik\u22121 low , respectively. The positive-current slope and negative-current slope of kth phase are sampled at tk on(III) and tk off (III) in Mode III, t kon(II) and t kon(II) in Mode II, and t kon(I) and tk off (I) in Mode I, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure3-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure3-1.png",
        "caption": "Fig. 3. Quantified time evolution of the centre, boundary and diameter of the weld pool. Wel (c) current:125 A DC, weld time 2 s. (d) current:100 A DC, weld time 3 s.",
        "texts": [
            " A relatively short time after stopping the arc (in this sequence just after 2 s), the next major transition starts. In this transition, the top surface of the entre liquid pool drops below the level of the original solid surface level and forms the final solidified shape of theweld pool. Evenwith different welding parameters, a basic similarity in the rising behavior of the melt pool surfaces was indicated. The quantitative figures on the weld pool height transitions extracted from the fast image sequences of different welding process are presented in Fig. 3. The way that the liquid-air interface (free surface) at the weld pool center and the raised interface position close to the circumference along with the weld pool diameter is shown in Fig. 3 for comparative welding conditions. In all 4 experimental cases presented here, the overall pool surface height increased at the beginning of the welding process and later dropped below the initial solid surface level. The surface height of the center section reaches its maximum much quicker than the maximum level of the edge in all the cases. As shown in Fig. 3b and d compared to DC same nominal AC (alternating current) power input will take a relatively long time for the center and edge surfaces to reach their peak positions. This is appeared to correlatewith the relatively lower heating capacity (produced at the sample/substrate) through theACmode. As a result of the reversingpolarity, ACmode generates heat only a half of the time at the sample. This relatively lower level of heating received at the weld pool (AC mode) is indicated by the slower growth of the weld pool [34]",
            " Higher rate of heating received (at the center of the pool) in a short time scale, compared to the thermal diffusion time scale [16,35], can accumulate and increase the temperature in the center of the weld pool. Thus, surface tension (Marangoni) force driven flow can be intensified as a result of the larger temperature difference across the pool. This is somewhat similar to the conditions between the low and the high welding currents. The diameter of the weld pool with the relatively high current (i.e. 125 A vs 100 A) is expanding faster and the peak values for the free surface levels appear much quicker as shown in Fig. 3c. However, once the pool is big enough and no solid boundaries to contain the liquid, surface of the melt pool tend to plunge below its original solid position, decanting through themolten sidewalls. This situation shows the significance of the self-weight of themelt for resulting dynamics. It indicates the dominance of the gravity over arc and surface tension forces to drive the major change of the weld pool shape. If the heating power is higher, the free surface of the weld pool is observed to plunge and decant much quicker. Further, if the arc force and the current is relatively high (e.g. Fig. 3c), faster increase in pool size facilitates the gravity to dominate with the self-weight much earlier [9]. Once the power input is stopped, increased domination of gravity driven self-weight is indicated though drastic drop of the free surface level. As further confirmed as shown in Fig. 3d, when the pool size is reached to a critical level, gravity driven self-weight inflicts the drop of the free surface level even arc and surface tension forces are continuing to present. When quantitatively evaluate the flow rates using the marker particle motion for a representative case (100 A, AC, 3 s), the flow rate of particles throughout the welding process was ranging from 10 mm/s to 30 mm/s. These values are far less than the values reported with a powder additive manufacturing melt pools [31]",
            " However, quite similar to values suggested for welding [14]. These differences directly result from the process that generates the melt pool. Melt pool size, heat source and thermal gradients can be predominant parameters affecting. Considering the time evolution, the flow rates were relatively slow (around 16 \u00b1 3 mm/s) within initial 0.5 s and peaked around 2 s (around 25 \u00b1 5 mm/s). The peak values are associated to the instances that melt pool-air interface rapidly rose, where the size of the melt pool reached to the peak size as shown in Fig. 3 (b). The increase in flow (particle motion) speed at the beginning is more consistence with the increase of surface tension (thermal) gradient with the continuous energy input. Thereafter, it was possible to gradual decrease in the flow rates. At the time of the arc is stopped, the average flow (particle motion) speed is about half compared to the peak levels (around 15 \u00b1 6 mm/s), indicating gradual reduction of surface tension driven force, as result of gradually decreasing thermal gradient across the pool",
            " 4 represent just the central cross section and one might not presume there are completely free of porosity, but we believe they represent overall conditions reasonably. Even though not the statement of the overall weld spectrum in general, according to the Fig. 4, observations help to confirm that varied current or a weld times can produce variations in the porosity levels and pore distribution. The flow pattern within the melt pool which dominated by arc or surface tension force can be notably reduced (for increased time period) with the increasing of weld time or higher welding current as shown in Fig. 3. The formation of pores in the weld pool is commonly observed in all the conditions. Of course, the external factors such as sample, environmental andweld conditions affect porosity a lot [36,37]. Nevertheless, as we maintained the same sample and overall welding procedure during the experiments, thus we can suggest that the flow patterns and driving forces significantly affected the retaining or escaping of the formed pores that dictate the final porosity levels in our experiments presented here",
            " As mentioned above, arc force generally triggered the inward force, surface tension gradient force caused outward force and gravity induced downward forces respectively within the moltenmetal [15,41], if there is no special alterations i.e. surface tension modifiers. As observed, the surface of the melt pool initially peaked at the center, followed by the rising at the pool periphery. This observation is quite consistent with the morphology evolution of the melt pool caused by inward and outwardflow. As presented in Fig. 3, the peak surface height at the center part is lower than the edge surface. At the latter instance; the both forces (+ gravity) are present, but surface tension drive flow is appeared to prevail indicating its relative strength as suggested by previous theoretical analysis [1]. In the initial stage of the welding, the pool diameter is small and a lower temperature difference in the small immatureweld pool is envisaged. Therefore, the surface tension gradient driven force is relatively lower in magnitude",
            "31 \u00d7 10\u22124N/(m\u00d7 K) and the average temperature gradient is calculated approximately \u22121.7 \u00d7 106K/m according ref. [51]. Even though the input values for calculations are basic approximations, it can be seen from Fig. 7(b) that when the diameter of the melt pool is smaller than 4 mm, the arc force should be the main driving ce and surface tension force vs. melt pool diameter. Weld parameters: current: 100 A DC, force for the flow of the entire molten metal. This is almost consistent with the position which the centre interface reached the highest point in Fig. 3(a). When the diameter of the melt pool is around 4 mm to 6 mm, as the surface temperature gradient rises, the surface tension dominates the internal flow in the melt pool. This corresponds to the highest point at the edge surface when the melt pool diameter reaches 6mm.With the expansion of themelt pool, the influence of buoyancy is getting larger and larger, which causes the interface of the entire melt pool to decline. Beyond our basic analytical calculations, enhanced theoretical predications can be extracted through numerical computations that can couple all these phenomena, which is beyond the scope of current work"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure5-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure5-1.png",
        "caption": "Fig. 5 Triggering instants and intervals of event generator using static ETM: t0 = 0, tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.1753xT(t)x(t) } . The rectangular window indicates that time intervals between two consecutive triggering events tk+1 \u2212 tk are positive, i.e., Zeno behavior does not happen",
        "texts": [],
        "surrounding_texts": [
            "By using Corollary 1, for given \u03c3 = 0.9, the LMI condition (44) is feasible with \u03b5 = 1.9633, P = \u23a1 \u23a3 0.354 \u22120.0228 0.0017 \u22120.0228 0.4749 0.0032 0.0017 0.0032 0.4148 \u23a4 \u23a6 , Y = [\u22120.0125 \u22120.0272 \u22121.0269 ] , the static ETM is tk+1 = inf { t > tk | eT(t)e(t) \u2265 0.1753xT(t)x(t) } (53) and the control law u(t) is obtained as u(t) = [\u22120.0056 \u22120.0159 \u22120.426 ] x(tk), for t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 5 and 6 show the triggering instants and intervals of the event generator using static ETM and the state responses of (42). It is clear from Fig. 6 that system (42) is asymptotically stable."
