Impedance control

Impedance control is an approach to dynamic control relating force and position. It is often used in applications where a manipulator interacts with its environment and the force position relation is of concern. Examples of such applications include humans interacting with robots, where the force produced by the human relates to how fast the robot should move/stop. Simpler control methods, such as position control or torque control, perform poorly when the manipulator experiences contacts. Thus impedance control is commonly used in these settings.
Mechanical impedance is the ratio of force output to motion input. This is analogous to electrical impedance that is the ratio of voltage output to current input (e.g. resistance is voltage divided by current). A "spring constant" defines the force output for a displacement (extension or compression) of the spring. A "damping constant" defines the force output for a velocity input. If we control the impedance of a mechanism, we are controlling the force of resistance to external motions that are imposed by the environment.
Mechanical admittance is the inverse of impedance - it defines the motions that result from a force input. If a mechanism applies a force to the environment, the environment will move, or not move, depending on its properties and the force applied. For example, a marble sitting on a table will react very differently to a given force than will a log floating in a lake.
The key theory behind the method is to treat the environment as an admittance and the manipulator as an impedance. It assumes the postulate that "no controller can make the manipulator appear to the environment as anything other than a physical system."
This rule of thumb can also be stated as: "in the most common case in which the environment is an admittance (e.g. a mass, possibly kinematically constrained) that relation should be an impedance, a function, possibly nonlinear, dynamic, or even discontinuous, specifying the force produced in response to a motion imposed by the environment."
Principle.
Impedance control doesn't simply regulate the force or position of a mechanism. Instead it regulates the relationship between force and position on the one hand, and velocity and acceleration on the other hand, i.e. the impedance of the mechanism. It requires a position (velocity or acceleration) as input and has a resulting force as output. The inverse of impedance is admittance. It imposes position.
So actually the controller imposes a spring-mass-damper behavior on the mechanism by maintaining a dynamic relationship between force formula_1 and position, velocity and acceleration formula_2: formula_3, with formula_4 being friction and formula_5 being static force.
Masses (formula_6) and springs (with stiffness formula_7) are energy storing elements, whereas a damper (with damping formula_8) is an energy dissipating device. If we can control impedance, we are able to control energy exchange during interaction,
i.e. the work being done. So impedance control is interaction control.
Note that mechanical systems are inherently multi-dimensional - a typical robot arm can place an object in three dimensions (formula_9 coordinates) and in three orientations (e.g. roll, pitch, yaw). In theory, an impedance controller can cause the mechanism to exhibit a multi-dimensional mechanical impedance. For example, the mechanism might act very stiff along one axis and very compliant along another. By compensating for the kinematics and inertias of the mechanism, we can orient those axes arbitrarily and in various coordinate systems. For example, we might cause a robotic part holder to be very stiff tangentially to a grinding wheel, while being very compliant (controlling force with little concern for position) in the radial axis of the wheel.
Mathematical Basics.
Joint space.
An uncontrolled robot can be expressed in Lagrangian formulation as
 + \boldsymbol{c}(\boldsymbol{q},\dot{\boldsymbol{q}}) + \boldsymbol{g}(\boldsymbol{q}) + \boldsymbol{h}(\boldsymbol{q},\dot{\boldsymbol{q}}) + \boldsymbol{\tau}_{\mathrm{ext}},
where formula_10 denotes joint angular position, formula_11 is the symmetric and positive-definite inertia matrix, formula_12 the Coriolis and centrifugal torque, formula_13 the gravitational torque, formula_14 includes further torques from, e.g., inherent stiffness, friction, etc., and formula_15 summarizes all the external forces from the environment. The actuation torque formula_16 on the left side is the input variable to the robot.
One may propose a control law of the following form:
_\mathrm{d}-\dot{\boldsymbol{q}}) + \hat{\boldsymbol{M}}(\boldsymbol{q})\ddot{\boldsymbol{q}}_\mathrm{d} + \hat{\boldsymbol{c}}(\boldsymbol{q},\dot{\boldsymbol{q}}) + \hat{\boldsymbol{g}}(\boldsymbol{q}) + \hat{\boldsymbol{h}}(\boldsymbol{q},\dot{\boldsymbol{q}}),

where formula_17 denotes the desired joint angular position, formula_18 and formula_19 are the control parameters, and formula_20, formula_21, formula_22, and formula_23 are the internal model of the corresponding mechanical terms.
Inserting  into  gives an equation of the closed-loop system (controlled robot):
formula_24
Let formula_25, one obtains
formula_26
Since the matrices formula_18 and formula_19 have the dimension of stiffness and damping, they are commonly referred to as stiffness and damping matrix, respectively. Clearly, the controlled robot is essentially a multi-dimensional mechanical impedance (mass-spring-damper) to the environment, which is addressed by formula_15.
Task space.
The same principle also applies to task space. An uncontrolled robot has the following task-space representation in Lagrangian formulation:
formula_30,
where formula_10 denotes joint angular position, formula_32 task-space position, formula_33 the symmetric and positive-definite task-space inertia matrix. The terms formula_34, formula_35, formula_36, and formula_37 are the generalized force of the Coriolis and centrifugal term, the gravitation, further nonlinear terms, and environmental contacts. Note that this representation only applies to robots with redundant kinematics. The generalized force formula_38 on the left side corresponds to the input torque of the robot.
Analogously, one may propose the following control law:
formula_39
where formula_40 denotes the desired task-space position, formula_41 and formula_42 are the task-space stiffness and damping matrices, and formula_43, formula_44, formula_45, and formula_46 are the internal model of the corresponding mechanical terms.
Similarly, one has
formula_47,

as the closed-loop system, which is essentially a multi-dimensional mechanical impedance to the environment (formula_37) as well. Thus, one can choose desired impedance (mainly stiffness) in the task space. For example, one may want to make the controlled robot act very stiff along one direction while relatively compliant along others by setting
formula_49
assuming the task space is a three-dimensional Euclidean space. The damping matrix formula_42 is usually chosen such that the closed-loop system  is stable.
Applications.
Impedance control is used in applications such as robotics as a general strategy to send commands to a robotics arm and end effector that takes into account the non-linear kinematics and dynamics of the object being manipulated.


Door control unit

In automotive electronics, a door control unit (DCU) is a generic term for an embedded system that controls a number of electrical systems associated with an advanced motor vehicle. A modern motor vehicle contains a number of ECUs (electronic control units), and the door control unit (DCU) is one of the minor ones.
The door control unit is responsible for controlling and monitoring various electronic accessories in a vehicle's door. Since most of the vehicles have more than one door, DCUs may be present in each door separately, or a single centralised one provided. A DCU associated with the driver's door has some additional functionalities. This additional features are the result of complex functions like locking, driver door switch pad, child lock switches, etc., which are associated with the driver's door. In most of the cases driver door module acts as a master and others act as slaves in communication protocols.
Features controlled by door control units.
In some advanced motor vehicles, luxury features like puddle lamps and BLIS (Blind spot Indicator System) are also supported by DCUs.


Iso-damping

Iso-damping is a desirable system property referring to a state where the open-loop phase Bode plot is flat—i.e., the phase derivative with respect to the frequency is zero, at a given frequency called the "tangent frequency", formula_1. At the "tangent frequency" the Nyquist curve of the open-loop system tangentially touches the sensitivity circle and the phase Bode is locally flat which implies that the system will be more robust to gain variations. For systems that exhibit iso-damping property, the overshoots of the closed-loop step responses will remain almost constant for different values of the controller gain. This will ensure that the closed-loop system is robust to gain variations.
The iso-damping property can be expressed as formula_2
where formula_3 is the tangent frequency and formula_4 is the open-loop system transfer function.
Bode's ideal transfer function.
In the middle of the 20th century, Bode proposed the first idea involving the use of fractional-order controllers in a feedback problem by what is known as Bode's ideal transfer function. Bode proposed that the ideal shape of the Nyquist plot for the open loop frequency response is a straight line in the complex plane, which provides theoretically infinite gain margin. Ideal open-loop transfer function is given by:
where formula_6 is the desired gain cross over frequency and formula_7 is the slope of the ideal cut-off characteristic.
The Bode diagrams of formula_8, formula_9, are very simple. The amplitude curve is a straight line of constant slope formula_10 dB/dec, and the phase curve is a horizontal line at formula_11 rad. The Nyquist curve consists of a straight line through the origin with formula_12 rad.
The major benefit achieved through this structure is iso-damping, i.e. overshoot being independent of the payload or the system gain. The usage of fractional elements for description of ideal Bode's control loop is one of the most promising applications of fractional calculus in the process control field. Bode's ideal control loop frequency response has the fractional integrator shape and provides the iso-damping property around the gain crossover frequency. This is due to the fact that the phase margin and the maximum overshoot are defined by one parameter only (the fractional power of formula_13), and are independent of open-loop gain.
Bode's ideal loop transfer function is probably the first design method that addressed robustness explicitly.


