Machining

Machining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The methods that have this common theme are collectively called subtractive manufacturing, which utilizes machine tools, in contrast to "additive manufacturing" (3D printing), which uses controlled addition of material.
Machining is a part of the manufacture of many metal products, but it can also be used on other materials such as wood, plastic, ceramic, and composite material. A person who specializes in machining is called a machinist. A room, building, or company where machining is done is called a machine shop. Much of modern-day machining is carried out by computer numerical control (CNC), in which computers are used to control the movement and operation of mills, lathes, and other cutting machines. This increases efficiency, as the CNC machine runs unmanned, reducing labor costs for machine shops.
History and terminology.
The precise meaning of the term "machining" has evolved over the past one and a half centuries as technology has advanced. In the 18th century, the word "machinist" meant a person who built or repaired machines. This person's work was primarily done by hand, using processes such as the carving of wood and the writing-forging and hand-filing of metal. At the time, millwrights and builders of new kinds of "engines" (meaning, more or less, machines of any kind), such as James Watt or John Wilkinson, would fit the definition. The noun "machine tool" and the verb "to machine" ("machined, machining") did not yet exist.
Around the middle of the 20th century, the latter words were coined as the concepts they described evolved into widespread existence. Therefore, during the Machine Age, "machining" referred to (what we today might call) the "traditional" machining processes, such as turning, boring, drilling, milling, broaching, sawing, shaping, planing, abrasive cutting, reaming, and tapping. In these "traditional" or "conventional" machining processes, machine tools, such as lathes, milling machines, drill presses, or others, are used with a sharp cutting tool to remove material to achieve a desired geometry.
Since the advent of new technologies in the post–World War II era, such as electrical discharge machining, electrochemical machining, electron beam machining, photochemical machining, and ultrasonic machining, the retronym "conventional machining" can be used to differentiate those classic technologies from the newer ones. Currently, "machining" without qualification usually implies the traditional machining processes.
In the decades of the 2000s and 2010s, as additive manufacturing (AM) evolved beyond its earlier laboratory and rapid prototyping contexts and began to become standard throughout all phases of manufacturing, the term "subtractive manufacturing" became common retronymously in logical contrast with AM, covering essentially any removal processes also previously covered by the term "machining". The two terms are effectively synonymous, although the long-established usage of the term "machining" continues. This is comparable to the idea that evolved because of the proliferation of ways to contact someone (telephone, email, IM, SMS, and so on) but did not entirely replace the earlier terms such as "call", "talk to", or "write to".
Machining operations.
The three principal machining processes are classified as turning, drilling and milling. Other operations falling into miscellaneous categories include shaping, planing, boring, broaching, and sawing.
An unfinished workpiece requiring machining must have some material cut away to create a finished product. A finished product would be a workpiece that meets the specifications set out for that workpiece by engineering drawings or blueprints. For example, a workpiece may require a specific outside diameter. A lathe is a machine tool that can create that diameter by rotating a metal workpiece so that a cutting tool can cut metal away, creating a smooth, round surface matching the required diameter and surface finish. A drill can remove the metal in the shape of a cylindrical hole. Other tools that may be used for metal removal are milling machines, saws, and grinding machines. Many of these same techniques are used in woodworking.
As a commercial venture, machining is generally performed in a machine shop, which consists of one or more workrooms containing primary machine tools. Although a machine shop can be a stand-alone operation, many businesses maintain internal machine shops that support the business's specialized needs.
Machining requires attention to many details for a workpiece to meet the specifications in the engineering drawings or blueprints. Besides the obvious problems related to correct dimensions, there is the problem of achieving the right finish or surface smoothness on the workpiece. The inferior finish found on the machined surface of a workpiece may be caused by incorrect clamping, a dull tool, or inappropriate presentation of a device. Frequently, this poor surface finish, known as chatter, is evident by an undulating or irregular finish and waves on the machined surfaces of the workpiece.
Overview of machining technology.
Machining is any process in which a cutting tool removes small chips of material from the workpiece (the workpiece is often called the "work"). Relative motion is required between the device and the work to perform the operation. This relative motion is achieved in most machining operations using a primary activity called "cutting speed" and a secondary movement called "feed". The shape of the tool and its penetration into the work surface, combined with these motions, produce the desired shape of the resulting work surface.
Machining operations.
There are many kinds of machining operations, each of which is capable of generating a specific part geometry and surface texture.
In turning, a cutting tool with a single cutting edge removes material from a rotating workpiece to generate a cylindrical shape. The primary motion is provided by rotating the workpiece, and the feed motion is achieved by moving the cutting tool slowly in a direction parallel to the workpiece's rotation axis.
Drilling is used to create a round hole. It is accomplished by a rotating tool that typically has two or four helical cutting edges. The device is fed in a direction parallel to its axis of rotation into the workpiece to form the round hole.
In boring, a tool with a single bent pointed tip is advanced into a roughly made hole in a spinning workpiece to enlarge the gap and improve its accuracy slightly. It is a fine-finishing operation used in the final stages of product manufacture.
Reaming is one of the sizing operations that removes a small amount of metal from a drilled hole.
In milling, a rotating tool with multiple cutting edges is moved slowly relative to the material to generate a plane or straight surface. The direction of the feed motion is perpendicular to the tool's axis of rotation. The rotating milling cutter provides speed motion. The two primary forms of milling are:
Other conventional machining operations include shaping, planing, broaching, and sawing. Also, grinding and similar abrasive operations are often included within the category of machining.
Cutting tool.
A cutting tool has one or more sharp cutting edges and is made of a harder material than the work material. The cutting edge serves to separate the chip from the parent work material. Connected to the cutting edge are the two surfaces of the tool:
The rake face, which directs the flow of the newly formed chip, is oriented at a certain angle and is called the rake angle "α." It is measured relative to the plane perpendicular to the work surface. The rake angle can be positive or negative. The flank of the tool provides a clearance between the tool and the newly formed work surface, thus protecting the surface from abrasion, which would degrade the finish. This angle between the work and flank surfaces is called the relief angle. There are two basic types of cutting tools:
A single-point tool has one cutting edge for turning, boring, and planning. During machining, the device's point penetrates below the work part's original work surface. The fact is sometimes rounded to a certain radius, called the nose radius.
Multiple cutting-edge tools have more than one cutting edge and usually achieve their motion relative to the work part by rotating. Drilling and milling use turning multiple-cutting-edge tools. Although the shapes of these tools are different from a single-point device, many elements of tool geometry are similar.
Cutting conditions.
Relative motion is required between the tool and work to perform a machining operation. The primary action is at a specific cutting speed. In addition, the device must be moved laterally across the work. This is a much slower motion called the feed. The remaining dimension of the cut is the penetration of the cutting tool below the original work surface, reaching the cut's depth. Speed, feed, and depth of cut are called the cutting conditions. They form the three dimensions of the machining process, and for certain operations, their product can be used to obtain the material removal rate for the process:
where
Stages in metal cutting.
Machining operations usually divide into two categories, distinguished by purpose and cutting conditions:
Roughing cuts are used to remove a large amount of material from the starting work part as rapidly as possible, i.e., with a significant Material Removal Rate (MRR), to produce a shape close to the desired form but leaving some material on the piece for a subsequent finishing operation.
Finishing cuts complete the part and achieve the final dimension, tolerances, and surface finish. In production machining jobs, one or more roughing cuts are usually performed on the work, followed by one or two finishing cuts. Roughing operations are done at high feeds and depths – feeds of 0.4–1.25  mm/rev (0.015–0.050 in/rev) and depths of 2.5–20 mm (0.100–0.750 in) are typical, but actual values depend on the workpiece materials. Finishing operations are carried out at low feeds and depths – dinners of 0.0125–0.04  mm/rev (0.0005–0.0015 in/rev) and depths of 0.75–2.0 mm (0.030–0.075 in) are typical. Cutting speeds are lower in roughing than in finishing.
A cutting fluid is often applied to the machining operation to cool and lubricate the cutting tool. Determining whether a cutting fluid should be used and, if so, choosing the proper cutting fluid is usually included within the scope of the cutting condition.
Today other forms of metal cutting are becoming increasingly popular. An example of this is water jet cutting. Water jet cutting involves pressurized water over 620 MPa (90 000 psi) and can cut metal and have a finished product. This process is called cold cutting, which eliminates the damage caused by a heat-affected zone, as opposed to laser and plasma cutting.
Relationship of subtractive and additive techniques.
With the recent proliferation of additive manufacturing technologies, conventional machining has been retronymously classified, in thought and language, as a subtractive manufacturing method. In narrow contexts, additive and subtractive methods may compete with each other. In the broad context of entire industries, their Relationship is complementary. Each method has its advantages over the other. While additive manufacturing methods can produce very intricate prototype designs impossible to replicate by machining, strength and material selection may be limited.