        ]
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure3-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure3-1.png",
        "caption": "Fig. 3. Incremental-inductance estimation error of phase A due to mutual flux.",
        "texts": [
            " In Mode III, at tk on(III) and tk off (III) , (k\u20131)th phase current slope has the same sign (either both negative or positive). Therefore, the mutual flux effect does not exist in Mode III Comparing (11) and (12), the absolute value of incrementalinductance estimation error in Mode I is slightly higher than that in Mode II. Based on the magnetic characteristics of the studied SRM shown in Fig. 1, the absolute value of incrementalinductance estimation error of phase A due to mutual flux from phase C in Mode I is shown in Fig. 3. Considering the magnetic saturation, incremental-inductance estimation error due to mutual flux is both rotor position and current dependent. As shown in Fig. 4, the mutual flux from phase C introduces around maximum 7% and minimum 1% error in phase A incrementalinductance estimation. Based on the error analysis in the last section, the mutual flux introduces a maximum\u00b17% incremental-inductance estimation error in Modes I and II, while the mutual flux effect does not exist in Mode III. Two methods will be proposed, which forces the incremental-inductance estimation to operate in Mode III exclusively: the variable-sampling method for the outgoing phase and variable-hysteresis-band current control for the incoming phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure6-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure6-1.png",
        "caption": "Fig. 6. Simulation results of rotor position estimation (Tref = 3 N \u00b7 m, Speed = 1500 r/min). (a) Rotor position estimation method without variable hysteresis band and sampling. (b) Proposed rotor position estimation.",
        "texts": [
            " Turn-on angle \u03b8on , turn-off angle \u03b8off , and overlapping angle \u03b8ov of linear TSF are set to 5\u00b0, 20\u00b0, and 2.5\u00b0, respectively. DC-link voltage is 300 V. The sampling time tsample is set to 5 \u03bcs and current hysteresis band is set to 0.5 A. The incremental-inductance estimation error and rotor position estimation error are denoted as errL = Lreal \u2212 Le Lreal ; err\u03b8 = \u03b8real \u2212 \u03b8e (13) where Lreal and Le are real and estimated inductance, respectively, and \u03b8real and \u03b8e are real position and estimated position, respectively. The torque reference is set to 3 N \u00b7 m. Fig. 6 shows simulation results of the proposed rotor position estimation with and without variable hysteresis band and sampling at 1500 r/min. As shown in Fig. 6, due to magnetic saturation, incremental inductance varies with rotor position and phase current. Since phase current is not constant, the SRM is operating either in saturated magnetic region or linear magnetic region. Therefore, both incremental inductance and phase current are necessary for estimating the rotor position. The maximum incrementalinductance estimation error without variable hysteresis band and sampling is \u00b17%, which matches theoretical analysis given in Fig. 4. Due to incremental-inductance estimation error, the maximum real-time rotor position estimation error is around \u00b12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure7-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure7-1.png",
        "caption": "Fig. 7 The triggering instants and intervals of event generator using dynamic ETM: t0 = 0, tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.25xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } . The rectangular window indicates that the time intervals between two consecutive triggering events tk+1 \u2212 tk are positive, i.e., Zeno behavior does not happen. Clearly, the next execution time given by this dynamic ETM is larger than that given by the static ETM shown in Fig. 5",
        "texts": [],
        "surrounding_texts": [
            "In this paper, we have proposed a systematic method for designing of robust stabilizing event-triggered feedback controllers for a class of systems with time-varying uncertainties and nonlinear Lipschitz functions. We have considered both static ETM and dynamic ETM and proved that for the considered ETMs, the Zeno phenomenon does not happen. Sufficient conditions based on linear matrix inequalities have been provided to guarantee the asymptotic stability of the closed-loop system. The eventtriggered feedback controllers are derived by using existing computationally effective convex algorithms. The effectiveness of the design method has been supported by two examples and simulation results. Further work is required to extend the results of this paper to systemswith time delays. Also, the problem of designing event-triggered state observers for nonlinear systems with time delays and disturbances is an interesting problem for future research. Acknowledgements The authors sincerely thank the anonymous reviewers for their constructive comments that helped improve the quality and presentation of this paper. The research of the first author was funded by the Ministry of Education and Training of Vietnam, under grant B2020-DQN-01."
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure15-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure15-1.png",
        "caption": "Fig. 15. Tracking error \u22061 of the two-link RM.",
        "texts": [],
        "surrounding_texts": [
            "e a t a t d l e o ( b t F\nc t r t t h p a r\nm o m m c t\n7\nf\nm s c t C\n7.1. Experimental setup description\nThe mechanical dimensions (longitudinal) of each robotic link satisfies l1 = 0.12 m, l2 = 0.12 m. All the pieces that integrate the xperimental platform has been designed by using a computer ssisted drawing software named SolidWorks. Fig. 10 depicts he mechanical design of the experimental platform. The main dvantage of design the RM by using the CAD software is that his method permits its posterior manufacture by using the threeimensional printing technologies. In this particular case, poly actic acid (PLA) was selected as manufacturing material for the xperimental setup. To regulate the movements of each joint f the robotic manipulator, two DC motors with a 99:1 ratio model 25Dx69L Pololu) attached to a bevel gear mechanism have een used. The ratio 1:1 was selected for the gear mechanism o transferred the movement on ninety degrees (See zoom in ig. 10). The electronic instrumentation used in the experimental setup\nan be summarized by the scheme provided in Fig. 11. As part of he electronic instrumentation stage an incremental encoder with esolution of 48 pulses per rotation has been used for each link, hese devices permit to measure the angular position. Related o the power stage, a Canakit L298 H-bridge evaluation board as been selected to manage the pulse width modulation signal rovided to each DC motor. Notice that each evaluation board is dual H-bridge, therefore only one evaluation board has been equire to control all the experimental setup. The central part of the electronic instrumentation is a low-cost\nicrocontroller, in this particular case an evaluation board based n a microcontroller TMS320C28x has been used. The selected icrocontroller was a TMS320F2837xD DualCore Delfino. The icrocontroller evaluation board features are: 32\u2212bit CPU, 24 hannels of enhanced pulse width modulator (ePWM) aside from hree modules of enhanced quadrature encoder pulse (eQEP).\n.2. Experimental results\nFig. 12 shows the actual experimental setup that satisfies the ollowing parameters l1 = l2 = 0.12 m and m1 = m2 = 0.35 Kg.\nFor this particular case, the proposed controller was impleented in the embedded evaluation board Delfino F28379D conidering a step size equal to 0.1 \u00b5s. In addition, two additional ontrol schemes (NTSM and NCNTSM) were implemented with he aim to providing a performance comparison between the NTSM and another control schemes based on the sliding mode\nFig. 11. Electronic instrumentation used for the experimental setup.\nFig. 12. Actual experimental setup.\ntheory. To develop the experimental results, the initial conditions of the experimental setup were set to x1,1(0) = x1,2(0) = 0, x2,1(0) = x2,2(0) = 0 under the consideration that the experimental setup starts from a static initial point where the encoders has a reference equal to zero. As reference trajectories, the following vector h = [ 1.25\u03c0 (sin(0.1t) + 535) 2.08\u03c0 (sin(0.5t) + 535)\n] were proposed. Therefore, the upper bounds for each reference trajectory (h+\n1,1, h + 1,2) and its derivatives (h+ 2,1, h + 2,2) can be easily obtained to compute the control gain.\nSimilar to the results provided in Section 6, the proposed CNTSM was compared with a NTSM. Also, the following results consider a NCNTSM, that is a variant of the proposed controller, but without considering for its mathematical design the time varying gain. Here, it should be noticed that the electronic instrumentation only considers the encoders to measure the angular position of each RM link. That means, only the state x1 is available. Therefore, the ASTA has been used to estimate the angular velocity at each RM joint. For this case, similar values to the used in the simulation results for the parameters of the ASTA has been used with the exception of \u03bb+\n1,1 = \u03bb+ 1,2 = 120, \u03bb+ 2,1 = \u03bb+ 2,2 = 100, \u039b+\n1,1 = \u039b+ 1,2 = 98 and \u039b+ 2,1 = \u039b+ 2,2 = 85. In this section, the values for pi and qi with i = {1, 2} to compute the sliding surfaces as well as the control gains were selected as follows q1 = 7, q2 = 5, p1 = 5, q2 = 3. In addition, to obtain the gains \u03b11 and \u03b12 represented by Eq. (35), the following parameters were selected \u03c81 = \u03c82 = 100 and \u03b91 = \u03b92 = 0. This experimental evaluation considers the upper bounds for",