Intelligent control

Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms.
Overview.
Intelligent control can be divided into the following major sub-domains:
New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them.
Neural network controller.
Neural networks have been used to solve problems in almost all spheres of science and technology. Neural network control basically involves two steps:
It has been shown that a feedforward network with nonlinear, continuous and differentiable activation functions have universal approximation capability. Recurrent networks have also been used for system identification. Given, a set of input-output data pairs, system identification aims to form a mapping among these data pairs. Such a network is supposed to capture the dynamics of a system. For the control part, deep reinforcement learning has shown its ability to control complex systems.
Bayesian controllers.
Bayesian probability has produced a number of algorithms that are in common use in many advanced control systems, serving as state space estimators of some variables that are used in the controller.
The Kalman filter and the Particle filter are two examples of popular Bayesian control components. The Bayesian approach to controller design often requires an important effort in deriving the so-called system model and measurement model, which are the mathematical relationships linking the state variables to the sensor measurements available in the controlled system. In this respect, it is very closely linked to the
system-theoretic approach to control design.


Constrained-layer damping

Constrained-layer damping is a mechanical engineering technique for suppression of vibration. Typically a viscoelastic or other damping material, is sandwiched between two sheets of stiff materials that lack sufficient damping by themselves. The ending result is, any vibration made on either side of the constraining materials (the two stiffer materials on the sides) are trapped and evidently dissipated in the viscoelastic or middle layer.


S-graph

The S-graph framework is an approach to solving batch process scheduling problems in chemical plants. S-graph is suited for the problems with a non-intermediate storage (NIS) policy, which often appears in chemical productions, but it is also capable of solving problems with an unlimited intermediate storage (UIS) policy.
Overview.
The S-graph representation exploits problem-specific knowledge to develop efficient scheduling algorithms. In the scheduling problem, there are products, and a set of tasks, which have to be performed to produce a product. There are dependencies between the tasks, and every task has a set of needed equipment that can perform the task. Different processing times can be set for the same task in different equipment types. It is possible to have more pieces of equipment of the same type, or define changeover times between two tasks performed on a single piece of equipment.
There are two types of the scheduling problems that can be handled:


Multimedia Acceleration eXtensions

The Multimedia Acceleration eXtensions or MAX are instruction set extensions to the Hewlett-Packard PA-RISC instruction set architecture (ISA). MAX was developed to improve the performance of multimedia applications that were becoming more prevalent during the 1990s.
MAX instructions operate on 32- or 64-bit SIMD data types consisting of multiple 16-bit integers packed in general purpose registers. The available functionality includes additions, subtractions and shifts.
The first version, MAX-1, was for the 32-bit PA-RISC 1.1 ISA. The second version, MAX-2, was for the 64-bit PA-RISC 2.0 ISA.
Notability.
The approach is notable because the set of instructions is much smaller than in other multimedia CPUs, and also more general-purpose. The small set and simplicity of the instructions reduce the recurring costs of the electronics, as well as the costs and difficulty of the design. The general-purpose nature of the instructions increases their overall value. These instructions require only small changes to a CPU's arithmetic-logic unit. A similar design approach promises to be a successful model for the multimedia instructions of other CPU designs. The set is also small because the CPU already included powerful shift and bit-manipulation instructions: "Shift pair" which shifts a pair of registers, "extract" and "deposit" of bit fields, and all the common bit-wise logical operations (and, or, exclusive-or, etc.).
This set of multimedia instructions has proven its performance, as well. In 1996 the 64-bit "MAX-2" instructions enabled real-time performance of MPEG-1 and MPEG-2 video while increasing the area of a RISC CPU by only 0.2%.
Implementations.
MAX-1 was first implemented with the PA-7100LC in 1994. It is usually attributed as being the first SIMD extensions to an ISA. The second version, MAX-2, was for the 64-bit PA-RISC 2.0 ISA. It was first implemented in the PA-8000 microprocessor released in 1996.
The basic approach to the arithmetic in MAX-2 is to "interrupt the carries" between the 16-bit subwords, and choose between modular arithmetic, signed and unsigned saturation. This requires only small changes to the arithmetic logic unit.
MAX-2.
MAX-2 instructions are register-to-register instructions that operate on multiple integers in 64-bit quantities. All have a one cycle latency in the PA-8000 microprocessor and its derivatives. Memory accesses are via the standard 64-bit loads and stores.
The "MIX" and "PERMH" instructions are a notable innovation because they permute words in the register set without accessing memory. This can substantially speed many operations.


Computer-automated design

Design Automation usually refers to electronic design automation, or Design Automation which is a Product Configurator. Extending Computer-Aided Design (CAD), automated design and Computer-Automated Design (CAutoD) are more concerned with a broader range of applications, such as automotive engineering, civil engineering, composite material design, control engineering, dynamic system identification and optimization, financial systems, industrial equipment, mechatronic systems, steel construction, structural optimisation, and the invention of novel systems.
The concept of CAutoD perhaps first appeared in 1963, in the IBM Journal of Research and Development, where a computer program was written.
More recently, traditional CAD simulation is seen to be transformed to CAutoD by biologically-inspired machine learning, including heuristic search techniques such as evolutionary computation, and swarm intelligence algorithms.
Guiding designs by performance improvements.
To meet the ever-growing demand of quality and competitiveness, iterative physical prototyping is now often replaced by 'digital prototyping' of a 'good design', which aims to meet multiple objectives such as maximised output, energy efficiency, highest speed and cost-effectiveness. The design problem concerns both finding the best design within a known range (i.e., through 'learning' or 'optimisation') and finding a new and better design beyond the existing ones (i.e., through creation and invention). This is equivalent to a search problem in an almost certainly, multidimensional (multivariate), multi-modal space with a single (or weighted) objective or multiple objectives.
Normalized objective function: cost vs. fitness.
Using single-objective CAutoD as an example, if the objective function, either as a cost function formula_1, or inversely, as a fitness function formula_2, where
is differentiable under practical constraints in the multidimensional space, the design problem may be solved analytically. Finding the parameter sets that result in a zero first-order derivative and that satisfy the second-order derivative conditions would reveal all local optima. Then comparing the values of the performance index of all the local optima, together with those of all boundary parameter sets, would lead to the global optimum, whose corresponding 'parameter' set will thus represent the best design. However, in practice, the optimization usually involves multiple objectives and the matters involving derivatives are a lot more complex.
Dealing with practical objectives.
In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such "a posteriori" learning or adjustments need to be repeated many times until a ‘satisfactory’ or ‘optimal’ design emerges.
Exhaustive search.
In theory, this adjustment process can be automated by computerised search, such as exhaustive search. As this is an exponential algorithm, it may not deliver solutions in practice within a limited period of time.
Search in polynomial time.
One approach to virtual engineering and automated design is evolutionary computation such as evolutionary algorithms.
Evolutionary algorithms.
To reduce the search time, the biologically-inspired evolutionary algorithm (EA) can be used instead, which is a (non-deterministic) polynomial algorithm. The EA based multi-objective "search team" can be interfaced with an existing CAD simulation package in a batch mode. The EA encodes the design parameters (encoding being necessary if some parameters are non-numerical) to refine multiple candidates through parallel and interactive search. In the search process, 'selection' is performed using 'survival of the fittest' "a posteriori" learning. To obtain the next 'generation' of possible solutions, some parameter values are exchanged between two candidates (by an operation called 'crossover') and new values introduced (by an operation called 'mutation'). This way, the evolutionary technique makes use of past trial information in a similarly intelligent manner to the human designer.
The EA based optimal designs can start from the designer's existing design database, or from an initial generation of candidate designs obtained randomly. A number of finely evolved top-performing candidates will represent several automatically optimized digital prototypes.
There are websites that demonstrate interactive evolutionary algorithms for design. EndlessForms.com allows you to evolve 3D objects online and have them 3D printed. PicBreeder.org allows you to do the same for 2D images.


SprutCAM

SprutCAM is a high-level Computer-Aided Manufacturing (CAM) software that provides off-line features for programming of various CNC machines used for cutting, wire electrical discharge (EDM), 2, 3, and multi axial (CNC Swiss-Type Lathe) machining.
The program was developed by SprutCAM Tech Ltd based in Limassol, Cyprus.
SprutCAM only supports Microsoft Windows 10/11 version.
History.
SPRUT Technology was founded in 1997 by Alexander Kharadziev, who recruited a team of engineers to build a company for developing CAx software. And released its own product, SprutCAM, in 1997. The company was relocated in 2021. The headquarters is now located in Limassol, Cyprus.
Version history.
Past Versions
Current Version:
System requirements.
The system requirements for SprutCAM:
Computer aided design products.
SprutCAM works with associative CAD geometry and toolpaths; this allows modified geometry or machining parameters to quickly obtain updated toolpaths.
File format.
SprutCAM opens/saves following file formats:
Export/Convert following Formats via CAD Plugin as Background Process to IGES an Import:


Catalog server

A catalog server provides a single point of access that allows users to centrally search for information across a distributed network. In other words, it indexes databases, files and information across large network and allows keywords, Boolean and other searches. If you need to provide a comprehensive searching service for your intranet, extranet or even the Internet, a catalog server is a standard solution.