List of CAx companies

This is a list of computer-aided technologies (CAx) companies and their software products. Software using computer-aided technologies (CAx) has been produced since the 1970s for a variety of computer platforms. This software may include applications for computer-aided design (CAD), computer-aided engineering (CAE), computer-aided manufacturing (CAM) and product data management (PDM).
The list is far from complete or representative as the CAD business landscape is very dynamic: almost every month new companies appear, old companies go out of business, and companies split and merge. Sometimes some names disappear and reappear again.
Past CAD Brands.
Acquired, orphaned, failed or rebranded.
In-house CAD software.
Developed by companies for their own use. Some are no longer used as the organizations are now using commercial systems.


Digital test controller

Digital test controllers are devices (usually computer based) that provide motion control by processing digital signals. Typically a controller has inputs connected to sensors on the device they control, which measure the feedback, its current state (for example the current position), and process this signal to provide an output to a hydraulical, electrical or other type of servomechanism control of the controlled device, with the aim of matching a control signal.
A good example is an elevator. The control signal is the button selects the floor the passenger wants to go. The controller of the elevator looks at which floor the elevator currently is (current position), at the floor selected (by the button) and by comparing them to each other derives a signal to control a servo (either hydraulic or electric) that makes the elevator move until the right floor is reached.
In the older days test controllers were usually analog, but with the rapid developments in digital signal processing and computer technology, test controllers are almost exclusively digital devices. This offers many advantages, because it allows the user to execute all kinds of additional operations on the digital signals, in addition to the standard PID controller. Digital test controllers offered by Moog, provide novel advantages for this type of system control.


Variable structure control

Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of a high-frequency "switching control". The state-feedback control law is "not" a continuous function of time; it "switches" from one smooth condition to another. So the "structure" of the control law "varies" based on the position of the state trajectory; the method switches from one smooth control law to another and possibly very fast speeds (e.g., for a countably infinite number of times in a finite time interval). VSC and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers.
The main mode of VSC operation is sliding mode control (SMC). The strengths of SMC include:
The weaknesses of SMC include:
However, the evolution of VSC is an active area of research.


2022–23 UEFA Europa Conference League qualifying phase and play-off round (Main Path)

This page summarises the Main Path matches of the 2022–23 UEFA Europa Conference League qualifying phase and play-off round.
Times are CEST , as listed by UEFA (local times, if different, are in parentheses).
First qualifying round.
Summary.

Matches.
"Ħamrun Spartans won 4–2 on aggregate."
"Lechia Gdańsk won 6–2 on aggregate."
"Drita won 3–1 on aggregate."
"4–4 on aggregate. Paide Linnameeskond won 6–5 on penalties."
"Milsami Orhei won 2–0 on aggregate."
"Laçi won 1–0 on aggregate."
"Liepāja won 3–2 on aggregate."
"Mura won 4–2 on aggregate."
"KuPS won 2–0 on aggregate."
"Ružomberok won 2–0 on aggregate."
"Budućnost Podgorica won 4–2 on aggregate."
"Gżira United won 2–1 on aggregate."
"3–3 on aggregate. B36 Tórshavn won 4–3 on penalties."
"Olimpija Ljubljana won 3–2 on aggregate."
"St Joseph's won 1–0 on aggregate."
"Breiðablik won 5–1 on aggregate."
"DAC Dunajská Streda won 5–1 on aggregate."
"Víkingur won 3–1 on aggregate."
"2–2 on aggregate. Sligo Rovers won 4–3 on penalties."
"Tre Fiori won 4–1 on aggregate."
"Dinamo Minsk won 3–2 on aggregate."
"Tuzla City won 8–0 on aggregate."
"1–1 on aggregate. Saburtalo Tbilisi won 5–4 on penalties."
"Shkëndija won 4–2 on aggregate."
"Petrocub Hîncești won 1–0 on aggregate."
"Pogoń Szczecin won 4–2 on aggregate."
"2–2 on aggregate. Newtown won 4–2 on penalties."
"Crusaders won 4–3 on aggregate."
"SJK won 4–3 on aggregate."
"Riga won 4–0 on aggregate."
Second qualifying round.
Summary.

Matches.
"5–5 on aggregate. Gżira United won 3–1 on penalties."
"Aris won 7–2 on aggregate."
"APOEL won 2–0 on aggregate."
"Fehérvár won 5–3 on aggregate."
"İstanbul Başakşehir won 2–1 on aggregate."
"Neftçi Baku won 3–2 on aggregate."
"Ħamrun Spartans won 2–0 on aggregate."
"FCSB won 4–3 on aggregate."
"CSKA Sofia won 4–0 on aggregate."
"Hapoel Be'er Sheva won 3–1 on aggregate."
"Maccabi Tel Aviv won 3–0 on aggregate."
"Universitatea Craiova won 4–1 on aggregate."
"0–0 on aggregate. Paide Linnameeskond won 5–3 on penalties."
"Kisvárda won 2–0 on aggregate."
"Konyaspor won 5–0 on aggregate."
"3–3 on aggregate. Sepsi Sfântu Gheorghe won 4–2 on penalties."
"Kyzylzhar won 3–2 on aggregate."
"Young Boys won 4–0 on aggregate."
"Rapid Wien won 2–1 on aggregate."
"Lillestrøm won 6–2 on aggregate."
"Breiðablik won 3–2 on aggregate."
"1–1 on aggregate. St Patrick's Athletic won 6–5 on penalties."
"Slavia Prague won 11–0 on aggregate."
"Spartak Trnava won 6–2 on aggregate."
"Viborg won 2–0 on aggregate."
"DAC Dunajská Streda won 4–0 on aggregate."
"Brøndby won 5–1 on aggregate."
"AZ won 5–0 on aggregate."
"Sligo Rovers won 3–0 on aggregate."
"Molde won 6–2 on aggregate."
"Vaduz won 2–1 on aggregate."
"B36 Tórshavn won 1–0 on aggregate."
"Riga won 5–1 on aggregate."
"Basel won 3–1 on aggregate."
"Antwerp won 2–0 on aggregate."
"Petrocub Hîncești won 4–1 on aggregate."
"Čukarički won 8–1 on aggregate."
"Levski Sofia won 3–1 on aggregate."
"Vitória de Guimarães won 3–0 on aggregate."
"Djurgårdens IF won 4–1 on aggregate."
"AIK won 4–3 on aggregate."
"Shkëndija won 5–2 on aggregate."
"Raków Częstochowa won 6–0 on aggregate."
"KuPS won 6–3 on aggregate."
"Viking won 2–1 on aggregate."
Third qualifying round.
Summary.