            "t r p\ng f \u03c4 T b s\ni d c k\ni t g c e C\np t s s w r\nt t g\nhe control gains \u03b11 and \u03b12 as \u03b1+ 1 = 0.95 and \u03b1+ 2 = 0.95, espectively. Also, the gains \u03b21 = 40 and \u03b22 = 52 have been roposed. For the particular case of the NCNTSM, the values for all the ains were selected as for CNTSM. Here, it should be noticed that or both controllers (NTSM and NCNTSM) the gains for \u03c42,1 and 2,2 were selected as constants that is \u03c42,1 = 79 and \u03c42,2 = 73. he previous values have been selected taking into account that oth control schemes (NTSM and NCNTSM) do not consider the tate constraints in their structure. The experimental results presented below consider the followng values kb1,1 = 1.3, kb1,2 = 1.55, kb2,1 = 0.71, kb2,2 = 0.76 efining the state constraints for each RM link. In this case, the onstraints for the TEs have been selected as k\u22061,1 = k\u22061,2 = 0.2, \u22062,1 = 0.31, k\u22062,2 = 0.36. Figs. 13 and 14 show the performance obtained with the mplementation of the three control schemes. From Fig. 13, notice hat the proposed controller (CNTSM) exhibits a faster converence to the reference trajectory in each robotic manipulator link ompared with the other control schemes. In addition, Fig. 14 vidences that state constraints where meet all the time when NTSM was implemented. Figs. 15 and 16 show the fulfillment of the constraints proosed for the TEs (\u22061 and \u22062). Notice that as in the simulaion, the controllers that are not considering in its mathematical tructure the error constraints do not satisfy the mentioned contraints. Also, the faster converge of the TEs when the CNTSM as implemented has been demonstrated in Figs. 15 and 16, espectively.\nTaking into consideration the results presented in Figs. 13\u201316, he last stage to verify the fulfillment of the state constraints is o verify the performance obtained in each sliding surface. To this oal, Fig. 17 evidences the fulfillment of the constraints proposed",
            "t t\nb t p\nf t d l N\n8\nhe constraints proposed to the SS. However, the main problem ackled with the proposed controller is to ensure the full-state\nm\nconstraints in the robotic system. That means, both states x1 and x2 must fulfill the predefined set of constraints. The last Figure presented in the experimental results section (Fig. 18), corresponds to the control signals provided to each DC Motor of the RM. From these figures, notice that both controllers (CNTSM and NCNTSM) exhibit similar control energy consumption. Therefore, one of the advantages of the CNTSM is to guarantee the fulfillment of the full state constraints in the RM without excessive consume of energy.\nWith the aim of evidencing the obtained performance of the proposed controller, the least mean square error (LMSE) of the TE (\u2206) as well as the integral of the absolute value of the control signal (\u03c4 ) obtained with the NTSM, NCNTSM, and CNTSM have een summarized in Table 1. This table compares the LMSE obained with all the tested controllers without adding an artificial erturbation. Notice that the implementation of the CNTSM improves LMSE\nrom 83.75% to 90.3% compared with the results obtained from he NCNTSM and the NTSM implementation, respectively. In adition, notice that the improvement requires from 7.92% to 28.7% ess energy consumption energy compared with the consumed by CNTSM and NTSM.\n. Conclusions\nAn output feedback finite-time controller based on the sliding odes theory was designed. The CNTSM controller included a"
        ]
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure4-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure4-1.png",
        "caption": "Fig. 4. Final fusion zonemicrostructures.Weld parameters: (a) current:100 A DC, weld time 2 s. DC, weld time 3 s.",
        "texts": [
            " At the time of the arc is stopped, the average flow (particle motion) speed is about half compared to the peak levels (around 15 \u00b1 6 mm/s), indicating gradual reduction of surface tension driven force, as result of gradually decreasing thermal gradient across the pool. So that flow velocity observations are also quite consistent with the force domination indicated through the weld pool shape evolution. Finalmetallographic cross-sections (opticalmicroscopy, etchedwith Keller's reagent) of the solidified samples are shown in Fig. 4 for comparison of the shape, microstructure and porosity in the fusion zones. DCmode appears to create a deeper weld pool than the nominally similar AC current. Inward flow will increase the depth of the weld pool, and the outward flow will promote the width of the weld pool. Under the set welding parameters used in these experiments, the final solidified microstructures inside the weld pools are mostly fine columnar crystal with substantial equiaxed crystals present in-between. Notably that the solidified AC weld pool appears to have a more porous center surface, while 100 A DC 2 s sample appear to have scattered porosity across the fusion zone. Other 2 samples represent relatively less porosity in the central cross sections. However, it needs to be kept inmind the images in Fig. 4 represent just the central cross section and one might not presume there are completely free of porosity, but we believe they represent overall conditions reasonably. Even though not the statement of the overall weld spectrum in general, according to the Fig. 4, observations help to confirm that varied current or a weld times can produce variations in the porosity levels and pore distribution. The flow pattern within the melt pool which dominated by arc or surface tension force can be notably reduced (for increased time period) with the increasing of weld time or higher welding current as shown in Fig. 3. The formation of pores in the weld pool is commonly observed in all the conditions. Of course, the external factors such as sample, environmental andweld conditions affect porosity a lot [36,37]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure16-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure16-1.png",
        "caption": "Fig. 16. Tracking error \u22062 of the two-link RM.",
        "texts": [],
        "surrounding_texts": [
            "t r p\ng f \u03c4 T b s\ni d c k\ni t g c e C\np t s s w r\nt t g\nhe control gains \u03b11 and \u03b12 as \u03b1+ 1 = 0.95 and \u03b1+ 2 = 0.95, espectively. Also, the gains \u03b21 = 40 and \u03b22 = 52 have been roposed. For the particular case of the NCNTSM, the values for all the ains were selected as for CNTSM. Here, it should be noticed that or both controllers (NTSM and NCNTSM) the gains for \u03c42,1 and 2,2 were selected as constants that is \u03c42,1 = 79 and \u03c42,2 = 73. he previous values have been selected taking into account that oth control schemes (NTSM and NCNTSM) do not consider the tate constraints in their structure. The experimental results presented below consider the followng values kb1,1 = 1.3, kb1,2 = 1.55, kb2,1 = 0.71, kb2,2 = 0.76 efining the state constraints for each RM link. In this case, the onstraints for the TEs have been selected as k\u22061,1 = k\u22061,2 = 0.2, \u22062,1 = 0.31, k\u22062,2 = 0.36. Figs. 13 and 14 show the performance obtained with the mplementation of the three control schemes. From Fig. 13, notice hat the proposed controller (CNTSM) exhibits a faster converence to the reference trajectory in each robotic manipulator link ompared with the other control schemes. In addition, Fig. 14 vidences that state constraints where meet all the time when NTSM was implemented. Figs. 15 and 16 show the fulfillment of the constraints proosed for the TEs (\u22061 and \u22062). Notice that as in the simulaion, the controllers that are not considering in its mathematical tructure the error constraints do not satisfy the mentioned contraints. Also, the faster converge of the TEs when the CNTSM as implemented has been demonstrated in Figs. 15 and 16, espectively.\nTaking into consideration the results presented in Figs. 13\u201316, he last stage to verify the fulfillment of the state constraints is o verify the performance obtained in each sliding surface. To this oal, Fig. 17 evidences the fulfillment of the constraints proposed",
            "t t\nb t p\nf t d l N\n8\nhe constraints proposed to the SS. However, the main problem ackled with the proposed controller is to ensure the full-state\nm\nconstraints in the robotic system. That means, both states x1 and x2 must fulfill the predefined set of constraints. The last Figure presented in the experimental results section (Fig. 18), corresponds to the control signals provided to each DC Motor of the RM. From these figures, notice that both controllers (CNTSM and NCNTSM) exhibit similar control energy consumption. Therefore, one of the advantages of the CNTSM is to guarantee the fulfillment of the full state constraints in the RM without excessive consume of energy.\nWith the aim of evidencing the obtained performance of the proposed controller, the least mean square error (LMSE) of the TE (\u2206) as well as the integral of the absolute value of the control signal (\u03c4 ) obtained with the NTSM, NCNTSM, and CNTSM have een summarized in Table 1. This table compares the LMSE obained with all the tested controllers without adding an artificial erturbation. Notice that the implementation of the CNTSM improves LMSE\nrom 83.75% to 90.3% compared with the results obtained from he NCNTSM and the NTSM implementation, respectively. In adition, notice that the improvement requires from 7.92% to 28.7% ess energy consumption energy compared with the consumed by CNTSM and NTSM.\n. Conclusions\nAn output feedback finite-time controller based on the sliding odes theory was designed. The CNTSM controller included a",
            "t t t a T s o n r r p\nD\nc t\nA\nc S\nA\nP\nf\nb d\n\u2212\nP i(\ns e\nV\nT w V\nV\nw\nT a\nime-varying gain to solve the singularity problem presented in he classical TSM. The control gain was designed in such a way hat it ensured the fulfillment of the full state constraints, as well s the constraints for the tracking error and the sliding variable. he numerical results and the practical implementation demontrated the fulfillment of the set of predefined constraints. Morever, the effectiveness of the proposed controller to handle exteral perturbations was also evidenced in the obtained numerical esults and practical implementation. Notice that both presented esults (simulation and experimental) showed the benefits of the roposed controller concerning similar control structures.\neclaration of competing interest\nThe authors declare that they have no known competing finanial interests or personal relationships that could have appeared o influence the work reported in this paper.\ncknowledgments\nThe authors thank the Instituto Polit\u00e9cnico Nacional the finanial support provided through the research grants with reference IP-2021-1220 and SIP-2021-0992.\nppendix\nroof of Lemma 1. Let define the function f (\u03bd) such as\n(\u03bd) = \u2212log(1 \u2212 \u03bd) \u2212 \u03bd\n1 \u2212 \u03bd ,\nthe derivative of f is given by df (\u03bd) d\u03bd = \u2212 1 1 \u2212 \u03bd \u2212 1 (1 \u2212 \u03bd)2 < 0.\nNotice that the previous equation is equivalent to df (\u03bd) d\u03bd = \u2212 2 \u2212 \u03bd (1 \u2212 \u03bd)2 < 0,\ny considering df (\u03bd) d\u03bd < 0, it is shown that f is continuously ecreasing. Thus, we have\nlog(1 \u2212 \u03bd) \u2264 \u03bd\n1 \u2212 \u03bd .