Machine tending

Machine tending refers to the automated operation of industrial machine tools in a manufacturing plant, primarily using robot automation systems. While loading and unloading is the primary function of machine tending systems, often the robot performs other valuable functions within the automation system such as part inspection, blow off, wash, deburring, sorting, packaging and gauging.
Benefits of machine tending systems include:
Because of the sophistication, functionality, and costs associated with machine tending systems, most manufacturers require a capital approval process prior to investing in these systems where executive management must approve the purchase. Typically, an ROI (return on investment) is calculated to justify the purchase.


Driveway alarm

A driveway alarm is a device that is designed to detect people or vehicles entering a property via the driveway. A driveway alarm system is often integrated as a component of a system which automatically performs a task or alerts home owners of an unexpected intruder or visitor. Driveway alarms can be a vital component of security, automated lighting control, home control, energy efficiency, and other useful systems.
Overview.
A driveway alarm always consists of two components, a sensor and receiver. The sensor is used to detect people or vehicles on the driveway and the receiver is the device which alerts the user or owner to this detection. Wireless driveway alarms consist of three components, the sensor, receiver and a transmitter which sends the wireless alert signal to the receiver.
A driveway alarm may be connected to a burglar alarm that is used to alert the home owner or security service after it detects an intruder. Such a driveway may also trigger a security camera. Driveway alarms have found great application in domestic and commercial applications, especially in retail drive thru applications. Some of the more popular residential or commercial applications include motion-activated outdoor lighting systems, motion sensor street lamps and motion sensor lanterns.
Sensors.
Three types of sensors are commonly used in driveway alarm systems:
Wireless and wired systems.
Driveway alarms come in both wired and wireless packages. Infrared and rubber hose systems are generally sold as wireless units while magnetic probe systems are equally available as hard wired and wireless systems. Choosing between wireless or wired systems is typically decided by the environment the unit is being installed in. The most common driveway alarms sold are wireless infrared units.


Boost controller

In turbocharged internal combustion engines, a boost controller is a device sometimes used to increase the boost pressure produced by the turbocharger. It achieves this by reducing the boost pressure seen by the wastegate.
Operation.
The purpose of a boost controller is to reduce the boost pressure seen by the wastegate's reference port, in order to trick the wastegate into allowing higher boost pressures than it was designed for.
Many boost controllers use a needle valve that is opened and closed by an electric solenoid. By varying the pulse width to the solenoid, the solenoid valve can be commanded to be open a certain percentage of the time. This effectively alters the flow rate of air pressure through the valve, changing the amount of air that is bled out instead of going to the wastegate's reference port. Solenoids may require small diameter restrictors be installed in the air control lines to limit airflow and even out the on/off nature of their operation. Two-port solenoid bleed systems with a PID controller tend to be common on factory turbocharged cars.
An alternative design is to use a stepper motor. These designs allow fine control of airflow based on position and speed of the motor, but may have low total airflow capability. Some systems use a solenoid in conjunction with a stepper motor, with the stepper motor allowing fine control and the solenoid coarse control.
Control system.
Most modern designs are "electronic boost controllers" that use an electronic control unit to control the boost via a solenoid or stepper motor. The operating principle is the same as older "manual boost controllers", which is to control the air pressure presented to the wastegate actuator. Electronic controllers add greater flexibility in management of boost pressures, compared with the manual controllers.
The actuation of an electronic boost controller can be managed by one of two control systems:
Advantages.
By keeping the wastegate in a closed position more often, a boost controller causes more of the exhaust gas to be routed through the turbocharger, thus reducing turbo lag and lowering the boost threshold.
Disadvantages.
Regardless of the effectiveness of the boost controller, wastegate actuator springs that are too soft can cause the wastegate to open before desired. This due to the exhaust gas backpressure pushing against the wastegate valve itself, causing the valve to open of the actuator at all. Therefore, there is an upper limit to the effectiveness of a boost controller for a given spring stiffness in the wastegate actuator.
To prevent excessive boost pressures in the event of a failure, the boost controller needs to be designed such that failure mode do not result in any pressure being bled off. For instance, a solenoid-type boost controller should direct all air to the wastegate when it is in the non-energized position (the common failure mode for a solenoid). Otherwise, the boost controller could get stuck in a position that lets no boost pressure reach the wastegate, causing boost to quickly rise out of control.
Also, the electronic systems, extra hoses, solenoids and control systems add cost and complexity. Nonetheless, in recent times most automobile manufacturers use boost controllers on their turbocharged engines.
Alternatives.
In the past, boost pressures have been controlled by restricting or bleeding off some intake air before it reaches the intake manifold. Designs which restrict the intake air can use a butterfly valve in the intake to restrict airflow as desired boost is approached. Designs which bleed off the intake air functioned similar to a blowoff valve, but on a constant basis to maintain the desired boost pressure. These methods are rarely used in modern system due to the large sacrifices in efficiency, heat, and reliability.
Variable geometry turbocharger can be used to manage boost levels, negating the need for an external boost controller. Also, the wastegate itself has a similar function to a boost controller, in that it is used to manage the turbocharger's boost pressure.


Adamant Namiki Precision Jewel Co

Adamant Namiki Precision Jewel Co., Ltd. ( アダマンド並木精密宝石 Adamant Namiki Seimitsu Houseki Kabushiki-gaisha) is a Japanese precision components manufacturer based in Tokyo, Japan.
Overview.
In 1939, Namiki Precision Jewel Co., Ltd. started business as a manufacturer of synthetic sapphire jewel bearings for electrical measuring instruments. It later began selling these jewel bearings for use in watches in the 1960s. In 1957, Adamant Shoji (renamed Adamant Kogyo Co., Ltd. in 1959, and Adamant Co., Ltd. in 2014) was founded as a spin-off of Namiki as a result of business practices of the time. Thereafter, Namiki developed its product lineup primarily focusing on industrial jewel components, DC coreless motors, and medical devices. Meanwhile, Adamant Shoji’s business focused mainly on optical communication components. In 2017, Namiki and Adamant mutually agreed to unite their specialties to take their technologies and products to the next level. As a result, Adamant Namiki Precision Jewel Co., Ltd. was established on January 1, 2018.
History.
See Namiki Precision Jewel Co., Ltd. and Adamant Co., Ltd. for the history of each company prior to the January 1, 2018 intragroup merger.
Namiki merged with its subsidiary company, Adamant Co., Ltd., on January 1, 2018 and changed its name to Adamant Namiki Precision Jewel Co., Ltd.
Primary business.
Industrial jewel components.
Adamant Namiki uses integrated manufacturing, handling its products from the raw material, to processing, through to polishing. Industrial jewels, such as diamond, sapphire, and ruby, are used for jewel bearings, sapphire substrates, exterior watch parts, semiconductor wire bonding capillaries, nozzles, LTCC(Co-fired ceramic) and so on.
For sapphire product growth, Adamant Namiki employs the highly productive EFG method.
In 2021, the company succeeded in developing a mass production method for 2-inch diamond wafers.
Adamant Namiki also supplies ceramic parts, combining precision processing and various molding technologies, such as injection, powder press, and CIP molding, to provide a diverse range of products.
Optical components.
Adamant Namiki offers optical components with a focus on ferrules, sleeves, and connectors.
A ferrule is a component to link optical fibers together and high-precision (less than 1 micrometer) processing technology is required to ensure the secure connection of several micrometer optical fiber cores.
Adamant Namiki also combines its high-precision processing and assembly technologies to provide optical device components such as receptacles and pigtails, optical switches using MEMS(Microelectromechanical systems) technology, and optical devices such as variable attenuators.
DC coreless motors.
Since developing the smallest coreless motor of the time in 1973, Adamant Namiki has been consistently producing miniature DC coreless motors. The core components have evolved with high-precision processing technology and a more optimal magnetic circuit has produced a high-efficiency motor. In 2009, Adamant Namiki successfully developed the world’s smallest DC brushless motor at 0.6mm in diameter. The company also produces motor units such as its de-energized locking system, micro robot servo, multi-finger robotic hand, and micro mechanisms.
Medical devices.
Since the start of OEM manufacturing of its computer-controlled infusion pump in 1987, Adamant Namiki has established a line of business that offers medical device development, manufacturing, and service.