Matches.
"Raków Częstochowa won 3–0 on aggregate."
"2–2 on aggregate. AIK won 3–2 on penalties."
"Viking won 5–2 on aggregate."
"İstanbul Başakşehir won 6–1 on aggregate."
"Young Boys won 5–0 on aggregate."
"Anderlecht won 5–0 on aggregate."
"Viborg won 5–1 on aggregate."
"Hajduk Split won 3–2 on aggregate."
"2–2 on aggregate. Basel won 3–1 on penalties."
"Antwerp won 5–1 on aggregate."
"CSKA Sofia won 2–1 on aggregate."
"AZ won 7–1 on aggregate."
"APOEL won 1–0 on aggregate."
"FCSB won 2–0 on aggregate."
"Gil Vicente won 5–1 on aggregate."
"Wolfsberger AC won 4–0 on aggregate."
"Maccabi Tel Aviv won 3–2 on aggregate."
"Molde won 4–2 on aggregate."
"Rapid Wien won 3–2 on aggregate."
"Hapoel Be'er Sheva won 5–1 on aggregate."
"2–2 on aggregate. Ħamrun Spartans won 4–1 on penalties."
"Twente won 7–2 on aggregate."
"Universitatea Craiova won 3–1 on aggregate."
"Vaduz won 5–3 on aggregate."
"Djurgårdens IF won 6–2 on aggregate."
"Fehérvár won 7–1 on aggregate."
"Slavia Prague won 3–1 on aggregate."
Play-off round.
Summary.

Matches.
"Basel won 2–1 on aggregate."
"Vaduz won 2–1 on aggregate."
"Slavia Prague won 3–2 on aggregate."
"Djurgårdens IF won 5–3 on aggregate."
"Nice won 2–1 on aggregate."
"2–2 on aggregate. Hapoel Be'er Sheva won 4–3 on penalties."
"İstanbul Başakşehir won 4–2 on aggregate."
"FCSB won 4–3 on aggregate."
"Partizan won 7–4 on aggregate."
"Fiorentina won 2–1 on aggregate."
"Villarreal won 6–2 on aggregate."
"1. FC Köln won 4–2 on aggregate."
"West Ham United won 6–1 on aggregate."
"1–1 on aggregate. Anderlecht won 3–1 on penalties."
"Slovácko won 4–0 on aggregate."
"Molde won 4–1 on aggregate."
"AZ won 6–1 on aggregate."


Nonlinear conjugate gradient method

In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function formula_1
the minimum of formula_3 is obtained when the gradient is 0:
Whereas linear conjugate gradient seeks a solution to the linear equation
formula_5, the nonlinear conjugate gradient method is generally
used to find the local minimum of a nonlinear function
using its gradient formula_6 alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at the minimum and the second derivative is non-singular there.
Given a function formula_1 of formula_8 variables to minimize, its gradient formula_6 indicates the direction of maximum increase.
One simply starts in the opposite (steepest descent) direction:
with an adjustable step length formula_11 and performs a line search in this direction until it reaches the minimum of formula_12:
After this first iteration in the steepest direction formula_15, the following steps constitute one iteration of moving along a subsequent conjugate direction formula_16, where formula_17:
With a pure quadratic function the minimum is reached within "N" iterations (excepting roundoff error), but a non-quadratic function will make slower progress. Subsequent search directions lose conjugacy requiring the search direction to be reset to the steepest descent direction at least every "N" iterations, or sooner if progress stops. However, resetting every iteration turns the method into steepest descent. The algorithm stops when it finds the minimum, determined when no progress is made after a direction reset (i.e. in the steepest descent direction), or when some tolerance criterion is reached.
Within a linear approximation, the parameters formula_11 and formula_24 are the same as in the
linear conjugate gradient method but have been obtained with line searches.
The conjugate gradient method can follow narrow (ill-conditioned) valleys, where the steepest descent method slows down and follows a criss-cross pattern.
Four of the best known formulas for formula_19 are named after their developers:
These formulas are equivalent for a quadratic function, but for nonlinear optimization the preferred formula is a matter of heuristics or taste. A popular choice is formula_30, which provides a direction reset automatically.
Algorithms based on Newton's method potentially converge much faster. There, both step direction and length are computed from the gradient as the solution of a linear system of equations, with the coefficient matrix being the exact Hessian matrix (for Newton's method proper) or an estimate thereof (in the quasi-Newton methods, where the observed change in the gradient during the iterations is used to update the Hessian estimate). For high-dimensional problems, the exact computation of the Hessian is usually prohibitively expensive, and even its storage can be problematic, requiring formula_31 memory (but see the limited-memory L-BFGS quasi-Newton method).
The conjugate gradient method can also be derived using optimal control theory. In this accelerated optimization theory, the conjugate gradient method falls out as a nonlinear optimal feedback controller,
formula_32for the double integrator system,
formula_33
The quantities formula_34 and formula_35 are variable feedback gains.


Feature-oriented scanning

Feature-oriented scanning (FOS) is a method of precision measurement of surface topography with a scanning probe microscope in which surface features (objects) are used as reference points for microscope probe attachment. With FOS method, by passing from one surface feature to another located nearby, the relative distance between the features and the feature neighborhood topographies are measured. This approach allows to scan an intended area of a surface by parts and then reconstruct the whole image from the obtained fragments. Beside the mentioned, it is acceptable to use another name for the method – object-oriented scanning (OOS).
Topography.
Any topography element that looks like a hill or a pit in wide sense may be taken as a surface feature. Examples of surface features (objects) are: atoms, interstices, molecules, grains, nanoparticles, clusters, crystallites, quantum dots, nanoislets, pillars, pores, short nanowires, short nanorods, short nanotubes, viruses, bacteria, organelles, cells, etc.
FOS is designed for high-precision measurement of surface topography (see Fig.) as well as other surface properties and characteristics. Moreover, in comparison with the conventional scanning, FOS allows obtaining a higher spatial resolution. Thanks to a number of techniques embedded in FOS, the distortions caused by thermal drifts and creeps are practically eliminated.
Applications.
FOS has the following fields of application: surface metrology, precise probe positioning, automatic surface characterization, automatic surface modification/stimulation, automatic manipulation of nanoobjects, nanotechnological processes of “bottom-up” assembly, coordinated control of analytical and technological probes in multiprobe instruments, control of atomic/molecular assemblers, control of probe nanolithographs, etc.
References.
1. (Russian translation is available).
2. (Russian translation is available).
3.
4. (in Russian).
5.
6.
7.
8.
9.
10.
11.
12.