\nA similar procedure is applied to prove the second inequality. Due to the limited space, this part of the proof is omitted. \u25a1\nProof of Lemma 2. By considering lemma 2 in [38] it is proven that for any constant \u03bd satisfying |\u03bd| < 1 the following inequality holds: log ( 1\n1\u2212\u03bd2\n) \u2264 \u03bd2\n1\u2212\u03bd2 . If both inequality sides are multiplied\nby \u22121 the direction of the inequality is inverted. Therefore, the fulfillment of the following inequality is proven.\n\u2212 \u03bd2\n1 \u2212 \u03bd2 \u2264 \u2212 log\n( 1\n1 \u2212 \u03bd2\n) . \u25a1\nroof of Lemma 3. Notice that for |\u03bd| < 1, the following nequality is valid\nlog (\n1 1 \u2212 \u03bd2\n)) 1 2\n\u2265 \u03bd,\nThe previous fact, implies that 1 \u03bd \u2265 1(\nlog (\n1 2\n)) 1 2 ,\n1 \u2212 \u03bd\nin consequence\n\u2212 1 \u03bd \u2264 \u2212 1( log (\n1 1 \u2212 \u03bd2\n)) 1 2 . \u25a1\nProof of Output feedback realization of the controller. The tability study for the closed-loop system (implementing the stimated velocity by the ASTA) consider a BLF given as follows\ni(\u03c3\u0302i, \u03b6i) = 0.5 ln\n( 1\n1 \u2212 \u03be\u0302 2i\n) + \u03b6\u22a4\ni Pi\u03b6i,\nwith \u03be\u0302i = \u03c3\u0302i k\u03c3 ,i , \u03c3\u0302i = \u2206\u03022,i +\u03b1i\u2206 qi pi 1,i and \u03b6 \u22a4 i = [ |e1,i|1/2sign(e1,i) e2,i ] .\nhe variable \u2206\u03022,i is the estimation of \u22062,i which is obtained ith the implementation of the ASTA. The full-time derivative of i(\u03c3\u0302i, \u03b6i) satisfies\n\u02d9i(\u03c3\u0302i, \u03b6i) = \u03be\u0302i\n\u02d9\u0302 \u03bei\n(1 \u2212 \u03be\u0302 2i ) + 2\u03b6\u22a4 i Pi\u03b6\u0307i, (58)\nhere the derivative of \u03be\u0302i is defined by the following expression\n\u02d9\u0302 \u03bei =\n\u02d9\u0302\u03c3i k\u03c3i . (59)\nThe time derivative of \u03b6i can be obtained following the ideas given in the seminal work [39].\nSubstituting (59) in the expression that defines V\u0307i(\u03c3\u0302i, \u03b6i) given in (58), one gets\nV\u0307i(\u03c3\u0302i, \u03b6i) = \u03be\u0302i \u02d9\u0302\u03c3ik\u03c3i\nk2\u03c3i (1 \u2212 \u03be\u0302 2i ) + 2\u03b6\u22a4 i Pi\u03b6\u0307i. (60)\naking into account the expression that defines the sliding varible \u03c3\u0302i, the full-time derivative of \u03c3\u0302i obeys the following expres-\nsion\n\u02d9\u0302\u03c3i = \u02d9\u0302 \u22062,i + \u03b1i qi pi \u2206\nqi pi \u22121 1,i \u2206\u03071,i + \u03b1\u0307i\u2206 qi pi 1,i. (61)\nAfter substituting the full-time derivative of sliding surface \u03c3\u0302i in Eq. (60), one gets\nV\u0307i(\u03c3\u0302i, \u03b6i) = 2\u03b6\u22a4 i Pi\u03b6\u0307i\n+\n\u03be\u0302i( \u02d9\u0302 \u22062,i + \u03b1i qi pi \u2206\nqi pi \u22121 1,i \u2206\u03071,i + \u03b1\u0307i\u2206 qi pi 1,i)\nk\u03c3i (1 \u2212 \u03be\u0302 2i ) .\n(62)\nTaking into account the dynamics of \u22061,i and \u22062,i, notice that \u2206\u03071,i = \u22062,i, as well as \u2206\u03072,i = \u02d9\u0302x2,i \u2212 h\u0308i. Therefore, (62) turns into\nV\u0307i(\u03c3\u0302i, \u03b6i) = 2\u03b6\u22a4 i Pi\u03b6\u0307i\n+\n\u03be\u0302i( \u02d9\u0302x2,i \u2212 h\u0308i + \u03b1i qi pi \u2206\nqi pi \u22121 1,i \u22062,i + \u03b1\u0307i\u2206 qi pi 1,i)\nk\u03c3i (1 \u2212 \u03be\u0302 2i )\n. (63)\nNow, consider that (63) is equivalent to\nV\u0307i(\u03c3\u0302i, \u03b6i) = 2\u03b6\u22a4 i Pi\u03b6\u0307i\n+\n\u03be\u0302i( \u02d9\u0302x2,i \u2212 x\u03072,i + \u2206\u03072,i + \u03b1i qi pi \u2206\nqi pi \u22121 1,i \u22062,i + \u03b1\u0307i\u2206 qi pi 1,i)\n2 ,\n(64)\nk\u03c3i (1 \u2212 \u03be\u0302i )"
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure2-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure2-1.png",
        "caption": "Fig. 2. Trajectory tracking of the state x1 .",
        "texts": [],
        "surrounding_texts": [
            "l\n[\nt a F \u03b2\nN\nFig. 1. Control diagram of the trajectory tracking case.\nt s ( s t t t c\nf k 0\nThe simulations results were developed considering the folowing parameters m1 = 0.35 Kg, m2 = 0.35 Kg, l1 = 0.12 m, l2 = 0.12 m. Also, the value g = \u22129.8 m\ns2 was considered as the\ngravitational constant. Notice that these values match with the real plant parameters.\nThe initial state conditions were set to x1,1(0) = 0.1, x1,2(0) = \u22120.12, x\u03072,1(0) = 1.5 and x\u03072,2(0) = 0.95. The vector h that contains the reference trajectories proposed for each link of the RM were selected as h = [ sin (2t) sin (1.5t)\n]\u22a4. Consequently, the upper bounds for each reference trajectory and its derivatives are given by h+\n1,1 = 1, h+ 1,2 = 1, h+ 2,1 = 2 and h+ 2,2 = 1.5. To facilitate the application of the proposed controller in the numerical simulations, Fig. 1 shows a control diagram that illustrates the interaction of all the parameters involved in the proposed control design (given in Section 4C).\nFor the numerical simulations, it is also assumed that from t = 4 to t = 11, an external disturbance \u03b7(q) is affecting the RM. Then, the external perturbation is given by \u03b7(q) =\n0.2 sin(4t) 0.09 sin(10t) ]\u22a4. To validate the effectiveness of the control scheme (CNTSM) the performance obtained with the proposed controller is compared with the non-singular terminal sliding mode (NTSM) controller developed in [25]. In this work,\nthe sliding manifold is selected as \u03c3i = \u22061,i + 1 \u03b1+\ni \u2206\npi qi 2,i. On the\nother hand, the CNTSM controller is also compared with its non constraint counterpart. That means, the time varying gain (28) is changed by a constant. Notice that this change induces that the CNTSM actuates like a classical NTSM. The non constraint version of the CNTSM is named NCNTSM in the following results.\nThe numerical results consider that only the state x1 of the RM is available. Then, the ASTA proposed in the current manuscript is used to obtain the estimation of the state x2.\nThe considered values to adjust the ASTA algorithms for each link of the RM are: \u03b6i = 0.998, \u03b31,i = 0.8, \u03b32,i = 0.82, \u039b+\n1,i = 30, \u039b+\n2,i = 35, \u03bd+ 1,i = 20, \u03bd+ 2,i = 22 \u03bb+ 1,i = 18, \u03bb+ 2,i = 20 with i = 1, 2 describing the link number.\nOn the other hand, the values that adjust the proposed control are p1 = p2 = 7 and q1 = q2 = 5. The corresponding control gains \u03b11 and \u03b12 satisfy the structure give in (23) with \u03c81 = 100, \u03c82 = 100. The parameters \u03b91 and \u03b92 are proposed equal to zero o avoid the singularity problem. The upper value of each gain \u03b11 nd \u03b12 are given by \u03b1+ 1 = 0.95 and \u03b1+\n2 = 0.75, respectively. inally, for the controls \u03c42,1 and \u03c42,2, the gains \u03b21 = 48 and 2 = 64 are selected. To compare the performance of the control schemes NTSM and CNTSM with the proposed controller (CNTSM), the values for\nhe gains p1, p2, q1 and q2 as well as the gains \u03b1+ 1 and \u03b1+ 2 are elected similar to the CNTSM case. Consider that in both cases NTSM and NCNTSM) the gains for the control \u03c42,1 and \u03c42,2 are elected as a constants, that is, k1 = 92.5 and k2 = 122.5. Because hese control schemes do not consider the state constraints in heir structures. The mentioned values are selected considering he mean value of the gains k1 and k2 obtained with the CNTSM ontroller. The results presented below consider that the state constraints or the two-link RM are given by kb1,1 = 1.25, kb1,2 = 1.25, b2,1 = 2.15 and kb2,2 = 2.65. The TEs constraints satisfy k\u22061,1 =\n.2, k\u22061,2 = 0.2 aside from k\u22062,1 = 0.6, k\u22062,2 = 0.6, all of them satisfying the conditions given in (11).\nRemark 5. It should be noticed that in the simulation section, the set of predefined constraints has been selected to evidence the following scenarios. (1) The same position constraint for both links of the RM. (2) Different velocities constraints for each RM link. (3) Different TE constraints for each RM joint. Moreover, Figs. 1\u20136 evidence the effectiveness of the CNTSM to solve the RM trajectory tracking.\nThe mentioned scenarios (Remark 4) have been selected to evidence the effectiveness of the CNTSM despite of the constraints selection. Obviously, taking into account that the initial conditions of the sliding surface must begin inside the set of the predefined constraints.\nFigs. 2 and 3 show a comparison of the performance obtained with the selected three controllers. Notice that for the case of the first link, all controllers solve the trajectory tracking. Nevertheless, in the case of the second link, the NTSM and NCNTSM cannot satisfy the state constraint given by kb1,2.\nThe previous fact evidences the effectiveness of the CNTSM controller to guarantee the state constraints fulfillment. Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated.\nFigs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6.\nThe norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the",
            "p N\nroposed CNTSM performed better than the NTSM as well as the CNTSM.\nt\nIn addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained",
            "w 5 w o N\na w c s H e t t s c s\nith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM). The control signals obtained with the three controller schemes re compared in Fig. 9. The depicted control signals are obtained ith the implementation of a first order low-pass filter with a ut-off frequency of 100 Hz. This value was obtained using the uggestions obtained from the seminal study provided in [8]. ere, it is important to notice that all the controllers use a similar nergy (See Fig. 9). Therefore, from the energetic point of view, he proposed controller yields the better option to solve the rajectory tracking problem of a RM, as well as to satisfy the tate constraints but without an excess of energy consumption ompared to the other considered controllers. This condition is ignificant because the fulfillment of the state restrictions yields\nFig. 8. Histogram of \u2206 obtained with tested controllers.\nFig. 9. Control signals.\nto get the realization of a bounded controller as well. Hence, the benefits of the proposed controller include the finite-time accelerated converge to the origin of the TEs, the output feedback realization and the realization of a competitive bounded controller (in terms of the consumed energy).\n7. Practical implementation\nThis section presents the experimental setup (mechanical and electronic instrumentation) as well as the proposed control implementation. In addition, to evidence the effectiveness of the proposed control scheme a comparison between the proposed controller, a NTSM and, a NCNTSM controller has been added.\nThe proposed experimental setup considers a two-link RM that satisfies the dynamic model given in (6). The following subsection describes the mechanical structure of the RM as well as its electronic instrumentation."