Electromechanical modeling

The purpose of electromechanical modeling is to model and simulate an electromechanical system, such that its physical parameters can be examined before the actual system is built. Parameter estimation utilizing different estimation theory coupled with physical experiments and physical realization by doing proper stability criteria evaluation of the overall system is the major objective of electromechanical modeling. Theory driven mathematical model can be used or applied to other system to judge the performance of the joint system as a whole. This is a well known and proven technique for designing large control system for industrial as well as academic multi-disciplinary complex system. This technique is also being employed in MEMS technology recently.
Different types of mathematical modeling.
The modeling of purely mechanical systems is mainly based on the Lagrangian which is a function of the generalized coordinates and the associated velocities. If all forces are derivable from a potential, then the time behavior of the dynamical systems is completely determined. For simple mechanical systems, the Lagrangian is defined as the difference of the kinetic energy and the potential energy.
There exists a similar approach for electrical system. By means of the electrical coenergy and well defined power quantities, the equations of motions are uniquely defined. The currents of the inductors and the voltage drops across the capacitors play the role of the generalized coordinates. All constraints, for instance caused by the Kirchhoff laws, are eliminated from the considerations. After that, a suitable transfer function is to be derived from the system parameters which eventually governs the behavior of the system.
In consequence, we have quantities (kinetic and potential energy, generalized forces) which determine the mechanical part and quantities (coenergy, powers) for the description of the electrical part. This offers a combination of the mechanical and electrical parts by means of an energy approach. As a result, an extended Lagrangian format is produced.
References.
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IEEE Transactions on Robotics

IEEE Transactions on Robotics is a bimonthly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE). It covers all aspects of robotics and is sponsored by the IEEE Robotics and Automation Society. The editor-in-chief is Kevin Lynch (Northwestern University).
Publication History.
The journal was established in 1985 as the IEEE Journal on Robotics and Automation, but changed name in 1989 to IEEE Transactions on Robotics and Automation. In 2004 the journal split into IEEE Transactions on Automation Science and Engineering and IEEE Transactions on Robotics.
Abstracting and indexing.
The journal is abstracted and indexed in:
According to the "Journal Citation Reports", the journal has a 2021 impact factor of 6.835, ranking it 7th out of 30 journals in the category "Robotics"


Bonding protocol

Bonding protocol (short for "Bandwidth On Demand Interoperability Group") is a generic name for a method of bonding or aggregation of multiple physical links to form a single logical link. Bonding is the term often used in Linux implementations: on Windows based systems the term teaming is often used, and between network-devices we talk about link aggregation, LAG and Link Aggregation Control Protocol.


Robotino

Robotino is a mobile robot system made by "Festo Didactic", and used for educational, training and research purposes.
Operation.
Robotino is based on an omnidirectional drive assembly, which enables the system to roam freely. The robot is controlled by an industry-standard PC system, which is powerful enough to plan routes for fully autonomous driving. Via a WLAN-Link, Robotino can send all sensor readings to an external PC. In the other direction, control commands can be issued by the external PC. This way, control programs can run on the external PC or on Robotino directly. Mixed mode or shared control are also possible.
For users with little prior robotics knowledge, Robotino can be readily programmed in its “native” programming environment RobotinoView II. More experienced programmers may find it useful that the robot can also be programmed in C, C++, Java, .NET, Matlab, Simulink, Labview and Microsoft Robotics Developer Studio.
Hardware.
The omnidirectional drive consists of three Mecanum wheels, all of which are individually controllable. These wheels are arranged at angles of 120°. Robotino has a bumper sensor around its circumference, infrared distance sensors, a color camera with VGA resolution, optical wheel encoders, power measurement for the entire system and the various motors, as well as a battery voltage monitor. Moreover, as optional additional sensors, Robotino can be equipped with a precise laser scanner, a gyroscope, and an indoor positioning system (created by Evolution Robotics). For signal input and output Robotino has several interfaces:
Power is supplied by two 12V/5Ah lead-acid batteries or optionally by two 12V/9Ah NiMH batteries.


Emergency Detection System

An Emergency Detection System (EDS) is a system that is used on crewed rocket missions. It monitors critical launch vehicle and spacecraft systems and issues status, warning and abort commands to the crew during their mission to low Earth orbit. It can trigger the Launch Abort System which will take the astronauts to safety.
References.
NASA Technical Note TN-D6487 (pdf), pp. 3, 6, vii


Ji-Feng Zhang

Ji-Feng Zhang (born 1963) was born in Shandong, China. He is currently the vice-chair of the technical board of the International Federation of Automatic Control (IFAC), the vice-president of the Systems Engineering Society of China (SESC), the vice-president of the Chinese Association of Automation (CAA), the chair of the technical committee on Control Theory (CAA), and the editor-in-chief for both "All About Systems and Control" and the "Journal of Systems Science and Mathematical Sciences".
Biography.
Ji-Feng Zhang was born in September 1963, Shandong, China. He received the B.S. degree in mathematics, from Shandong University in 1985, and M.S. and Ph.D. in control theory and stochastic systems, from Institute of Systems Science (ISS), Chinese Academy of Sciences (CAS) in 1988 and 1991, respectively. From November 1991 to December 1992, he was a postdoctoral fellow was with McGill University, Canada. From December 1996 to February 1998, he was with the Chinese University of Hong Kong. Since 1985 he has been with the ISS, CAS, where he is now a Guan Zhapzhi Chair Professor of the Academy of Mathematics and System Sciences (AMSS), and the director of the ISS.
Contributions to the field.
Job history.
Zhang has served as a vice-chair of the technical board of IFAC (2014–present), convener of Systems Science Discipline, Academic Degree Committee of the State Council, China (2009–present), vice-president of the Systems Engineering Society of China (2010–present), vice- president of the Chinese Association of Automation (CAA, 2014–present), chair of the Technical Committee on Control Theory (TCCT), CAA (2010–present), standing member of the Chinese Mathematical Society (2008–2015), vice-president of the Beijing Mathematical Society, China (2006–2013), member of the board of governors, IEEE Control Systems Society (2013), member of the steering committee, Asian Control Association, (2009–2014), vice-general secretary of CAA (2002–2008), vice-chair of TCCT, CAA (2002–2007), general secretary of TCCT, CAA (1993–2002), senior member of IEEE (1997–2013), member of the IFAC Technical Committee on Modeling, identification and Signal Processing (2009–present).
He also has been a general co-chair of the 32nd and 33rd Chinese Control Conference (2013, 2014), program chair/co-chair of the 17th IFAC Symposium on System Identification (2015), the 30th Chinese Control Conference (2011), the 9th World Congress on Intelligent Control and Automation, Beijing, China (2012), the IEEE International Conference on Control Applications, part of the IEEE Multi-Conference on Systems and Control (2012), vice-chair of the 20th IFAC World Congress (2017), and an organizing committee co-chair of the 21st-26th Chinese Control Conferences (2002–2007), the 1st-4th Chinese-Swedish Conference on Control (2003–2008), the 1st-8th Conference on Frontier Problems in Systems and Control (2000–2008), and a finance co-chair of the 48th Conference on Decision and Control (2009).
He is/was the founding editor-in-chief of "All About Systems and Control" (2014–present), editor-in-chief of the "Journal of Systems Science and Mathematical Sciences" (2014–present), managing editor of "Journal of Systems Science and Complexity" (2007–2014), deputy editor-in-chief of the following journals: "Science China: Information Sciences" (2014–present), "Scientia Sinica: Informationis" (2014–present), "Journal of Systems Science and Mathematical Sciences" (2004–2013), "Acta Automatica Sinica" (2005–2010), "Control Theory and Applications" (2008–2013), "Systems Engineering: Theory and Practice" (2011–present); and associate editor or an editorial board member of the following journals: "IEEE Transactions on Automatic Control" (2007–2009), "SIAM" "Journal on Control and Optimization" (2008–2013), "Aerospace Control and Application" (2008–present), "Mathematics in Practice and Theory" (2006–2013), "Acta Automatica Sinica" (1999–2010), "Control Theory and Applications" (2003–2008), "Journal of Control Theory and Applications" (2003–2008), and the "Journal of Shandong University" "(Engineering Science)" (2011–2015).
Research areas.
Zhang’s current research interests are system identification, adaptive control, stochastic systems, and multi-agent systems.
System identification.
He made original contributions on system identification, including the estimation of the orders, time-delays and parameters of stochastic systems. He gave a criterion for time-delay estimate, with which one can get a strong consistent time-delay estimate. He with co-authors initiated the research on the parameter identification and adaptive control of the systems with quantized observations, and investigated the optimal adaptive control and identification errors, time complexity, optimal input design, and impact of disturbances and unmodeled dynamics on identification accuracy and complexity in both stochastic and deterministic frameworks. With a series of significant results, he has established a solid framework for the identification and adaptive control of uncertainty systems with quantized information. This is of great importance for many practical systems, especially, when digital communications are needed.
Adaptive control.
He investigated the capability issues of robust and adaptive control in dealing with uncertainty, and revealed that to capture the intrinsic limitations of adaptive control, it is necessary to use sup-types of transient and persistent performance, rather than limsup-types which reflect only asymptotic behavior of a system. This indicates that intimate interaction and inherent conflict between identification and control result in a certain performance lower bound which does not approach the nominal performance even when the system varies very slowly. For nonlinear hybrid stochastic systems with unknown jump-Markov parameters, he with co-authors used the Wonham nonlinear filter to estimate the unknown parameters and presented an estimation error bound, which is a basic tool and plays an important role in performance analysis of adaptive control of nonlinear hybrid stochastic systems. He also attacked a series of hard problems related on global output-feedback control of nonlinear stochastic systems with inverse dynamics, including practical output-feedback risk-sensitive control, robust adaptive stabilization, small-gain theorem of general nonlinear stochastic systems. Different from the existing literature, the systems considered in his work are so complicated that renders any control design for them is much difficult. He developed a set of predominant methods and obtained many innovative results. The work represents an accomplishment for both the field of stochastic nonlinear stabilization and the backstepping method.
Stochastic multi-agent systems.
In control of stochastic multi-agent systems, Zhang thoroughly studied the interaction of interest coupled decision-makers and the uncertainty of individual behavior, which is the prominent characteristic of multi-agent systems (MASs). He made a systematic study of the sample path behavior of the closed-loop system in relation to Nash Equilibria (NE) and a substantial contribution to the developing theory of Nash Certainty Equivalence (NCE) for large population stochastic dynamic games. He introduced the concepts of asymptotic Nash- equilibrium in probability and almost surely, and elucidated the relationship between these concepts, which provides necessary tools for analyzing the optimality of the decentralized control laws. With respect to the decentralized quadratic-type and tracking-type performance indices, by using Nash Certainty Equivalence he developed decentralized optimal controls, and proved the optimality of the closed-loop systems. He also initiated the study on consensusability and formability of MAS and obtained necessary and sufficient conditions which reflect the intrinsic relationships between the consensusability/formability and the agents’ dynamics, admissible control sets and communication topologies. These works are of great significance, since they break through the framework of conventional control theory and extend the methodology and tools in the stochastic adaptive control theory to analyzing MAS.
Index-coupled example.
The multi-agent system Zhang mentioned could be used to describe an engineering or economic system. The uncertainty in his work is a kind of random noise appearing in the agent’s dynamic model. Brownian agent swarm systems are such examples, where the acceleration of agent depends on not only its own state variables (e.g. position, velocity, and energy), control, Gaussian white noise, but also the population position average. The dynamic equations are coupled together via the population position average. Other interest or performance index-coupled examples can be found in wireless communication networks and stock markets. In a wireless communication network with users, the changing rate of the received power for user depends on, its neighbors’ powers, control, random noise. Each user makes its own power control strategy to ensure the signal-to- interference-ratio to approach a desired level. This can be formulated by the following model (for simplicity, here we use a linear model with constant parameters) and a coupled-index group: where is the neighbor of user, are system parameters, is the constant background noise intensity, and. In a stock market with investigators, suppose that profits of each investigator is influenced by his recent profits situation and the profits situation of his neighbors, and each investigator wants to get something around the average value. Then, the problem can be described by the following model (for simplicity, here we use a linear model with constant parameters) and a coupled-interest index group: When a=1 and b=0, the coupled-interest index becomes.
Publications and awards.
Zhang was elected as a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and as a Fellow of the International Federation of Automatic Control (IFAC). He was the second-place winner of the State Natural Science Award (China) in both 2010 and 2015. Zhang has also received the Distinguished Young Scholar Fund from National Natural Science Foundation of China in 1997; the First Prize of the Young Scientist Award of CAS in 1995; Excellent Chinese Doctoral Dissertation Supervisor in 2009; Excellent Graduate Student Supervisor of Chinese Academy of Sciences (CAS) in 2007, 2008 and 2009; the Best Paper award of the 7th Asian Control Conference in 2009; and the Guan Zhaozhi Best Paper award of the 23rd Chinese Control Conference in 2004.
Zhang’s current research interests are system identification, adaptive control, stochastic systems, and multi-agent systems. He has published 2 books, over 110 journal papers and 70 conference papers, in journals such as "IEEE Transactions on Automatic Control", "Automatica", and "SIAM Journal on Control and Optimization". He has 5 papers listed in "Highly Cited Papers" by the ISI Web of Knowledge, Essential Science Indicators from Aug 2007 to Aug 2015.