Classical control theory

Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback, using the Laplace transform as a basic tool to model such systems.
The usual objective of control theory is to control a system, often called the "plant", so its output follows a desired control signal, called the "reference", which may be a fixed or changing value. To do this a "controller" is designed, which monitors the output and compares it with the reference. The difference between actual and desired output, called the "error" signal, is applied as feedback to the input of the system, to bring the actual output closer to the reference.
Classical control theory deals with linear time-invariant (LTI) single-input single-output (SISO) systems. The Laplace transform of the input and output signal of such systems can be calculated. The transfer function relates the Laplace transform of the input and the output.
Feedback.
To overcome the limitations of the open-loop controller, classical control theory introduces feedback. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop.
Closed-loop controllers have the following advantages over open-loop controllers:
In some systems, closed-loop and open-loop control are used simultaneously. In such systems, the open-loop control is termed feedforward and serves to further improve reference tracking performance.
A common closed-loop controller architecture is the PID controller.
Classical vs modern.
A Physical system can be modeled in the "time domain", where the response of a given system is a function of the various inputs, the previous system values, and time. As time progresses, the state of the system and its response change. However, time-domain models for systems are frequently modeled using high-order differential equations which can become impossibly difficult for humans to solve and some of which can even become impossible for modern computer systems to solve efficiently.
To counteract this problem, classical control theory uses the Laplace transform to change an Ordinary Differential Equation (ODE) in the time domain into a regular algebraic polynomial in the frequency domain. Once a given system has been converted into the frequency domain it can be manipulated with greater ease.
Modern control theory, instead of changing domains to avoid the complexities of time-domain ODE mathematics, converts the differential equations into a system of lower-order time domain equations called state equations, which can then be manipulated using techniques from linear algebra.
Laplace transform.
Classical control theory uses the Laplace transform to model the systems and signals. The Laplace transform is a frequency-domain approach for continuous time signals irrespective of whether the system is stable or unstable. The Laplace transform of a function , defined for all real numbers , is the function , which is a unilateral transform defined by
where "s" is a complex number frequency parameter
Closed-loop transfer function.
A common feedback control architecture is the servo loop, in which the output of the system "y(t)" is measured using a sensor "F" and subtracted from the reference value "r(t)" to form the servo error "e". The controller "C" then uses the servo error "e" to adjust the input "u" to the plant (system being controlled) "P" in order to drive the output of the plant toward the reference. This is shown in the block diagram below. This kind of controller is a closed-loop controller or feedback controller.
This is called a single-input-single-output ("SISO") control system; "MIMO" (i.e., Multi-Input-Multi-Output) systems, with more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).
If we assume the controller "C", the plant "P", and the sensor "F" are linear and time-invariant (i.e., elements of their transfer function "C(s)", "P(s)", and "F(s)" do not depend on time), the systems above can be analysed using the Laplace transform on the variables. This gives the following relations:
Solving for "Y"("s") in terms of "R"("s") gives
The expression formula_7 is referred to as the "closed-loop transfer function" of the system. The numerator is the forward (open-loop) gain from formula_8 to formula_9, and the denominator is one plus the gain in going around the feedback loop, the so-called loop gain. If formula_10, i.e., it has a large norm with each value of "s", and if formula_11, then formula_12 is approximately equal to formula_13 and the output closely tracks the reference input.
formula_14PID controller.
The PID controller is probably the most-used (alongside much cruder Bang-bang control) feedback control design. "PID" is an initialism for "Proportional-Integral-Derivative", referring to the three terms operating on the error signal to produce a control signal. If is the control signal sent to the system, formula_15 is the measured output and formula_16 is the desired output, and tracking error formula_17, a PID controller has the general form
The desired closed loop dynamics is obtained by adjusting the three parameters formula_19, formula_20 and formula_21, often iteratively by "tuning" and without specific knowledge of a plant model. Stability can often be ensured using only the proportional term. The integral term permits the rejection of a step disturbance (often a striking specification in process control). The derivative term is used to provide damping or shaping of the response. PID controllers are the most well established class of control systems: however, they cannot be used in several more complicated cases, especially if multiple-input multiple-output systems (MIMO) systems are considered.
Applying Laplace transformation results in the transformed PID controller equation
with the PID controller transfer function
There exists a nice example of the closed-loop system discussed above. If we take
PID controller transfer function in series form
1st order filter in feedback loop
linear actuator with filtered input
and insert all this into expression for closed-loop transfer function formula_29, then tuning is very easy: simply put
and get formula_31 identically.
For practical PID controllers, a pure differentiator is neither physically realisable nor desirable due to amplification of noise and resonant modes in the system. Therefore, a phase-lead compensator type approach is used instead, or a differentiator with low-pass roll-off.
Tools.
Classical control theory uses an array of tools to analyze systems and design controllers for such systems. Tools include the root locus, the Nyquist stability criterion, the Bode plot, the gain margin and phase margin. More advanced tools include Bode integrals to assess performance limitations and trade-offs, and describing functions to analyze nonlinearities in the frequency domain.


EICASLAB

EICASLAB is a software suite providing a laboratory for automatic control design and time-series forecasting developed as final output of the European ACODUASIS Project IPS-2001-42068 funded by the European Community within the Innovation Programme. The Project - during its lifetime - aimed at delivering in the robotic field the scientific breakthrough of a new methodology for the automatic control design.
To facilitate such a knowledge transfer, EICASLAB was equipped with an “automated algorithm and code generation” software engine, that allows to obtain a control algorithm algorithm even without a deep knowledge of the theory and the methodology that are otherwise normally required with traditional control design methodologies.
EICASLAB has been and is actually adopted in other European Research Projects dealing with robotics (ARFLEX IST-NMP2-016880 and PISA Project NMP2-CT-2006-026697) and automotive (HI-CEPS Project TIP5-CT-2006-031373 and ERSEC Project FP7 247955). EICASLAB is used in European industries, research institutes and academia to design control systems and time series forecasting documented in the scientific and technical literature.
EICASLAB includes tools for modelling plants, designing and testing embedded control systems, assisting the phases of the design process of the control strategy, from system concept to generation of the control software code for the final target.
Software organisation.
EICASLAB is a software suite composed by a main program, called MASTER, able to assist and manage all the control design steps by means a set of tools, respectively:
Features to support to control design phases.
Support to system concept.
EICASLAB includes the following features to support the system concept:
Hardware architectures including multi-processors and software architectures including multi-level hierarchical control are considered. The control software is subdivided into functions allocated by the designer to the different processors. Each control function has its own sampling frequency and a time window for its execution, which are scheduled by the designer by means of the EICASLAB scheduler.
Data can be exchanged among the control functions allocated to the same processor and among the different processors belonging to the plant control system. The delay time in the data transmission is considered.
The final “application software” generated in C is subdivided into files each one related to a specific processor.
Support to system simulation.
EICASLAB includes specific working areas for developing, optimizing and testing algorithms and software related to the “plant controller”, including both the “automatic control” and the “trajectory generation” and the "disturbances" acting on the plant. To perform such a task three different working areas are available as follows.
Support to control algorithm design.
EICASLAB includes the following tools and features to support the control algorithm design:
The Automatic Algorithm Generation tool, starting from the “plant simplified model” and from the "control required performance" generates the control algorithm. On the basis of the plant design data, the applied control design methodology allows design of controllers with guaranteed performance without requiring any tuning in field in spite of the unavoidable uncertainty which always exists between any mathematical model built on the basis of plant design data and the plant actual performance (for fundamentals on control in presence of uncertainty see ).
The designer can choose among three control basic schemes and for each one he has the option of selecting control algorithms at different level of complexity.
In synthesis, the automatically generated control is performed by the resultant of three actions:
The plant's state observer task may be extended to estimate and predict the disturbance acting on the plant. The plant disturbance prediction and compensation is an original control feature, which allows significant reduction of control error.
Model Parameter Identification is a tool which allows the identification of the most appropriate values of the simplified model parameters from recorded experimental data or simulated trials performed by using the “plant fine model”. The parameter's "true" value does not exist: the model is an approximated description of the plant and then, the parameter's "best" value depends on the cost function adopted to evaluate the difference between model and plant. The identification method estimates the best values of the simplified model parameters from the point of view of the closed loop control design.
Control Parameter Optimization is a tool which performs control parameter tuning in simulated environment. The optimization is performed numerically over a predefined simulated trial, that is for a given mission (host command sequence and disturbance acting on the plant and any other potential event related to the plant performance) and for a given functional cost associated to the plant control performance.
Support to code generation for the final target.
The EICASLAB Automatic Code Generation tool provides the ANSI C source code related to the control algorithm developed.
The final result of the designer work is the “application software” in ANSI C, debugged and tested, ready to be compiled and linked in the plant control processors. The “application software” includes the software related to the “automatic control” and the “trajectory generation” functions. The simulated control functions are strictly the same one that the designer can transfer in field in the actual plant controller.
Support to control tuning.
EICASLAB includes the following tools to support the control tuning:
Slow Motion View is a tool to be used in the phase of setting up of the plant control, providing a variable by variable analysis of the control software performance during experimental trials performed by means of the actual plant.
The plant input and output and the host commands sent to the controller are recorded during experimental trials and then they can be processed by EICASLAB as follows. The recorded plant input and output variables are used in the Plant Area inside of the input and output variables obtained by the plant simulation. The recorded host commands are used in the Control Mission area inside of the host command generated by the Control Mission function.
Then, when a simulated trial is performed, the control function receives the recorded outputs of the actual plant and the related recorded host commands inside of the simulated ones. Because the control function running in the EICASLAB is strictly the same one, which is running in the actual plant controller, then, the commands resulting from the simulated control function and sent from the simulated control to the simulated plant should be strictly the same of the recorded plant inputs (unless there are numerical errors depending on the differences between the processor where the EICASLAB is running and the one used in the actual plant controller, but the experience has shown that the effects of such differences are negligible).
Then, the recorded experimental trial performed by the actual plant controller is completely repeated in the EICASLAB, with the difference that now the process can be performed in slow-motion and, if useful, step by step by using a debugger program.
Automatic Code Generation tool can be used to insert the controller code in a Linux Real-time operating system (RTOS) (in two available versions, namely, Linux RTAI and Linux RT with kernel preemption), in order to test the control algorithm in the PC environment instead of the final target hardware, performing Rapid Control Prototyping (RCP) tests. EICASLAB RCP includes a real-time scheduler based on multithreading programming techniques and able to run on a multi-core processor.
Automatic Code Generation tool can be used to insert the controller code in the final Hardware Target.
Once performed such operation, Hardware In the Loop (HIL) tests may be performed, consisting in piloting – instead of the actual plant - the plant simulated in EICASLAB and running on your PC, suitable configured and connected through the necessary hardware interfaces with the final Hardware Target.