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure14-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure14-1.png",
        "caption": "Fig. 14. Experimental trajectory tracking of the state x2 .",
        "texts": [
            "3, kb1,2 = 1.55, kb2,1 = 0.71, kb2,2 = 0.76 efining the state constraints for each RM link. In this case, the onstraints for the TEs have been selected as k\u22061,1 = k\u22061,2 = 0.2, \u22062,1 = 0.31, k\u22062,2 = 0.36. Figs. 13 and 14 show the performance obtained with the mplementation of the three control schemes. From Fig. 13, notice hat the proposed controller (CNTSM) exhibits a faster converence to the reference trajectory in each robotic manipulator link ompared with the other control schemes. In addition, Fig. 14 vidences that state constraints where meet all the time when NTSM was implemented. Figs. 15 and 16 show the fulfillment of the constraints proosed for the TEs (\u22061 and \u22062). Notice that as in the simulaion, the controllers that are not considering in its mathematical tructure the error constraints do not satisfy the mentioned contraints. Also, the faster converge of the TEs when the CNTSM as implemented has been demonstrated in Figs. 15 and 16, espectively. Taking into consideration the results presented in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure10-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure10-1.png",
        "caption": "Fig. 10. Mechanical design of experimental setup.",
        "texts": [
            " The proposed experimental setup considers a two-link RM that satisfies the dynamic model given in (6). The following subsection describes the mechanical structure of the RM as well as its electronic instrumentation. e a t a t d l e o ( b t F c t r t t h p a r m o m m c t 7 f m s c t C 7.1. Experimental setup description The mechanical dimensions (longitudinal) of each robotic link satisfies l1 = 0.12 m, l2 = 0.12 m. All the pieces that integrate the xperimental platform has been designed by using a computer ssisted drawing software named SolidWorks. Fig. 10 depicts he mechanical design of the experimental platform. The main dvantage of design the RM by using the CAD software is that his method permits its posterior manufacture by using the threeimensional printing technologies. In this particular case, poly actic acid (PLA) was selected as manufacturing material for the xperimental setup. To regulate the movements of each joint f the robotic manipulator, two DC motors with a 99:1 ratio model 25Dx69L Pololu) attached to a bevel gear mechanism have een used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure4-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure4-1.png",
        "caption": "Fig. 4 Responses of x1(t), x2(t) and x3(t) of the closed-loop system (5) using dynamic ETM: t0 = 0, tk+1 = inf { t > tk | 0.01e\u22120.101t +10[0.18xT(t)x(t)\u2212eT(t)e(t)] \u2264 0 } .The rectangular window indicates that the stabilizability of the closed-loop system (5) using the above dynamic ETM is guaranteed",
        "texts": [
            "1657 \u22120.0038 0.0559 0.009 \u22120.1657 0.009 0.4244 \u23a4 \u23a6 , Y = [\u22120.1813 \u22120.6678 \u22120.7928 ] , the dynamic ETM is tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.18xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } , (50) and the control law u(t) is obtained as u(t) = [\u22120.2179 \u22120.0555 \u22120.3854 ] x(tk), t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 3 and 4 show the triggering instants and intervals of the event generator using dynamic ETM and the state responses of system (5). It is clear from Fig. 4 that the closed-loop system is asymptotically stable. Let us now consider the following Population model structured into three stages: \u23a7 \u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 x\u03071(t) = \u2212\u03b11x1(t) \u2212 m1x1(t) + u(t) + r(t, x3(t)), t \u2265 0, x\u03072(t) = \u03b11x1(t) \u2212 \u03b12x2(t) \u2212 m2x2(t) + 2u(t), t \u2265 0, x\u03073(t) = \u03b12x2(t) \u2212 m3x3(t) \u2212 c(t)x3(t) + 3u(t), t \u2265 0, x1(0) \u2265 0, x2(0) \u2265 0, x2(0) \u2265 0. (51) In the above model, x1(t) > 0, x2(t) > 0 and x3(t) > 0 are larvae, juveniles and adults, respectively. The positive coefficients \u03b1i and mi represent the growth and mortality rates, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure5-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure5-1.png",
        "caption": "Fig. 5. Tracking error \u22062 of the two-link RM.",
        "texts": [],
        "surrounding_texts": [
            "l\n[\nt a F \u03b2\nN\nFig. 1. Control diagram of the trajectory tracking case.\nt s ( s t t t c\nf k 0\nThe simulations results were developed considering the folowing parameters m1 = 0.35 Kg, m2 = 0.35 Kg, l1 = 0.12 m, l2 = 0.12 m. Also, the value g = \u22129.8 m\ns2 was considered as the\ngravitational constant. Notice that these values match with the real plant parameters.\nThe initial state conditions were set to x1,1(0) = 0.1, x1,2(0) = \u22120.12, x\u03072,1(0) = 1.5 and x\u03072,2(0) = 0.95. The vector h that contains the reference trajectories proposed for each link of the RM were selected as h = [ sin (2t) sin (1.5t)\n]\u22a4. Consequently, the upper bounds for each reference trajectory and its derivatives are given by h+\n1,1 = 1, h+ 1,2 = 1, h+ 2,1 = 2 and h+ 2,2 = 1.5. To facilitate the application of the proposed controller in the numerical simulations, Fig. 1 shows a control diagram that illustrates the interaction of all the parameters involved in the proposed control design (given in Section 4C).\nFor the numerical simulations, it is also assumed that from t = 4 to t = 11, an external disturbance \u03b7(q) is affecting the RM. Then, the external perturbation is given by \u03b7(q) =\n0.2 sin(4t) 0.09 sin(10t) ]\u22a4. To validate the effectiveness of the control scheme (CNTSM) the performance obtained with the proposed controller is compared with the non-singular terminal sliding mode (NTSM) controller developed in [25]. In this work,\nthe sliding manifold is selected as \u03c3i = \u22061,i + 1 \u03b1+\ni \u2206\npi qi 2,i. On the\nother hand, the CNTSM controller is also compared with its non constraint counterpart. That means, the time varying gain (28) is changed by a constant. Notice that this change induces that the CNTSM actuates like a classical NTSM. The non constraint version of the CNTSM is named NCNTSM in the following results.\nThe numerical results consider that only the state x1 of the RM is available. Then, the ASTA proposed in the current manuscript is used to obtain the estimation of the state x2.\nThe considered values to adjust the ASTA algorithms for each link of the RM are: \u03b6i = 0.998, \u03b31,i = 0.8, \u03b32,i = 0.82, \u039b+\n1,i = 30, \u039b+\n2,i = 35, \u03bd+ 1,i = 20, \u03bd+ 2,i = 22 \u03bb+ 1,i = 18, \u03bb+ 2,i = 20 with i = 1, 2 describing the link number.\nOn the other hand, the values that adjust the proposed control are p1 = p2 = 7 and q1 = q2 = 5. The corresponding control gains \u03b11 and \u03b12 satisfy the structure give in (23) with \u03c81 = 100, \u03c82 = 100. The parameters \u03b91 and \u03b92 are proposed equal to zero o avoid the singularity problem. The upper value of each gain \u03b11 nd \u03b12 are given by \u03b1+ 1 = 0.95 and \u03b1+\n2 = 0.75, respectively. inally, for the controls \u03c42,1 and \u03c42,2, the gains \u03b21 = 48 and 2 = 64 are selected. To compare the performance of the control schemes NTSM and CNTSM with the proposed controller (CNTSM), the values for\nhe gains p1, p2, q1 and q2 as well as the gains \u03b1+ 1 and \u03b1+ 2 are elected similar to the CNTSM case. Consider that in both cases NTSM and NCNTSM) the gains for the control \u03c42,1 and \u03c42,2 are elected as a constants, that is, k1 = 92.5 and k2 = 122.5. Because hese control schemes do not consider the state constraints in heir structures. The mentioned values are selected considering he mean value of the gains k1 and k2 obtained with the CNTSM ontroller. The results presented below consider that the state constraints or the two-link RM are given by kb1,1 = 1.25, kb1,2 = 1.25, b2,1 = 2.15 and kb2,2 = 2.65. The TEs constraints satisfy k\u22061,1 =\n.2, k\u22061,2 = 0.2 aside from k\u22062,1 = 0.6, k\u22062,2 = 0.6, all of them satisfying the conditions given in (11).\nRemark 5. It should be noticed that in the simulation section, the set of predefined constraints has been selected to evidence the following scenarios. (1) The same position constraint for both links of the RM. (2) Different velocities constraints for each RM link. (3) Different TE constraints for each RM joint. Moreover, Figs. 1\u20136 evidence the effectiveness of the CNTSM to solve the RM trajectory tracking.\nThe mentioned scenarios (Remark 4) have been selected to evidence the effectiveness of the CNTSM despite of the constraints selection. Obviously, taking into account that the initial conditions of the sliding surface must begin inside the set of the predefined constraints.\nFigs. 2 and 3 show a comparison of the performance obtained with the selected three controllers. Notice that for the case of the first link, all controllers solve the trajectory tracking. Nevertheless, in the case of the second link, the NTSM and NCNTSM cannot satisfy the state constraint given by kb1,2.\nThe previous fact evidences the effectiveness of the CNTSM controller to guarantee the state constraints fulfillment. Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated.\nFigs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6.\nThe norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the",