Agile tooling

Agile tooling is the design and fabrication of manufacturing related-tools such as dies, molds, patterns, jigs and fixtures in a configuration that aims to maximise the tools' performance, minimise manufacturing time and cost, and avoid delay in prototyping. A fully functional agile tooling laboratory consists of CNC milling, turning and routing equipment. It can also include additive manufacturing platforms (such as fused filament fabrication, selective laser sintering, Stereolithography, and direct metal laser sintering), hydroforming, vacuum forming, die casting, stamping, injection molding and welding equipment.
Agile tooling is similar to rapid tooling, which uses additive manufacturing to make tools or tooling quickly, either directly by making parts that serve as the actual tools or tooling components, such as mold inserts; or indirectly by producing patterns that are in turn used in a secondary process to produce the actual tools. Another similar technique is prototype tooling, where molds, dies and other devices are used to produce prototypes. Rapid manufacturing, and specifically rapid tooling technologies, are earlier in their development than rapid prototyping (RP) technologies, and are often extensions of RP.
The aim of all toolmaking is to catch design errors early in the design process; improve product design better products, reduce product cost, and reduce time to market.
Users.
Hundreds of universities and research centers around the globe are investing in additive manufacturing equipment in order to be positioned to make prototypes and tactile representations of real parts. Few have fully committed the concept of using additive manufacturing (AM) to create manufacturing tools (fixturing, clamps, molds, dies, patterns, negatives, etc.). AM experts seem to agree that tooling is a large, namely untapped market. Deloitte University Press estimated that in 2012 alone, the AM Tooling market $1.2 Billion. At that point in the development cycle of AM Tooling, much of the work was performed under the guise of “let’s try it and see what happens”.
Industry applications.
Additive manufacturing, starting with today's infancy period, requires manufacturing firms to be flexible, ever-improving users of all available technologies to remain competitive. Advocates of additive manufacturing also predict that this arc of technological development will counter globalization, as end users will do much of their own manufacturing rather than engage in trade to buy products from other people and corporations. The real integration of the newer additive technologies into commercial production, however, is more a matter of complementing traditional subtractive methods rather than displacing them entirely.
Automotive – approaching niche vehicle markets (making less than 100, 000 vehicles), rather than high production volume
Aircraft – the U.S. aircraft industry operates in an environment where production volumes are relatively low and resulting product costs are relatively high. Agile tooling can be applied in the early design stage of the development cycle to minimize the high cost of redesign.
Medical – cast tooling would benefit a great deal from agile tooling. However, the cost for the tooling may still be significantly greater than the cost of a casting piece, with high lead times. Since only several dozen or several hundred metal parts are needed, the challenge for mass production is still prevalent. A balance between these four areas – quantity, design, material, and speed are key to designing and producing a fully functional product.


State-transition matrix

In control theory, the state-transition matrix is a matrix whose product with the state vector formula_1 at an initial time formula_2 gives formula_1 at a later time formula_4. The state-transition matrix can be used to obtain the general solution of linear dynamical systems.
Linear systems solutions.
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form
where formula_6 are the states of the system, formula_7 is the input signal, formula_8 and formula_9 are matrix functions, and formula_10 is the initial condition at formula_2. Using the state-transition matrix formula_12, the solution is given by:
The first term is known as the zero-input response and represents how the system's state would evolve in the absence of any input. The second term is known as the zero-state response and defines how the inputs impact the system.
Peano–Baker series.
The most general transition matrix is given by the Peano–Baker series
where formula_15 is the identity matrix. This matrix converges uniformly and absolutely to a solution that exists and is unique.
Other properties.
The state transition matrix formula_16 satisfies the following relationships:
1. It is continuous and has continuous derivatives.
2, It is never singular; in fact formula_17 and formula_18, where formula_19 is the identity matrix.
3. formula_20 for all formula_4 .
4. formula_22 for all formula_23.
5. It satisfies the differential equation formula_24 with initial conditions formula_25.
6. The state-transition matrix formula_12, given by
where the formula_28 matrix formula_29 is the fundamental solution matrix that satisfies
7. Given the state formula_32 at any time formula_33, the state at any other time formula_4 is given by the mapping
Estimation of the state-transition matrix.
In the time-invariant case, we can define formula_16, using the matrix exponential, as formula_37.
In the time-variant case, the state-transition matrix formula_38 can be estimated from the solutions of the differential equation formula_39 with initial conditions formula_40 given by formula_41, formula_42, ..., formula_43. The corresponding solutions provide the formula_44 columns of matrix formula_38. Now, from property 4,
formula_46 for all formula_47. The state-transition matrix must be determined before analysis on the time-varying solution can continue.