Indexing (motion)

Indexing in reference to motion is moving (or being moved) into a new position or location quickly and easily but also precisely. When indexing a machine part, its new location is known to within a few hundredths of a millimeter (thousandths of an inch), or often even to within a few thousandths of a millimeter (ten-thousandths of an inch), despite the fact that no elaborate measuring or layout was needed to establish that location. In reference to multi-edge cutting inserts, indexing is the process of exposing a new cutting edge for use. Indexing is a necessary kind of motion in many areas of mechanical engineering and machining. An object that indexes, or can be indexed, is said to be indexable.
Usually when the word "indexing" is used, it refers specifically to rotation. That is, indexing is most often the quick and easy but precise rotation of a machine part through a certain known number of degrees. For example, "Machinery's Handbook", 25th edition, in its section on milling machine indexing, says, "Positioning a workpiece at a precise angle or interval of rotation for a machining operation is called indexing." In addition to that most classic sense of the word, the swapping of one part for another, or other controlled movements, are also sometimes referred to as "indexing", even if rotation is not the focus.
Examples from everyday life.
There are various examples of indexing that laypersons (non-engineers and non-machinists) can find in everyday life. These motions are not always called by the name "indexing", but the idea is essentially similar:
Manufacturing applications.
Indexing is vital in manufacturing, especially mass production, where a well-defined cycle of motions must be repeated quickly and easily—but precisely—for each interchangeable part that is made. Without indexing capability, all manufacturing would have to be done on a craft basis, and interchangeable parts would have very high unit cost because of the time and skill needed to produce each unit. In fact, the evolution of modern technologies depended on the shift in methods from crafts (in which toolpath is controlled via operator skill) to indexing-capable toolpath control. A prime example of this theme was the development of the turret lathe, whose turret indexes tool positions, one after another, to allow successive tools to move into place, take precisely placed cuts, then make way for the next tool.
How indexing is achieved in manufacturing.
Indexing capability is provided in two fundamental ways: with or without Information technology (IT).
Non-IT-assisted physical guidance.
Non-IT-assisted physical guidance was the first means of providing indexing capability, via purely mechanical means. It allowed the Industrial Revolution to progress into the Machine Age. It is achieved by jigs, fixtures, and machine tool parts and accessories, which control toolpath by the very nature of their shape, physically limiting the path for motion. Some archetypal examples, developed to perfection before the advent of the IT era, are drill jigs, the turrets on manual turret lathes, indexing heads for manual milling machines, rotary tables, and various indexing fixtures and blocks that are simpler and less expensive than indexing heads, and serve quite well for most indexing needs in small shops. Although indexing heads of the pre-CNC era are now mostly obsolete in commercial manufacturing, the principle of purely mechanical indexing is still a vital part of current technology, in concert with IT, even as it has been extended to newer uses, such as the indexing of CNC milling machine toolholders or of indexable cutter inserts, whose precisely controlled size and shape allows them to be rotated or replaced quickly and easily without changing overall tool geometry.
IT-assisted physical guidance.
IT-assisted physical guidance (for example, via NC, CNC, or robotics) has been developed since the World War II era and uses electromechanical and electrohydraulic servomechanisms to translate digital information into position control. These systems also ultimately physically limit the path for motion, as jigs and other purely mechanical means do; but they do it not simply through their own shape, but rather using changeable information.


Behavioral modeling

The behavioral approach to systems theory and control theory was initiated in the late-1970s by J. C. Willems as a result of resolving inconsistencies present in classical approaches based on state-space, transfer function, and convolution representations. This approach is also motivated by the aim of obtaining a general framework for system analysis and control that respects the underlying physics.
The main object in the behavioral setting is the behavior – the set of all signals compatible with the system. An important feature of the behavioral approach is that it does not distinguish a priority between input and output variables. Apart from putting system theory and control on a rigorous basis, the behavioral approach unified the existing approaches and brought new results on controllability for nD systems, control via interconnection, and system identification.
Dynamical system as a set of signals.
In the behavioral setting, a dynamical system is a triple
where
formula_8 means that formula_9 is a trajectory of the system, while formula_10 means that the laws of the system forbid the trajectory formula_9 to happen. Before the phenomenon is modeled, every signal in formula_5 is deemed possible, while after modeling, only the outcomes in formula_13 remain as possibilities.
Special cases:
Linear time-invariant differential systems.
System properties are defined in terms of the behavior. The system formula_1 is said to be
where formula_24 denotes the formula_25-shift, defined by
In these definitions linearity articulates the superposition law, while time-invariance articulates that the time-shift of a legal trajectory is in its turn a legal trajectory.
A "linear time-invariant differential system" is a dynamical system formula_27 whose behavior formula_13 is the solution set of a system of constant coefficient linear ordinary differential equations formula_29, where formula_30 is a matrix of polynomials with real coefficients. The coefficients of formula_30 are the parameters of the model. In order to define the corresponding behavior, we need to specify when we consider a signal formula_32 to be a solution of formula_29. For ease of exposition, often infinite differentiable solutions are considered. There are other possibilities, as taking distributional solutions, or solutions in formula_34, and with the ordinary differential equations interpreted in the sense of distributions. The behavior defined is
This particular way of representing the system is called "kernel representation" of the corresponding dynamical system. There are many other useful representations of the same behavior, including transfer function, state space, and convolution.
For accessible sources regarding the behavioral approach, see
Observability of latent variables.
A key question of the behavioral approach is whether a quantity w1 can be deduced given an observed quantity w2 and a model. If w1 can be deduced given w2 and the model, w2 is said to be observable. In terms of mathematical modeling, the to-be-deduced quantity or variable is often referred to as the latent variable and the observed variable is the manifest variable. Such a system is then called an observable (latent variable) system.


Glossary of robotics

Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots. Robotics is related to the sciences of electronics, engineering, mechanics, and software.
The following is a list of common definitions related to the Robotics field.
External links.
Online Robotics glossary repositories:


Vehicle fire suppression system

A vehicle fire suppression system is a pre-engineered fire suppression system safety accessory permanently mounted on any type of vehicle. These systems are especially prevalent in the mobile heavy equipment segment and are designed to protect equipment assets from fire damage and related losses. Vehicle fire suppression systems have become a vital safety feature to several industries and are most commonly used in the mining, forestry, landfill, and mass transit industries.
Parts of a Typical System.
A typical vehicle fire suppression system has five key components:
To mitigate a fire as soon as it happens, fire-detecting linear wire or sensors are strategically placed around the machine. When the high heat of a fire penetrates the linear wire or is detected by the sensors, a signal is sent to the control panel in the vehicle cab.
The control panel alarms and alerts the driver to quickly evacuate the machine. At the same time, the panel automatically initiates the actuator, which discharges the fire-fighting agent inside the onboard tanks and sends it through a distribution network composed of stainless steel tubing and/or hydraulic hosing. An actuator can also activate the system when pressed manually by the operator.
At the end of the distribution network, the agent is disbursed into the equipment’s protected areas via nozzles aimed at the machine's high-hazard components, like turbochargers, starters, fuel filters, batteries, alternators, and transmissions to extinguish the fire quickly and efficiently.