            "p N\nroposed CNTSM performed better than the NTSM as well as the CNTSM.\nt\nIn addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained",
            "w 5 w o N\na w c s H e t t s c s\nith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM). The control signals obtained with the three controller schemes re compared in Fig. 9. The depicted control signals are obtained ith the implementation of a first order low-pass filter with a ut-off frequency of 100 Hz. This value was obtained using the uggestions obtained from the seminal study provided in [8]. ere, it is important to notice that all the controllers use a similar nergy (See Fig. 9). Therefore, from the energetic point of view, he proposed controller yields the better option to solve the rajectory tracking problem of a RM, as well as to satisfy the tate constraints but without an excess of energy consumption ompared to the other considered controllers. This condition is ignificant because the fulfillment of the state restrictions yields\nFig. 8. Histogram of \u2206 obtained with tested controllers.\nFig. 9. Control signals.\nto get the realization of a bounded controller as well. Hence, the benefits of the proposed controller include the finite-time accelerated converge to the origin of the TEs, the output feedback realization and the realization of a competitive bounded controller (in terms of the consumed energy).\n7. Practical implementation\nThis section presents the experimental setup (mechanical and electronic instrumentation) as well as the proposed control implementation. In addition, to evidence the effectiveness of the proposed control scheme a comparison between the proposed controller, a NTSM and, a NCNTSM controller has been added.\nThe proposed experimental setup considers a two-link RM that satisfies the dynamic model given in (6). The following subsection describes the mechanical structure of the RM as well as its electronic instrumentation."
        ]
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure13-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure13-1.png",
        "caption": "Fig. 13. Experimental trajectory tracking of the state x1 .",
        "texts": [
            " he previous values have been selected taking into account that oth control schemes (NTSM and NCNTSM) do not consider the tate constraints in their structure. The experimental results presented below consider the followng values kb1,1 = 1.3, kb1,2 = 1.55, kb2,1 = 0.71, kb2,2 = 0.76 efining the state constraints for each RM link. In this case, the onstraints for the TEs have been selected as k\u22061,1 = k\u22061,2 = 0.2, \u22062,1 = 0.31, k\u22062,2 = 0.36. Figs. 13 and 14 show the performance obtained with the mplementation of the three control schemes. From Fig. 13, notice hat the proposed controller (CNTSM) exhibits a faster converence to the reference trajectory in each robotic manipulator link ompared with the other control schemes. In addition, Fig. 14 vidences that state constraints where meet all the time when NTSM was implemented. Figs. 15 and 16 show the fulfillment of the constraints proosed for the TEs (\u22061 and \u22062). Notice that as in the simulaion, the controllers that are not considering in its mathematical tructure the error constraints do not satisfy the mentioned contraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000027_d0an02029j-Figure2-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000027_d0an02029j-Figure2-1.png",
        "caption": "Fig. 2 (A) Grayscale response of Alg@QDS-Uox MSs in different protein solutions (1 \u03bcg ml\u22121 each). (B) Fluorescence response of the CdZnTeS QD solution in different protein solutions (1 \u03bcg ml\u22121 each). The error bars were obtained based on three repetitive experiments. Excitation wavelength: 340 nm.",
        "texts": [
            " The morphology of Scheme 2 Schematic description of (A) the preparation of CdZnTeS QDs, (B) the principle of uric acid detection based on CdZnTeS QDs, and (C) the preparation of Alg@QDs-UOx MSs and uric acid detection. This journal is \u00a9 The Royal Society of Chemistry 2020 Analyst Pu bl is he d on 1 8 N ov em be r 20 20 . D ow nl oa de d by C ar le to n U ni ve rs ity o n 11 /3 0/ 20 20 2 :2 2: 53 P M . the Alg@QDs-UOx MSs characterized by scanning electron microscopy (SEM) is shown in Fig. 1C and D, which exhibit a dense multilayer network structure. The ability of CdZnTeS QDs to resist protein interference is shown in Fig. 2. CdZnTeS QDs in the Alg@QDs-UOx MSs had no significant effect on the high-concentration of the protein environment such as BSA, Muc-1, AFP and C-RP. However, the same concentration of BSA, Muc-1 and C-RP could enhance the fluorescence of CdZnTeS QDs in solution, and the same concentration of AFP could quench the fluorescence of CdZnTeS QDs in solution. This phenomenon was related to the overlapping multilayer network structure of the surface of Alg@QDs-UOx MSs. It could prevent CdZnTeS QDs (2\u20135 nm in diameter) from diffusing freely to the outside solution of the Alg@QDs-UOx MSs and could also block protein (1\u2013100 nm in diameter) from the outside solution into the Alg@QDs-UOx MSs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure5-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure5-1.png",
        "caption": "Fig. 5. Poresmotion in themelt pool during the arcwelding process. (a\u2013c) at the initial stage of thewelding. (d\u2013f) latter stage ofweldingwhere theweld pool is considerably dominated by gravity driven forces. The image sequence shown in this figure is used 100A DC welding current and 2 s welding time. The selected pores were highlighted using by super imposing the extracted bubble positions with the respective radiographic images.",
        "texts": [
            " Nevertheless, as we maintained the same sample and overall welding procedure during the experiments, thus we can suggest that the flow patterns and driving forces significantly affected the retaining or escaping of the formed pores that dictate the final porosity levels in our experiments presented here. It is specifically need to note that the higher welding times can allow more time pores to develop. The observations we presented and interpreted here is therefore most only related to the pore transportation and retention with the different force regimes in the weld pools. The example for observed formation of pores and their motion trajectory during welding process are presented in Fig. 5. The images shown are constructed through superimposing extracted bubble position with the ordinary projection of 100A DC, 2 s welding sequence (a sample of the gray scale adjusted original images were shown in Supplementary material S2). In each image brighter color represent the current bubble position with historic positions with lighter shades indicating moving paths. As shown in Fig. 5 it was observed that when the arc is present (i.e. t b 2 s), the buoyancy driven initial upward trajectory of the pores are greatly suppressed, and also its horizontal motion is affected to by the fluid flow. In this early stage, pores moved slowly upward and the late being temporarily retained nearly static in the melt pool just below the surface. However, after the arc is stopped (i.e. t N 2 s), the pores will move rapidly upwards and the pores escaped from the melt pool. It is possible to (b) current:100 A AC, weld time 3 s",
            " (c) current:125 A DC, weld time 2 s. (d) current:100A observe that the pores' upward motion is limited to maximum about 2.5 mm/s when the arc is active. Once the arc is stopped, the upward moving velocity exceeds 500 mm/s. Basically, when arc is not present, there is no strong force or strong flow to contain within the liquid metal, thus the pores with a lower density moves upwards rapidly. In addition, example of coalescence of the pores within the weld pool is indicated the in the green color pores in Fig. 5b. Further theoretical calculation on the each forces as shown in ref. [38] will allow quantitatively compare the resulting observations with the underling forces. Importantly, one might not forget our radiographic observations hide the dynamics and resulting effects one dimension along the beam direction completely. X-radiography at the synchrotron facilities allows fast imaging at very high rates and very short exposure times [39,40]. However, radiographic experiments can easily conceal information along the beam direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure4-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure4-1.png",
        "caption": "Fig. 4. Illustration of incremental-inductance estimation of (k\u20131)th phase using the proposed variable-sampling scheme.",
        "texts": [