Microextrusion

Microextrusion is a microforming extrusion process performed at the submillimeter range. Like extrusion, material is pushed through a die orifice, but the resulting product's cross section can fit through a 1mm square. Several microextrusion processes have been developed since microforming was envisioned in 1990. Forward (ram and billet move in the same direction) and backward (ram and billet move in the opposite direction) microextrusion were first introduced, with forward rod-backward cup and double cup extrusion methods developing later. Regardless of method, one of the greatest challenges of creating a successful microextrusion machine is the manufacture of the die and ram. "The small size of the die and ram, along with the stringent accuracy requirement, needs suitable manufacturing processes." Additionally, as Fu and Chan pointed out in a 2013 state-of-the-art technology review, several issues must still be resolved before microextrusion and other microforming technologies can be implemented more widely, including deformation load and defects, forming system stability, mechanical properties, and other size-related effects on the crystallite (grain) structure and boundaries.
Development and use.
Microextrusion is an outgrowth of microforming, a science that was in its infancy in the early 1990s. In 2002, Engel "et al." expressed that up to that point, only a few research experiments involving micro-deep drawing and extruding processes had been attempted, citing limitations in shearing on billets and difficulties in tool manufacturing and handling. By the mid- to late 2000s, researchers were working on issues such as billet flow, interfacial friction, extrusion force, and size effects, "the deviations from the expected results that occur when the dimension of a workpiece or sample is reduced." Most recently, research into using ultrafine-grained material at higher formation temperatures and applying ultrasonic vibration to the process has pushed the science further. However, before bulk production of microparts such as pins, screws, fasteners, connectors, and sockets using microforming and microextrusion techniques can occur, more research into billet production, transportation, positioning, and ejection are required.
Microextrusion techniques have also been applied to bioceramic and plastic extrusion and the manufacture of components for resorbable and implantable medical devices, from bioresorbable stents to controlled drug release systems.
Microextrusion processes.
Like normal macro-level extrusion, several similar microextrusion processes have been described over the years. The most basic processes were forward (direct) and backward (indirect) microextrusion. The ram (which propels the billet forward) and billet both move in the same direction with forward microextrusion, while in backward microextrusion has the ram and billet moving in opposite directions. These in turn have been applied to specialized applications such as the manufacture of microbillet, brass micropins, microgear shafts, and microcondensers. However, other processes have been applied to microextrusion, including forward rod–backward cup extrusion and double cup (one forward, one backward) extrusion.
Strengths and limitations.
Strengths of microextrusion over other manufacturing processes include its ability to create very complex cross-sections, preserve chemical properties, condition physical properties, and process materials which are delicate or dependent on physical or chemical properties. However, microextrusion has some limitations, though primarily related to the need for improvement of the relatively young process. Dixit and Das described it thus in 2012:
With the scaling down of dimensions and increasing geometric complexity of objects, currently available technologies and systems may not be able to meet the development needs. New measuring devices, principles and instrumentation, tolerance rules, and procedures have to be developed. Materials databases with detailed information on various materials and their properties/interface properties including microstructures and size effect would be very useful for product innovation and process design. More studies are necessary on micro/nanowear and damages/failures of the micromanufacturing tools. The forming limits for different types of materials at the microlevel must be prescribed. More specific considerations must be incorporated into the design of machines that are scaled down for microforming to meet engineering applications and requirements.


Hautus lemma

In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Belevitch-Hautus test or PBH test, can prove to be a powerful tool. This result appeared first in and. Today it can be found in most textbooks on control theory.
The main result.
There exist multiple forms of the lemma.
Hautus Lemma for controllability.
The Hautus lemma for controllability says that given a square matrix formula_1 and a formula_2 the following are equivalent:
Hautus Lemma for stabilizability.
The Hautus lemma for stabilizability says that given a square matrix formula_1 and a formula_2 the following are equivalent:
Hautus Lemma for observability.
The Hautus lemma for observability says that given a square matrix formula_1 and a formula_17 the following are equivalent:
Hautus Lemma for detectability.
The Hautus lemma for detectability says that given a square matrix formula_1 and a formula_17 the following are equivalent:


Pilot valve

A pilot valve is a small valve that controls a limited-flow control feed to a separate piloted valve. Typically, this separate valve controls a high pressure or high flow feed. Pilot valves are useful because they allow a small and easily operated feed to control a much higher pressure or higher flow feed, which would otherwise require a much larger force to operate; indeed, this is even useful when a solenoid is used to operate the valve.
Pilot valves are often used in critical applications (e.g., emergency and SIS controls) and are human-operated. They can be set up as a push-to-activate or dead man's switch.


Massera's lemma

In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2. In 2004, Massera's original lemma for single variable functions was extended to the multivariable case, and the resulting lemma was used to prove the stability of switched dynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals.
Massera's original lemma.
Massera’s lemma is used in the construction of a converse Lyapunov function of the following form (also known as the integral construction)
for an asymptotically stable dynamical system whose stable trajectory starting from formula_2
The lemma states:
Let formula_3 be a positive, continuous, strictly decreasing function with formula_4 as formula_5. Let formula_6 be a positive, continuous, nondecreasing function. Then there exists a function formula_7 such that
Extension to multivariable functions.
Massera's lemma for single variable functions was extended to the multivariable case by Vu and Liberzon.
Let formula_3 be a positive, continuous, strictly decreasing function with formula_4 as formula_5. Let formula_6 be a positive, continuous, nondecreasing function. Then there exists a differentiable function formula_7 such that


Extended Kalman filter

In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the "de facto" standard in the theory of nonlinear state estimation, navigation systems and GPS.
History.
The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for "linear"
system models with additive independent white noise in both the transition and the measurement systems.
Unfortunately, in engineering, most systems are "nonlinear", so attempts were made to apply
this filtering method to nonlinear systems; most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point. If the system model (as described below) is not well known or is inaccurate, then Monte Carlo methods, especially particle filters, are employed for estimation. Monte Carlo techniques predate the existence of the EKF but are more computationally expensive for any moderately dimensioned state-space.
Formulation.
In the extended Kalman filter, the state transition and observation models don't need to be linear functions of the state but may instead be differentiable functions.
Here w"k" and v"k" are the process and observation noises which are both assumed to be zero mean multivariate Gaussian noises with covariance Q"k" and R"k" respectively. u"k" is the control vector.
The function "f" can be used to compute the predicted state from the previous estimate and similarly the function "h" can be used to compute the predicted measurement from the predicted state. However, "f" and "h" cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian) is computed.
At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate.
See the Kalman Filter article for notational remarks.
Discrete-time predict and update equations.
Notation formula_3 represents the estimate of formula_4 at time "n" given observations up to and including at time .
Update.
where the state transition and observation matrices are defined to be the following Jacobians
Disadvantages and alternatives.
Unlike its linear counterpart, the extended Kalman filter in general is "not" an optimal estimator (it is optimal if the measurement and the state transition model are both linear, as in that case the extended Kalman filter is identical to the regular one). In addition, if the initial estimate of the state is wrong, or if the process is modeled incorrectly, the filter may quickly diverge, owing to its linearization. Another problem with the extended Kalman filter is that the estimated covariance matrix tends to underestimate the true covariance matrix and therefore risks becoming inconsistent in the statistical sense without the addition of "stabilising noise"
More generally one should consider the infinite dimensional nature of the nonlinear filtering problem and the inadequacy of a simple mean and variance-covariance estimator to fully represent the optimal filter. It should also be noted that the extended Kalman filter may give poor performances even for very simple one-dimensional systems such as the cubic sensor, where the optimal filter can be bimodal and as such cannot be effectively represented by a single mean and variance estimator, having a rich structure, or similarly for the quadratic sensor.
In such cases the projection filters have been studied as an alternative, having been applied also to navigation. Other general nonlinear filtering methods like full particle filters may be considered in this case.
Having stated this, the extended Kalman filter can give reasonable performance, and is arguably the de facto standard in navigation systems and GPS.
Generalizations.
Continuous-time extended Kalman filter.
Model
Initialize
Predict-Update
Unlike the discrete-time extended Kalman filter, the prediction and update steps are coupled in the continuous-time extended Kalman filter.
Discrete-time measurements.
Most physical systems are represented as continuous-time models while discrete-time measurements are frequently taken for state estimation via a digital processor. Therefore, the system model and measurement model are given by
where formula_11.
Initialize
Predict
where
Update
where
The update equations are identical to those of discrete-time extended Kalman filter.
Higher-order extended Kalman filters.
The above recursion is a first-order extended Kalman filter (EKF). Higher order EKFs may be obtained by retaining more terms of the Taylor series expansions. For example, second and third order EKFs have been described. However, higher order EKFs tend to only provide performance benefits when the measurement noise is small.
Non-additive noise formulation and equations.
The typical formulation of the EKF involves the assumption of additive process and measurement noise. This assumption, however, is not necessary for EKF implementation. Instead, consider a more general system of the form:
Here w"k" and v"k" are the process and observation noises which are both assumed to be zero mean multivariate Gaussian noises with covariance Q"k" and R"k" respectively. Then the covariance prediction and innovation equations become
where the matrices formula_23 and formula_24 are Jacobian matrices:
The predicted state estimate and measurement residual are evaluated at the mean of the process and measurement noise terms, which is assumed to be zero. Otherwise, the non-additive noise formulation is implemented in the same manner as the additive noise EKF.
Implicit extended Kalman filter.
In certain cases, the observation model of a nonlinear system cannot be solved for formula_27, but can be expressed by the implicit function:
where formula_29 are the noisy observations.
The conventional extended Kalman filter can be applied with the following substitutions:
where:
Here the original observation covariance matrix formula_33 is transformed, and the innovation formula_34 is defined differently. The Jacobian matrix formula_33 is defined as before, but determined from the implicit observation model formula_36.
Modifications.
Iterated extended Kalman filter.
The iterated extended Kalman filter improves the linearization of the extended Kalman filter by recursively modifying the centre point of the Taylor expansion. This reduces the linearization error at the cost of increased computational requirements.
Robust extended Kalman filter.
The extended Kalman filter arises by linearizing the signal model about the current state estimate and using the linear Kalman filter to predict the next estimate. This attempts to produce a locally optimal filter, however, it is not necessarily stable because the solutions of the underlying Riccati equation are not guaranteed to be positive definite. One way of improving performance is the faux algebraic Riccati technique
which trades off optimality for stability. The familiar structure of the extended Kalman filter is retained but stability is achieved by selecting a positive definite solution to a faux algebraic Riccati equation for the gain design.
Another way of improving extended Kalman filter performance is to employ the H-infinity results from robust control. Robust filters are obtained by adding a positive definite term to the design Riccati equation. The additional term is parametrized by a scalar which the designer may tweak to achieve a trade-off between mean-square-error and peak error performance criteria.
Invariant extended Kalman filter.
The invariant extended Kalman filter (IEKF) is a modified version of the EKF for nonlinear systems possessing symmetries (or "invariances"). It combines the advantages of both the EKF and the recently introduced symmetry-preserving filters. Instead of using a linear correction term based on a linear output error, the IEKF uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from a linear state error, but from an invariant state error. The main benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the EKF, which results in a better convergence of the estimation.
Unscented Kalman filters.
A nonlinear Kalman filter which shows promise as an improvement over the EKF is the unscented Kalman filter (UKF). In the UKF, the probability density is approximated by a deterministic sampling of points which represent the underlying distribution as a Gaussian. The nonlinear transformation of these points are intended to be an estimation of the posterior distribution, the moments of which can then be derived from the transformed samples. The transformation is known as the unscented transform. The UKF tends to be more robust and more accurate than the EKF in its estimation of error in all the directions.
"The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization."
A 2012 paper includes simulation results which suggest that some published variants of the UKF fail to be as accurate as the Second Order Extended Kalman Filter (SOEKF), also known as the augmented Kalman filter. The SOEKF predates the UKF by approximately 35 years with the moment dynamics first described by Bass et al. The difficulty in implementing any Kalman-type filters for nonlinear state transitions stems from the numerical stability issues required for precision, however the UKF does not escape this difficulty in that it uses linearization as well, namely linear regression. The stability issues for the UKF generally stem from the numerical approximation to the square root of the covariance matrix, whereas the stability issues for both the EKF and the SOEKF stem from possible issues in the Taylor Series approximation along the trajectory.
Ensemble Kalman Filter.
The UKF was in fact predated by the Ensemble Kalman filter, invented by Evensen in 1994. It has the advantage over the UKF that the number of ensemble members used can be much smaller than the state dimension, allowing for applications in very high-dimensional systems, such as weather prediction, with state-space sizes of a billion or more.
Fuzzy Kalman Filter.
Fuzzy Kalman filter with a new method to represent possibility distributions was recently proposed to replace probability distributions by possibility distributions in order to obtain a genuine possibilistic filter, enabling the use of non-symmetric process and observation noises as well as higher inaccuracies in both process and observation models.