Formability

Formability is the ability of a given metal workpiece to undergo plastic deformation without being damaged. The plastic deformation capacity of metallic materials, however, is limited to a certain extent, at which point, the material could experience tearing or fracture (breakage).
Processes affected by the formability of a material include: rolling, extrusion, forging, rollforming, stamping, and hydroforming.
Fracture strain.
A general parameter that indicates the formability and ductility of a material is the fracture strain which is determined by a uniaxial tensile test (see also fracture toughness). The strain identified by this test is defined by elongation with respect to a reference length. For example, a length of is used for the standardized uniaxial test of flat specimens, pursuant to EN 10002. It is important to note that deformation is homogeneous up to uniform elongation. Strain subsequently localizes until fracture occurs. Fracture strain is not an engineering strain since distribution of the deformation is inhomogeneous within the reference length. Fracture strain is nevertheless a rough indicator of the formability of a material. Typical values of the fracture strain are: 7% for ultra-high-strength material, and over 50% for mild-strength steel.
Forming limits for sheet forming.
One main failure mode is caused by tearing of the material. This is typical for sheet-forming applications.
A neck may appear at a certain forming stage. This is an indication of localized plastic deformation. Whereas more or less homogeneous deformation takes place in and around the subsequent neck location in the early stable deformation stage, almost all deformation is concentrated in the neck zone during the quasi-stable and unstable deformation phase. This leads to material failure manifested by tearing. Forming-limit curves depict the extreme, but still possible, deformation which a sheet material may undergo during any stage of the stamping process. These limits depend on the deformation mode and the ratio of the surface strains. The major surface strain has a minimum value when plane strain deformation occurs, which means that the corresponding minor surface strain is zero. Forming limits are a specific material property. Typical plane strain values range from 10% for high-strength grades and 50% or above for mild-strength materials and those with very good formability.
Forming limit diagrams are often used to graphically or mathematically represent formability. It is recognized by many authors that the nature of fracture and therefore the Forming limit diagrams are intrinsically non-deterministic since large variations might be observed even within a single experimental campaign.
Deep drawability.
A classic form of sheetforming is deep drawing, which is done by drawing a sheet by means of a punch tool pressing on the inner region of the sheet, whereas the side material held by a blankholder can be drawn toward the center. It has been observed that materials with outstanding deep drawability behave anisotropically (see: anisotropy). Plastic deformation in the surface is much more pronounced than in the thickness. The lankford coefficient (r) is a specific material property indicating the ratio between width deformation and thickness deformation in the uniaxial tensile test. Materials with very good deep drawability have an "r" value of 2 or below. The positive aspect of formability with respect to the forming limit curve (forming limit diagram) is seen in the deformation paths of the material that are concentrated in the extreme left of the diagram, where the forming limits become very large.
Ductility.
Another failure mode that may occur without any tearing is ductile fracture after plastic deformation (ductility). This may occur as a result of bending or shear deformation (inplane or through the thickness). The failure mechanism may be due to void nucleation and expansion on a microscopic level. Microcracks and subsequent macrocracks may appear when deformation of the material between the voids has exceeded the limit. Extensive research has focused in recent years on understanding and modeling ductile fracture. The approach has been to identify ductile forming limits using various small-scale tests that show different strain ratios or stress triaxialities. An effective measure of this type of forming limit is the minimum radius in roll-forming applications (half the sheet thickness for materials with good and three times the sheet thickness for materials with low formability).
Use of formability parameters.
Knowledge of the material formability is very important to the layout and design of any industrial forming process. Simulations using the finite-element method and use of formability criteria such as the forming limit curve (forming limit diagram) enhance and, in some cases, are indispensable to certain tool design processes (also see: Sheet metal forming simulation and Sheet metal forming analysis).
IDDRG.
One major objective of the International Deep Drawing Research Group (IDDRG, from 1957) is the investigation, exchange and dissemination of knowledge and experience about the formability of sheet materials.


Micromax IN Note 1

The Micromax In Note 1 is an Android smartphone developed by the Indian Smartphone manufacturer Micromax Informatics. Announced on November 3, 2020, and released on November 24, 2020, the In Note 1 marks the re-entry of the company into the Indian smartphone market.
Specifications.
Hardware.
The In Note 1 is powered by a Mediatek Helio G85 SoC including an octa-core 2.0 GHz CPU, an ARM G52 MC2 GPU. The internal storage is of 64 GB or 128 GB .
The In Note 1 features a 6.67-inch IPS LCD punch hole display with a 1080× 2400 FHD+ pixel display resolution and a pixel density of  395 ppi. The rear camera has a quad camera setup of 48MP+5MP+2MP+2MP sensors. Camera modes include night mode, HDR, Panorama, AI Scene Detection, Beauty, Pro, GIF, Time lapse, Slow-Motion and Portrait mode. The front camera features 16 MP and f/2.0 aperture.
Software.
The In Note 1 is originally shipped with Android 10 and runs Stock Android. Micromax officially promised for software upgrade but nothing is happening from past 1.5 year except a security patch provided Recently.
Current security patch - 05/07/22
It's seems to be fake promise of Android Update done by the co-founder of Micromax Rahul Sharma.


Parallel parking problem

The parallel parking problem is a motion planning problem in control theory and mechanics to determine the path a car must take to parallel park into a parking space. The front wheels of a car are permitted to turn, but the rear wheels must stay aligned. When a car is initially adjacent to a parking space, to move into the space it would need to move in a direction perpendicular to the allowed path of motion of the rear wheels. The admissible motions of the car in its configuration space are an example of a nonholonomic system.


Comparison of structured storage software

Structured storage is computer storage for structured data, often in the form of a distributed database. Computer software formally known as structured storage systems include Apache Cassandra, Google's Bigtable and Apache HBase.
Comparison.
The following is a comparison of notable structured storage systems.


Hyperparameter optimization

In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process. By contrast, the values of other parameters (typically node weights) are learned.
The same kind of machine learning model can require different constraints, weights or learning rates to generalize different data patterns. These measures are called hyperparameters, and have to be tuned so that the model can optimally solve the machine learning problem. Hyperparameter optimization finds a tuple of hyperparameters that yields an optimal model which minimizes a predefined loss function on given independent data. The objective function takes a tuple of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it.
Approaches.
Grid search.
The traditional way of performing hyperparameter optimization has been "grid search", or a "parameter sweep", which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set
or evaluation on a hold-out validation set.
Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search.
For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant "C" and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say
Grid search then trains an SVM with each pair ("C", γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure.
Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other.
Random search.
Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods.
Bayesian optimization.
Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run.
Gradient-based optimization.
For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression.
A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory.
In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights.
Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search.
Evolutionary optimization.
Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution:
Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks.
Population-based.
Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures.
PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training.
Early stopping-based.
A class of early stopping-based hyperparameter optimization algorithms is purpose built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly.
Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate and prune low-performing models. Hyperband is a higher level early stopping-based algorithm that invokes SHA or ASHA multiple times with varying levels of pruning aggressiveness, in order to be more widely applicable and with fewer required inputs.
Others.
RBF and spectral approaches have also been developed.
Issues with hyperparameter optimization.
When hyperparameter optimization is done, the set of hyperparameters are often fitted on a training set and selected based on the generalization performance, or score, of a validation set. However, this procedure is at risk of overfitting the hyperparameters to the validation set. Therefore, the generalization performance score of the validation set (which can be several sets in the case of a cross-validation procedure) cannot be used to simultaneously estimate the generalization performance of the final model. In order to do so, the generalization performance has to be evaluated on a set independent (which has no intersection) of the set (or sets) used for the optimization of the hyperparameters, otherwise the performance might give a value which is too optimistic (too large). This can be done on a second test set, or through an outer cross-validation procedure called nested cross-validation, which allows an unbiased estimation of the generalization performance of the model, taking into account the bias due to the hyperparameter optimization.