            " Therefore, the mutual flux effect does not exist in Mode III Comparing (11) and (12), the absolute value of incrementalinductance estimation error in Mode I is slightly higher than that in Mode II. Based on the magnetic characteristics of the studied SRM shown in Fig. 1, the absolute value of incrementalinductance estimation error of phase A due to mutual flux from phase C in Mode I is shown in Fig. 3. Considering the magnetic saturation, incremental-inductance estimation error due to mutual flux is both rotor position and current dependent. As shown in Fig. 4, the mutual flux from phase C introduces around maximum 7% and minimum 1% error in phase A incrementalinductance estimation. Based on the error analysis in the last section, the mutual flux introduces a maximum\u00b17% incremental-inductance estimation error in Modes I and II, while the mutual flux effect does not exist in Mode III. Two methods will be proposed, which forces the incremental-inductance estimation to operate in Mode III exclusively: the variable-sampling method for the outgoing phase and variable-hysteresis-band current control for the incoming phase. Illustration of the variable-sampling scheme for (k\u20131)th phase (outgoing phase) is shown in Fig. 4. The positive phase current slope of (k\u20131)th phase is sampled at time instants tk\u22121(I) on and tk\u22121(II) on , which are fixed. During commutation, the sign of kth phase current slope is changed several times during (k\u20131)th phase self-inductance estimation. Therefore, in Mode I or II, the (k\u20131)th phase negative-phase-current-slope sampling point tk\u22121(I) off can be adjusted to ensure kth phase current slope at tk\u22121(I) off and tk\u22121(I) on have the same signs. Therefore, errk(I) = \u2212Minc k,k\u22121 Linc k\u22121 + Minc k,k\u22121 (L in c k \u22121 \u2212M in c k , k \u22121 ) (L in c k\u2212M in c k , k \u22121 ) \u2212 Minc k,k\u22121 (11) errk(II) = Minc k,k\u22121 Linc k\u22121 + Minc k,k\u22121 L in c k \u22121 +M in c k , k \u22121 L in c k \u2212M in c k , k \u22121 + Minc k,k\u22121 (12) the outgoing-phase incremental-inductance estimation is always operating in Mode III by using this scheme",
            " 6 shows simulation results of the proposed rotor position estimation with and without variable hysteresis band and sampling at 1500 r/min. As shown in Fig. 6, due to magnetic saturation, incremental inductance varies with rotor position and phase current. Since phase current is not constant, the SRM is operating either in saturated magnetic region or linear magnetic region. Therefore, both incremental inductance and phase current are necessary for estimating the rotor position. The maximum incrementalinductance estimation error without variable hysteresis band and sampling is \u00b17%, which matches theoretical analysis given in Fig. 4. Due to incremental-inductance estimation error, the maximum real-time rotor position estimation error is around \u00b12.0\u00b0. By using the proposed variable-hysteresis-band current controller and variable-sampling self-inductance estimation, the maximum inductance estimation error is decreased to \u00b10.7%. As a result, the maximum real-time rotor position estimation error are decreased to +0.5\u00b0. Therefore, the proposed rotor position estimation method demonstrates around 2\u00b0 accuracy improvement by eliminating the mutual flux effect on rotor position estimation of the SRM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure6-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure6-1.png",
        "caption": "Fig. 6. The evolution of the difference force domination in the arcweld poolswith correspondin welding power levels also indicated in the figure.",
        "texts": [
            " Considering our experiments presented here, from a single radiographic view it is inconceivable to extract full 3D fast time resolved information related to the flow behavior. Therefore we do not attempt to present g flow attributes, and poresmotion. Evolution of the free surface heightwith respect to the direct comparison with our radiographic observations with the theoretical calculations. Irrespective of the welding parameters or welding time, a common weld pool behavior is observed from different experiments. Fig. 6 bridges the connections between the time evolution of the driving forces and their corresponding dominative characteristics during typical short welding periods. As mentioned above, arc force generally triggered the inward force, surface tension gradient force caused outward force and gravity induced downward forces respectively within the moltenmetal [15,41], if there is no special alterations i.e. surface tension modifiers. As observed, the surface of the melt pool initially peaked at the center, followed by the rising at the pool periphery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000014_tpel.2014.2337111-Figure7-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000014_tpel.2014.2337111-Figure7-1.png",
        "caption": "Fig. 7. Experimental result of rotor position estimation at 1500 r/min (Tref = 3 N \u00b7 m). (a) Rotor position estimation without variable hysteresis band and sampling. (b) Proposed rotor position estimation.",
        "texts": [
            " The proposed variable-hysteresis-band current control and variable-sampling position estimation methods are compared to the position estimation methods without variable hysteresis band and sampling experimentally on a 2.3 kW, 6000 r/min, three-phase 12/8 SRM. Current hysteresis band is set to 0.5 A and dc-link voltage is set to 300 V. Field-programmable gate array EP3C25Q240 is used for digital implementation of the rotor position estimation methods. The torque reference is set to 3 N \u00b7 m and the speed is 1500 r/min. From the experimental results shown in Fig. 7, it can be noticed that real-time rotor position estimation error has positive bias. This is because the selected digital-to-analog conversion chip is unipolar. Therefore, 5.625\u00b0 offset is added to position error in the next a couple of figures. The real-time position estimation error without variable hysteresis band and sampling is +4.6\u00b0 and \u22123.4\u00b0. By using the proposed method, the real-time rotor position estimation error of the proposed method is decreased to +3.3\u00b0 and \u22121.3\u00b0. Due to the noise and quantization error in the current sensing, phase current slope sensing error is higher, leading to the increase in the real-time rotor position estimation error compared with simulation results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure6-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure6-1.png",
        "caption": "Fig. 6. Performance of the sliding surface.",
        "texts": [
            " Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated. Figs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6. The norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the p N roposed CNTSM performed better than the NTSM as well as the CNTSM. t In addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained w 5 w o N a w c s H e t t s c s ith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000027_d0an02029j-Figure1-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000027_d0an02029j-Figure1-1.png",
        "caption": "Fig. 1 (A) Photograph of Alg@QDs-UOx MSs under natural light. Inset: Photograph of Alg@QDs-UOx MSs under the self-made device (\u03bbex = 365 nm). (B) The size distribution of Alg@QDs-UOx MSs. (C) SEM images of the Alg@QDs-UOx MSs. (D) SEM images of the surface of Alg@QDsUOx MSs.",
        "texts": [
            " The design principle of uric acid detection was based on the fluorescence change of CdZnTeS QDs quenched by H2O2 which is the oxidation product of uric acid in the presence of the urate oxidase. As shown in Scheme 2B and C, uric acid as small molecules can enter the Alg@QDs-UOx MSs and be oxidized by urate oxidase to produce H2O2. The fluorescence changes of Alg@QDs-UOx MSs could be observed with the naked-eye and photographed with the built-in camera of the smartphone. The pictures of Alg@QDs-UOx MSs were obtained under natural light and UV light. As shown in Fig. 1A, the Alg@QDsUOx MSs showed round shapes and uniform particle sizes, and emitted strong fluorescence. The average size of the particles was about 3.0 \u00b1 0.11 mm (Fig. 1B). The morphology of Scheme 2 Schematic description of (A) the preparation of CdZnTeS QDs, (B) the principle of uric acid detection based on CdZnTeS QDs, and (C) the preparation of Alg@QDs-UOx MSs and uric acid detection. This journal is \u00a9 The Royal Society of Chemistry 2020 Analyst Pu bl is he d on 1 8 N ov em be r 20 20 . D ow nl oa de d by C ar le to n U ni ve rs ity o n 11 /3 0/ 20 20 2 :2 2: 53 P M . the Alg@QDs-UOx MSs characterized by scanning electron microscopy (SEM) is shown in Fig. 1C and D, which exhibit a dense multilayer network structure. The ability of CdZnTeS QDs to resist protein interference is shown in Fig. 2. CdZnTeS QDs in the Alg@QDs-UOx MSs had no significant effect on the high-concentration of the protein environment such as BSA, Muc-1, AFP and C-RP. However, the same concentration of BSA, Muc-1 and C-RP could enhance the fluorescence of CdZnTeS QDs in solution, and the same concentration of AFP could quench the fluorescence of CdZnTeS QDs in solution. This phenomenon was related to the overlapping multilayer network structure of the surface of Alg@QDs-UOx MSs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000021_s00034-020-01399-6-Figure8-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000021_s00034-020-01399-6-Figure8-1.png",
        "caption": "Fig. 8 Responses of x1(t), x2(t) and x3(t) of the closed-loop system (42) using dynamic ETM: t0 = 0, tk+1 = inf { t > tk | 0.01e\u22120.101t +10[0.25xT(t)x(t)\u2212eT(t)e(t)] \u2264 0 } .The rectangular window indicates that the stabilizability of the closed-loop system (42) using the above dynamic ETM is guaranteed",