SVN Notifier

SVN Notifier is a tool to monitor one's Subversion project repository for changes. SVN Notifier notifies a person about recent commits and helps you keep one's local copy up to date. A person reviews all the changes and updates their local copy right from the application. It is free software released under the GNU General Public License. It uses SVN, TortoiseSVN and Microsoft .NET Framework 2.0.
Comparison with other tools.
"SVN Notifier" differs from the tool CommitMonitor in that it watches repository URLs via working copies rather than directly. "SVN Notifier" is tightly integrated with TortoiseSVN. It implements the "monitoring/notification" feature only (that is missing in TortoiseSVN) and thus has a very simple user interface.


Comparison of platforms for software agents

There several platforms for software agents or also agent development toolkits, which can facilitate the development of multi-agent systems. Hereby, software agents are implemented as independent threads which communicate with each other using agent communication languages. Below is a chart intended to capture many of the features that are important to such platforms.


System analysis

System analysis in the field of electrical engineering characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio speakers; electrical engineers often use it because of its direct relevance to many areas of their discipline, most notably signal processing, communication systems and control systems.
Characterization of systems.
A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals. Therefore, one natural characterization of systems is by how many inputs and outputs they have:
It is often useful (or necessary) to break up a system into smaller pieces for analysis. Therefore, we can regard a SIMO system as multiple SISO systems (one for each output), and similarly for a MIMO system. By far, the greatest amount of work in system analysis has been with SISO systems, although many parts inside SISO systems have multiple inputs (such as adders).
Signals can be continuous or discrete in time, as well as continuous or discrete in the values they take at any given time:
With this categorization of signals, a system can then be characterized as to which type of signals it deals with:
Another way to characterize systems is by whether their output at any given time depends only on the input at that time or perhaps on the input at some time in the past (or in the future!).
Analog systems with memory may be further classified as "lumped" or "distributed". The difference can be explained by considering the meaning of memory in a system. Future output of a system with memory depends on future input and a number of state variables, such as values of the input or output at various times in the past. If the number of state variables necessary to describe future output is finite, the system is lumped; if it is infinite, the system is distributed.
Finally, systems may be characterized by certain properties which facilitate their analysis:
There are many methods of analysis developed specifically for linear time-invariant ("LTI") deterministic systems. Unfortunately, in the case of analog systems, none of these properties are ever perfectly achieved. Linearity implies that operation of a system can be scaled to arbitrarily large magnitudes, which is not possible. Time-invariance is violated by aging effects that can change the outputs of analog systems over time (usually years or even decades). Thermal noise and other random phenomena ensure that the operation of any analog system will have some degree of stochastic behavior. Despite these limitations, however, it is usually reasonable to assume that deviations from these ideals will be small.
LTI systems.
As mentioned above, there are many methods of analysis developed specifically for Linear time-invariant systems (LTI systems). This is due to their simplicity of specification. An LTI system is completely specified by its transfer function (which is a rational function for digital and lumped analog LTI systems). Alternatively, we can think of an LTI system being completely specified by its frequency response. A third way to specify an LTI system is by its characteristic linear differential equation (for analog systems) or linear difference equation (for digital systems). Which description is most useful depends on the application.
The distinction between lumped and distributed LTI systems is important. A lumped LTI system is specified by a finite number of parameters, be it the zeros and poles of its transfer function, or the coefficients of its differential equation, whereas specification of a distributed LTI system requires a complete function, or partial differential equations.


LAPACK++

LAPACK++, the Linear Algebra PACKage in C++, is a computer software library of algorithms for numerical linear algebra that solves systems of linear equations and eigenvalue problems.
It supports various matrix classes for vectors, non-symmetric matrices, SPD matrices, symmetric matrices, banded, triangular, and tridiagonal matrices. However, it does not include all of the capabilities of original LAPACK library.
History.
The original LAPACK++ (up to v1.1a) was written by R. Pozo et al. at the University of Tennessee and Oak Ridge National Laboratory.
In 2000, R. Pozo et al. left the project, with the projects' web page stating LAPACK++ would be superseded by the Template Numerical Toolkit (TNT).
The current LAPACK++ (versions 1.9 onwards) started off as a fork from the original LAPACK++. There are extensive fixes and changes, such as more wrapper functions for LAPACK and BLAS routines.


Automation engineering

Automation engineering is the provision of automated solutions to physical activities and industries.
Automation engineer.
Automation engineers are experts who have the knowledge and ability to design, create, develop and manage machines and systems, for example, factory automation, process automation and warehouse automation.
Automation technicians are also involved.
Scope.
Automation engineering is the integration of standard engineering fields. Automatic control of various control systems for operating various systems or machines to reduce human efforts & time to increase accuracy. Automation engineers design and service electromechanical devices and systems to high-speed robotics and programmable logic controllers (PLCs).
Work and career after graduation.
Graduates can work for both government and private sector entities such as industrial production,
companies that create and use automation systems, for example paper industry, automotive industry, food and agricultural industry, water treatment, and oil & gas sector such as refineries, power plants.
Job Description.
Automation engineers can design, program, simulate and test automated machinery and processes, and usually are employed in industries such as the energy sector in plants, car manufacturing facilities or food processing plants and robots. Automation engineers are responsible for creating detailed design specifications and other documents, developing automation based on specific requirements for the process involved, and conforming to international standards like IEC-61508, local standards, and other process specific guidelines and specifications, simulate, test and commission electronic equipment for automation.