Laser cutting

Laser cutting is a technology that uses a laser to vaporize materials, resulting in a cut edge. While typically used for industrial manufacturing applications, it is now used by schools, small businesses, architecture, and hobbyists. Laser cutting works by directing the output of a high-power laser most commonly through optics. The laser optics and CNC (computer numerical control) are used to direct the laser beam to the material. A commercial laser for cutting materials uses a motion control system to follow a CNC or G-code of the pattern to be cut onto the material. The focused laser beam is directed at the material, which then either melts, burns, vaporizes away, or is blown away by a jet of gas, leaving an edge with a high-quality surface finish.
History.
In 1965, the first production laser cutting machine was used to drill holes in diamond dies. This machine was made by the Western Electric Engineering Research Center. In 1967, the British pioneered laser-assisted oxygen jet cutting for metals. In the early 1970s, this technology was put into production to cut titanium for aerospace applications. At the same time, CO2 lasers were adapted to cut non-metals, such as textiles, because, at the time, CO2 lasers were not powerful enough to overcome the thermal conductivity of metals.
Process.
The laser beam is generally focused using a high-quality lens on the work zone. The quality of the beam has a direct impact on the focused spot size. The narrowest part of the focused beam is generally less than in diameter. Depending upon the material thickness, kerf widths as small as are possible. In order to be able to start cutting from somewhere other than the edge, a pierce is done before every cut. Piercing usually involves a high-power pulsed laser beam which slowly makes a hole in the material, taking around 5–15 seconds for stainless steel, for example.
The parallel rays of coherent light from the laser source often fall in the range between in diameter. This beam is normally focused and intensified by a lens or a mirror to a very small spot of about to create a very intense laser beam. In order to achieve the smoothest possible finish during contour cutting, the direction of the beam polarization must be rotated as it goes around the periphery of a contoured workpiece. For sheet metal cutting, the focal length is usually .
Advantages of laser cutting over mechanical cutting include easier work holding and reduced contamination of workpiece (since there is no cutting edge which can become contaminated by the material or contaminate the material). Precision may be better since the laser beam does not wear during the process. There is also a reduced chance of warping the material that is being cut, as laser systems have a small heat-affected zone. Some materials are also very difficult or impossible to cut by more traditional means.
Laser cutting for metals has the advantage over plasma cutting of being more precise and using less energy when cutting sheet metal; however, most industrial lasers cannot cut through the greater metal thickness that plasma can. Newer laser machines operating at higher power (6000 watts, as contrasted with early laser cutting machines' 1500-watt ratings) are approaching plasma machines in their ability to cut through thick materials, but the capital cost of such machines is much higher than that of plasma cutting machines capable of cutting thick materials like steel plate.
Types.
There are three main types of lasers used in laser cutting. The laser is suited for cutting, boring, and engraving. The neodymium (Nd) and neodymium yttrium-aluminium-garnet  lasers are identical in style and differ only in the application. Nd is used for boring and where high energy but low repetition are required. The Nd:YAG laser is used where very high power is needed and for boring and engraving. Both and Nd/Nd:YAG lasers can be used for welding.
 lasers are commonly "pumped" by passing a current through the gas mix (DC-excited) or using radio frequency energy (RF-excited). The RF method is newer and has become more popular. Since DC designs require electrodes inside the cavity, they can encounter electrode erosion and plating of electrode material on glassware and optics. Since RF resonators have external electrodes they are not prone to those problems.
 lasers are used for the industrial cutting of many materials including titanium, stainless steel, mild steel, aluminium, plastic, wood, engineered wood, wax, fabrics, and paper. YAG lasers are primarily used for cutting and scribing metals and ceramics.
In addition to the power source, the type of gas flow can affect performance as well. Common variants of lasers include fast axial flow, slow axial flow, transverse flow, and slab. In a fast axial flow resonator, the mixture of carbon dioxide, helium, and nitrogen is circulated at high velocity by a turbine or blower. Transverse flow lasers circulate the gas mix at a lower velocity, requiring a simpler blower. Slab or diffusion-cooled resonators have a static gas field that requires no pressurization or glassware, leading to savings on replacement turbines and glassware.
The laser generator and external optics (including the focus lens) require cooling. Depending on system size and configuration, waste heat may be transferred by a coolant or directly to air. Water is a commonly used coolant, usually circulated through a chiller or heat transfer system.
A "laser microjet" is a water-jet-guided laser in which a pulsed laser beam is coupled into a low-pressure water jet. This is used to perform laser cutting functions while using the water jet to guide the laser beam, much like an optical fiber, through total internal reflection. The advantages of this are that the water also removes debris and cools the material. Additional advantages over traditional "dry" laser cutting are high dicing speeds, parallel kerf, and omnidirectional cutting.
Fiber lasers are a type of solid-state laser that is rapidly growing within the metal cutting industry. Unlike CO2, Fiber technology utilizes a solid gain medium, as opposed to a gas or liquid. The “seed laser” produces the laser beam and is then amplified within a glass fiber. With a wavelength of only 1064 nanometers fiber lasers produce an extremely small spot size (up to 100 times smaller compared to the CO2) making it ideal for cutting reflective metal material. This is one of the main advantages of Fiber compared to CO2.
Fibre laser cutter benefits include:-
Methods.
There are many different methods of cutting using lasers, with different types used to cut different materials. Some of the methods are vaporization, melt and blow, melt blow and burn, thermal stress cracking, scribing, cold cutting, and burning stabilized laser cutting.
Vaporization cutting.
In vaporization cutting, the focused beam heats the surface of the material to a flashpoint and generates a keyhole. The keyhole leads to a sudden increase in absorptivity quickly deepening the hole. As the hole deepens and the material boils, vapor generated erodes the molten walls blowing ejection out and further enlarging the hole. Nonmelting materials such as wood, carbon, and thermoset plastics are usually cut by this method.
Melt and blow.
Melt and blow or fusion cutting uses high-pressure gas to blow molten material from the cutting area, greatly decreasing the power requirement. First, the material is heated to melting point then a gas jet blows the molten material out of the kerf avoiding the need to raise the temperature of the material any further. Materials cut with this process are usually metals.
Thermal stress cracking.
Brittle materials are particularly sensitive to thermal fracture, a feature exploited in thermal stress cracking. A beam is focused on the surface causing localized heating and thermal expansion. This results in a crack that can then be guided by moving the beam. The crack can be moved in order of m/s. It is usually used in the cutting of glass.
Stealth dicing of silicon wafers.
The separation of microelectronic chips as prepared in semiconductor device fabrication from silicon wafers may be performed by the so-called stealth dicing process, which operates with a pulsed , the wavelength of which (1064 nm) is well adapted to the electronic band gap of silicon (1.11 eV or 1117 nm).
Reactive cutting.
Reactive cutting is also called "burning stabilized laser gas cutting" and "flame cutting". Reactive cutting is like oxygen torch cutting but with a laser beam as the ignition source. Mostly used for cutting carbon steel in thicknesses over 1 mm. This process can be used to cut very thick steel plates with relatively little laser power.
Tolerances and surface finish.
Laser cutters have a positioning accuracy of 10 micrometers and repeatability of 5 micrometers.
Standard roughness Rz increases with the sheet thickness, but decreases with laser power and cutting speed. When cutting low carbon steel with laser power of 800 W, standard roughness Rz is 10 μm for sheet thickness of 1 mm, 20 μm for 3 mm, and 25 μm for 6 mm.
formula_1
Where: formula_2 steel sheet thickness in mm; formula_3 laser power in kW (some new laser cutters have laser power of 4 kW); formula_4 cutting speed in meters per minute.
This process is capable of holding quite close tolerances, often to within 0.001 inch (0.025 mm). Part geometry and the mechanical soundness of the machine have much to do with tolerance capabilities. The typical surface finish resulting from laser beam cutting may range from 125 to 250 micro-inches (0.003 mm to 0.006 mm).
Machine configurations.
There are generally three different configurations of industrial laser cutting machines: moving material, hybrid, and flying optics systems. These refer to the way that the laser beam is moved over the material to be cut or processed. For all of these, the axes of motion are typically designated X and Y axis. If the cutting head may be controlled, it is designated as the Z-axis.
Moving material lasers have a stationary cutting head and move the material under it. This method provides a constant distance from the laser generator to the workpiece and a single point from which to remove cutting effluent. It requires fewer optics but requires moving the workpiece. This style of machine tends to have the fewest beam delivery optics but also tends to be the slowest.
Hybrid lasers provide a table that moves in one axis (usually the X-axis) and moves the head along the shorter (Y) axis. This results in a more constant beam delivery path length than a flying optic machine and may permit a simpler beam delivery system. This can result in reduced power loss in the delivery system and more capacity per watt than flying optics machines.
Flying optics lasers feature a stationary table and a cutting head (with a laser beam) that moves over the workpiece in both of the horizontal dimensions. Flying optics cutters keep the workpiece stationary during processing and often do not require material clamping. The moving mass is constant, so dynamics are not affected by varying the size of the workpiece. Flying optics machines are the fastest type, which is advantageous when cutting thinner workpieces.
Flying optic machines must use some method to take into account the changing beam length from the near field (close to the resonator) cutting to the far field (far away from the resonator) cutting. Common methods for controlling this include collimation, adaptive optics, or the use of a constant beam length axis.
Five and six-axis machines also permit cutting formed workpieces. In addition, there are various methods of orienting the laser beam to a shaped workpiece, maintaining a proper focus distance and nozzle standoff, etc.
Pulsing.
Pulsed lasers which provide a high-power burst of energy for a short period are very effective in some laser cutting processes, particularly for piercing, or when very small holes or very low cutting speeds are required, since if a constant laser beam were used, the heat could reach the point of melting the whole piece being cut.
Most industrial lasers have the ability to pulse or cut CW (continuous wave) under NC (numerical control) program control.
Double pulse lasers use a series of pulse pairs to improve material removal rate and hole quality. Essentially, the first pulse removes material from the surface and the second prevents the ejecta from adhering to the side of the hole or cut.
Power consumption.
The main disadvantage of laser cutting is the high power consumption. Industrial laser efficiency may range from 5% to 45%. The power consumption and efficiency of any particular laser will vary depending on output power and operating parameters. This will depend on the type of laser and how well the laser is matched to the work at hand. The amount of laser cutting power required, known as "heat input", for a particular job depends on the material type, thickness, process (reactive/inert) used, and desired cutting rate.
Production and cutting rates.
The maximum cutting rate (production rate) is limited by a number of factors including laser power, material thickness, process type (reactive or inert), and material properties. Common industrial systems (≥1 kW) will cut carbon steel metal from in thickness. For many purposes, a laser can be up to thirty times faster than standard sawing.