        "texts": [
            "0022 0.0214 0.1458 0.0026 0.0022 0.0026 0.463 \u23a4 \u23a6 , Y = [ 0.0129 \u22120.0544 \u22120.9428 ] , the dynamic ETM is tk+1 = inf { t > tk | 0.01e\u22120.101t + 10[0.25xT(t)x(t) \u2212 eT(t)e(t)] \u2264 0 } , (54) and the control law u(t) is obtained as u(t) = [ 0.0009 \u22120.0101 \u22120.4366 ] x(tk), t \u2208 [tk, tk+1). For simulation, we choose the initial condition x(0) = [ 1 2 3 ]T. Figures 7 and 8 show the triggering instants and intervals of the event generator using dynamic ETM and the state responses of system (42). It is clear from Fig. 8 that the closed-loop system is asymptotically stable. Remark 3 From Figs. 1, 3, 5 and 7, it is clear that for a given state of the system, the next execution time given by a dynamic ETM (14) is larger than that given by a static ETM (7). This emphasizes that dynamic ETM is better than the static ETM in utilizing limited communication and energy resources. In this paper, we have proposed a systematic method for designing of robust stabilizing event-triggered feedback controllers for a class of systems with time-varying uncertainties and nonlinear Lipschitz functions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000027_d0an02029j-Figure3-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000027_d0an02029j-Figure3-1.png",
        "caption": "Fig. 3 (A) Grayscale intensity of Alg@QDS-Uox MSs within 30 days. (B) Fluorescence intensity of the CdZnTeS QD solution within 30 days. (C) Grayscale response of Alg@QDS-Uox MSs in uric acid detection within 15 days. (D) Fluorescence response of the mixed solution of CdZnTeS QDs and urate oxidase in uric acid detection within 15 days. The error bars were obtained based on three repetitive experiments. CdZnTeS QDs: 15 nM; uric acid: 500 \u03bcM; and urate oxidase: 0.25 units per ml.",
        "texts": [
            " This phenomenon was related to the overlapping multilayer network structure of the surface of Alg@QDs-UOx MSs. It could prevent CdZnTeS QDs (2\u20135 nm in diameter) from diffusing freely to the outside solution of the Alg@QDs-UOx MSs and could also block protein (1\u2013100 nm in diameter) from the outside solution into the Alg@QDs-UOx MSs. Based on this, the Alg@QDs-UOx MSs could avoid the interference of protein in the internal CdZnTeS QDs. The stability of CdZnTeS QDs and urate oxidase in the Alg@QDs-UOx MSs were investigated. As shown in Fig. 3A and B, the Alg@QDs-UOx MSs maintained a stable grayscale intensity, and this indicated that the fluorescence of the internal CdZnTeS QDs remained stable during storage, while the CdZnTeS QDs in the solution were slowly quenched about 40% within 30 days. Fig. 3C and D show that the Alg@QDs-UOx MSs had a similar effect for uric acid detection within 15 days. Conversely, when urate oxidase solution was used for uric acid detection, the quenching efficiency of CdZnTeS QDs decreased from 78% to 50%. These indicated that Alg@QDs-UOx MSs could avoid the quenching of CdZnTeS QDs and the inactivation of urate oxidase during storage. The selection of the divalent cations is shown in Fig. S4;\u2020 the alginate hydrogel microspheres embedded with CdZnTeS QDs (Alg@QDs MSs) were obtained by cross-linking with Ba2+ and they showed the strongest fluorescence, and the filtrate showed the weakest fluorescence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure1-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure1-1.png",
        "caption": "Fig. 1. Schematic experimental configuration that transmit X-ray beam through the weld pool.",
        "texts": [
            " For all the experiments, tungsten tip was kept approximately 1.5 mm above the center position of the 6 mm (wide) and 25 mm (long) face of the sample. Argon was used as the shielding gas. Different welding sequences carried out with 100 A, 125 A input currents and 2 s and 3 s welding durations. All the experiments applied welding voltage is 11.5 V. This sample/ welding configuration was oriented in a way that the synchrotron Xray beam travels through the sample 6 mm thick side towards the imaging detector, as shown in Fig. 1. 60 keV monochromatic X-rays were used for the experiments while the imaging system consists of a 1 mm thick Nd:YAG Scintillator which is coupled to a Vision Research Inc. MIRO 310 M camera through a visible light optics system. The spatial resolution of the imaging system was 10 \u03bcm. Fig. 2 presents an example for the evolution of a weld pool during a representative arc welding process with 100 A welding current, 12 V voltage DC (direct current) and 2 s duration (see Supplementary Video 1 also)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000020_j.matdes.2020.108534-Figure2-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000020_j.matdes.2020.108534-Figure2-1.png",
        "caption": "Fig. 2. The typical weld pool shape changes during the arc welding process. The image sequence shown in this figure is used 100A DC welding current and 2 s welding time. The white dashed line represents the real-time morphology of the melt pool, and the red solid lines indicate the motion trajectory of some tracking particles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " All the experiments applied welding voltage is 11.5 V. This sample/ welding configuration was oriented in a way that the synchrotron Xray beam travels through the sample 6 mm thick side towards the imaging detector, as shown in Fig. 1. 60 keV monochromatic X-rays were used for the experiments while the imaging system consists of a 1 mm thick Nd:YAG Scintillator which is coupled to a Vision Research Inc. MIRO 310 M camera through a visible light optics system. The spatial resolution of the imaging system was 10 \u03bcm. Fig. 2 presents an example for the evolution of a weld pool during a representative arc welding process with 100 A welding current, 12 V voltage DC (direct current) and 2 s duration (see Supplementary Video 1 also). As shown in the figure, once the arc is activated, melting starts and the surface of the weld pool that forms beneath the tungsten tip rises rapidly. When the size of the weld pool is increased (Fig. 2c), the zenith of the pool starts to appear divided and then the level of the center surface of the pool drops slightly. Even though the center of the pool drops down relative to the position before this transition, it still remains above the initial solid-air interface position. A relatively short time after stopping the arc (in this sequence just after 2 s), the next major transition starts. In this transition, the top surface of the entre liquid pool drops below the level of the original solid surface level and forms the final solidified shape of theweld pool",
            " In the initial stage of the welding, the pool diameter is small and a lower temperature difference in the small immatureweld pool is envisaged. Therefore, the surface tension gradient driven force is relatively lower in magnitude. Thus, the flow caused by the arc force is appeared to dominate a short period within the melt pool. It caused the inward flow inside the melt pool and an apparent increase of free surface [17,31]. The further evidence shown to confirm this hypothesis is the inward flow of the tracking particles in the weld pool at the beginning, as indicated in Fig. 2. With continuous heat input from the arc, the diameter of the weld pool increased. But asmore andmore heat are fed to the center of the pool, even though the excess heat is transported away, temperature based surface tension difference between the center and the edges of the pool increases. This makesMarangoni forces to eventually dominate the internal weld pool flow with outward direction, thus making the weld pool interface elevated at the edge, for a reasonable period of time during the welding process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_0_0000001_j.isatra.2021.04.001-Figure7-1.png",
        "original_path": "designv11-0/openalex_figure/designv11_0_0000001_j.isatra.2021.04.001-Figure7-1.png",
        "caption": "Fig. 7. Norm of the tracking error \u2206.",
        "texts": [
            " Moreover, the capability of the CNTSM controller to handle with the disturbance is demonstrated. Figs. 4 and 5 evidence the fulfillment of the TE constraints when the CNTSM controller is implemented. Evidently, in the case of NTSM and NCNTSM controllers the constraints given for the TE are not satisfied. Taking into the account the proposed controller design, if the state constraints as well as the TE constraints are fulfilled, then, the sliding surface also must be bounded satisfying the constraints give by (24). This fact is evidenced in Fig. 6. The norm of the TE is shown in Fig. 7. Notice that the CNTSM controller achieves the lowest value of the TE norm. Thus, the p N roposed CNTSM performed better than the NTSM as well as the CNTSM. t In addition, to sum up the performance comparison between he three tested controllers Fig. 8 provides a histogram obtained w 5 w o N a w c s H e t t s c s ith the TE data. The proposed histogram has been divided into 0 bars. From this figure, it is clear that the TE values obtained ith the proposed controller (black bars) remain near to the rigin compared with the other tested controllers (NTSM and CNTSM)"
        ],
        "surrounding_texts": []
    }
]