Automation technician

Automation technicians repair and maintain the computer-controlled systems and robotic devices used within industrial and commercial facilities to reduce human intervention and maximize efficiency. Their duties require knowledge of electronics, mechanics and computers. Automation technicians perform routine diagnostic checks on automated systems, monitor automated systems, isolate problems and perform repairs. If a problem occurs, the technician needs to be able to troubleshoot the issue and determine if the problem is mechanical, electrical or from the computer systems controlling the process. Once the issue has been diagnosed, the technician must repair or replace any necessary components, such as a sensor or electrical wiring. In addition to troubleshooting, Automation technicians design and service control systems ranging from electromechanical devices and systems to high-speed robotics and programmable logic controllers (PLCs). These types of systems include robotic assembly devices, conveyors, batch mixers, electrical distribution systems, and building automation systems. These machines and systems are often found within industrial and manufacturing plants, such as food processing facilities. Alternate job titles include field technician, bench technician, robotics technician, PLC technician, production support technician and maintenance technician.
Education and training.
Automation technician programs integrate computer programming with mechanics, electronics and process controls, They also commonly include coursework in hydraulics, pneumatics, programmable logic controllers, electrical circuits, electrical machinery and human-machine interfaces. Typical courses include math, communications, circuits, digital devices and electrical controls. Other courses include robotics, automation, electrical motor controls, programmable logic controllers, and computer-aided design. Good math and analytic skills are essential to understand automated systems and isolate problems. In addition to programming, Automation Technicians are expected to become proficient with various instruments and hand tools for troubleshooting, such as electrical multimeters, signal analyzers, and frequency counters.
Employers generally prefer applicants who have completed an automation technician certificate or associate degree. These programs can be completed at colleges and universities in either an in-class or online format. Some colleges, such as George Brown College, offer an online automation technician program that uses simulation software, LogixSim, to complete automation lab projects and assignments.
Other relevant credentials to become an automation technician include mechatronics, robotics, and PLCs. Up-to-date credentials and certifications can enhance employment opportunities and keep technicians current with the latest technological developments. In addition to colleges and universities, other organizations and companies also offer credential programs in automation, including equipment manufacturers such as Rockwell and professional associations, such as the Electronics Technicians Association, Robotics Industries Association and the Manufacturing Skill Standards Council.
Career prospects.
Career opportunities for automation technicians include a wide range of manufacturing and service industries such as automotive, pharmaceutical, power distribution, food processing, mining, and transportation. Other career prospects include areas as machine assembly, troubleshooting and testing, systems integration, application support, maintenance, component testing and assembly, automation programming, robot maintenance and programming, technical sales and services.
Typical job-related activities may involve:
Experienced automation technicians with advanced training may become specialists or troubleshooters who help other technicians diagnose difficult problems, or work with engineers in designing equipment and developing maintenance procedures. Automation technicians with leadership ability also may eventually become maintenance supervisors or service managers. Due to the highly specialized skills and knowledge required, there are many opportunities available to automation technicians in the service sector where there is a great demand for contract and sub-contract work with smaller manufacturing and distribution companies. Some experienced automation technicians open their own design, installation and maintenance companies. They can also become wholesalers or retailers of automation equipment, including inside and outside sales of automation equipment and systems.
Because of their familiarity with control systems and equipment, automation technicians are particularly well qualified to become manufacturers' sales representatives. Other related opportunities include customer service, quality-control, quality-assurance and consulting.


The IEEE Transactions on Control Systems Technology is published bimonthly by the IEEE Control Systems Society. The journal publishes papers, letters, tutorials, surveys, and perspectives on control systems technology. The editor-in-chief is Prof. Andrea Serrani (Ohio State University). According to the "Journal Citation Reports", the journal has a 2019 impact factor of 5.312.


Single-pass bore finishing

Single-pass bore finishing is a machining process similar to honing to finish a bore, except the tool only takes a single pass. The process was originally developed to improve bore quality in cast iron workpieces.
Process.
This process uses multiple diamond-plated, barrel-shaped tools to finish a bore. The tool has a single layer of diamonds bonded to the tool, with about half of each diamond exposed. These special tools are made to a specific diameter and are only meant to open up the hole to that size.
The tools are usually mounted in a dedicated bore finishing machine, however they can also be mounted in a milling machine. In either case the tool, workpiece, or both are rotated and the tool is plunged into the bore and removed. The part is then transferred to the next station or a larger tool is mounted and a larger bore machined, and the process repeated until the desired bore geometry is reached. The number of tools required to achieve the desired bore size is dependent on the workpiece material, the amount of stock to be removed and geometrical requirements, with four to six tool pieces being common. Each tool is progressively larger than the last, but in diminishing increments; as the stock removal is reduced, so is the tool's diamond grit size.
The process is similar to honing, in that the tool follows the existing center line of the bore. To make sure the tool follows the existing center line, the tool, workpiece, or both are allowed to float. Usually just the workpiece is floated, but both pieces may be floated to get the tightest tolerances, however this greatly increases complexity. For workpieces that are larger than approximately it may be more feasible to float the tool. The process can achieve a size tolerance of and a geometry tolerance of in production.
Machine tool.
Single-pass bore finishing is not usually done in a milling machine for several reasons. Firstly, most milling machines have only one spindle, so changing the tool more than four to six times can increase cycle times significantly. Secondly, most workpieces that require this process are made on horizontal machining centers (HMC), which reduces float-ability due to gravity. Thirdly, the lubrication may not be sufficient, which can lead to material build-up between diamonds, diminishing the tool's effectiveness. Finally, if any chips remain from previous operations they can ruin the tool.
Instead, typically a dedicated machine tool is used. It has four to eight spindles and usually a rotary table. The cycle time for this type of setup is determined by the longest individual operation, which in this situation is determined by how long it takes to plunge and retract the tool through the bore. Throughput can be increased by completing two workpieces on each cycle; this is achieved by having two identical stations for each tool size so that two workpieces can be operated on concurrently.
Advantages and disadvantages.
There is little downtime due to tool changes because tools usually last from tens of thousands of passes to over a million. The perishable tool cost can be as low as a 0.01 USD per bore for very large quantity runs. To make the process cost effective minimum runs would be on the order of one to two hundred parts with several runs each year.
Single-pass bore finishing is not well suited for blind holes because the tool has a tapered lead on it which prevents the bottom of the hole from being finished. The process can be performed on blind holes, but it requires an alternative tool design and suitable manufacturing conditions. A better alternative is ID grinding.
Commonly processed materials include soft and hard steels, aluminum, bronze, brass, ceramics, and chrome. Note that gummy grades of stainless steel, aluminum, and all but the hardest grades of plastic are much tougher for this process. The gumminess problem can be overcome with special oil based cutting fluids. Also, the process does not work well on thin-walled workpieces owing to a tendency to expand when the tool is inserted.
This method of bore finishing is better suited for bores with relatively low length-to-diameter ratios, usually less than 2:1. However, if there are cross-holes, or other interruptions in the bore, then a ratio greater than 2:1 is possible, because swarf and fluids may be expelled via these routes. This process is also not well suited for surfaces that require cross-hatching.


Plant operator

A plant operator is an employee who supervises the operation of an industrial plant. The term is usually applied to workers employed in utilities, wastewater treatment plants, power plants or chemical plants such as gas extraction facilities, petrochemical or oil refineries.
Modern industrial plants are generally highly automated, with control of the plant's processes centralised in a control room from which valves, gauges, alarms and switches may be operated. Employees working in these environments are sometimes known as control room, panel or board operators - conversely, workers carrying out field operations may be known as 'outside operators'. Generally, operators are assigned to a particular unit, on which they are responsible for a certain function or area of equipment. Operators are also often responsible for ensuring work is being done in a safe manner, including managing 'permit to work' systems covering other workers.


List of SIP software

This list of SIP software documents notable software applications which use Session Initiation Protocol (SIP) as a voice over IP (VoIP) protocol.
Servers.
Free and open-source license.
A SIP server, also known as a SIP proxy, manages all SIP calls within a network and takes responsibility for receiving requests from user agents for the purpose of placing and terminating calls.


Exponential stability

In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts. (i.e., in the left half of the complex plane). A discrete-time input-to-output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. Systems that are not LTI are exponentially stable if their convergence is bounded by exponential decay.
Exponential stability is a form of asymptotic stability, valid for more general dynamical systems.
Practical consequences.
An exponentially stable LTI system is one that will not "blow up" (i.e., give an unbounded output) when given a finite input or non-zero initial condition. Moreover, if the system is given a fixed, finite input (i.e., a step), then any resulting oscillations in the output will decay at an exponential rate, and the output will tend asymptotically to a new final, steady-state value. If the system is instead given a Dirac delta impulse as input, then induced oscillations will die away and the system will return to its previous value. If oscillations do not die away, or the system does not return to its original output when an impulse is applied, the system is instead marginally stable.
Example exponentially stable LTI systems.
The graph on the right shows the impulse response of two similar systems. The green curve is the response of the system with impulse response formula_1, while the blue represents the system formula_2. Although one response is oscillatory, both return to the original value of 0 over time.
Real-world example.
Imagine putting a marble in a ladle. It will settle itself into the lowest point of the ladle and, unless disturbed, will stay there. Now imagine giving the ball a push, which is an approximation to a Dirac delta impulse. The marble will roll back and forth but eventually resettle in the bottom of the ladle. Drawing the horizontal position of the marble over time would give a gradually diminishing sinusoid rather like the blue curve in the image above.
A step input in this case requires supporting the marble away from the bottom of the ladle, so that it cannot roll back. It will stay in the same position and will not, as would be the case if the system were only marginally stable or entirely unstable, continue to move away from the bottom of the ladle under this constant force equal to its weight.
It is important to note that in this example the system is not stable for all inputs. Give the marble a big enough push, and it will fall out of the ladle and fall, stopping only when it reaches the floor. For some systems, therefore, it is proper to state that a system is exponentially stable "over a certain range of inputs".