Algorithmic mechanism design

Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system performance. Typical objectives studied include revenue maximization and social welfare maximization. Algorithmic mechanism design differs from classical economic mechanism design in several respects. It typically employs the analytic tools of theoretical computer science, such as worst case analysis and approximation ratios, in contrast to classical mechanism design in economics which often makes distributional assumptions about the agents. It also considers computational constraints to be of central importance: mechanisms that cannot be efficiently implemented in polynomial time are not considered to be viable solutions to a mechanism design problem. This often, for example, rules out the classic economic mechanism, the Vickrey–Clarke–Groves auction.
History.
Noam Nisan and Amir Ronen first coined "Algorithmic mechanism design" in a research paper published in 1999.


Variable rate application

In precision agriculture, variable rate application (VRA) refers to the application of a material, such that the rate of application is based on the precise location, or qualities of the area that the material is being applied to. This is different from uniform application, and can be used to save money (using less product), and lessen the environmental impact.
Variable rate application can be either map based or sensor based.
Applications of VRA.
In precision agriculture, VRA is known to be used in the following areas.
Seeding.
Planters and drills can be made into VRA sensors, by attaching a motor or gear box. With this, you can vary the rate of the seeds. The seeding rates can also be connected to match the application of agrochemicals.
Weed control.
For variable rate weed control you need both a task computer and a system to physically change the flow rate of the agrochemicals.
Fertilizer.
Crops do not always require a uniform application, as some areas will have different nutrient requirements due to their location (soil properties, sunlight). Variable rate fertilizer spreaders can be used to increase or decrease fertilizer application rate, using a global positioning system (GPS). They can also use "on-the-go" sensors, or a combination of the two.


Gear manufacturing

Gear manufacturing refers to the making of gears. Gears can be manufactured by a variety of processes, including casting, forging, extrusion, powder metallurgy, and blanking. As a general rule, however, machining is applied to achieve the final dimensions, shape and surface finish in the gear. The initial operations that produce a semifinishing part ready for gear machining as referred to as blanking operations; the starting product in gear machining is called a gear blank.
Selection of materials.
The gear material should have the following properties:
Gear manufacturing processes.
There are multiple ways in which gear blanks can be shaped through the cutting and finishing processes.
Gear forming.
In gear form cutting, the cutting edge of the cutting tool has a shape identical with the shape of the space between the gear teeth. Two machining operations, milling and broaching can be employed to form cut gear teeth.
Form milling.
In form milling, the cutter called a form cutter travels axially along the length of the gear tooth at the appropriate depth to produce the gear tooth. After each tooth is cut, the cutter is withdrawn, the gear blank is rotated, and the cutter proceeds to cut another tooth. The process continues until all teeth are cut
Broaching.
Broaching can also be used to produce gear teeth and is particularly applicable to internal teeth. The process is rapid and produces fine surface finish with high dimensional accuracy. However, because broaches are expensive and a separate broach is required for each size of gear, this method is suitable mainly for high-quality production.
Gear generation.
In gear generation, the tooth flanks are obtained as an outline of the subsequent positions of the cutter, which resembles in shape the mating gear in the gear pair. There are two machining processes employed shaping and milling. There are several modifications of these processes for different cutting tool used.
Gear hobbing.
Gear hobbing is a machining process in which gear teeth are progressively generated by a series of cuts with a helical cutting tool. All motions in hobbing are rotary, and the hob and gear blank rotate continuously as in two gears meshing until all teeth are cut.
Finishing operations.
As produced by any of the process described, the surface finish and dimensional accuracy may not
be accurate enough for certain applications. Several finishing operations are available, including the
conventional process of shaving, and a number of abrasive operations, including grinding, honing, and lapping.


Tellegen's theorem

Tellegen's theorem is one of the most powerful theorems in network theory. Most of the energy distribution theorems and extremum principles in network theory can be derived from it. It was published in 1952 by Bernard Tellegen. Fundamentally, Tellegen's theorem gives a simple relation between magnitudes that satisfy Kirchhoff's laws of electrical circuit theory.
The Tellegen theorem is applicable to a multitude of network systems. The basic assumptions for the systems are the conservation of flow of extensive quantities (Kirchhoff's current law, KCL) and the uniqueness of the potentials at the network nodes (Kirchhoff's voltage law, KVL). The Tellegen theorem provides a useful tool to analyze complex network systems including electrical circuits, biological and metabolic networks, pipeline transport networks, and chemical process networks.
The theorem.
Consider an arbitrary lumped network that has formula_1 branches and formula_2 nodes. In an electrical network, the branches are two-terminal components and the nodes are points of interconnection. Suppose that to each branch we assign arbitrarily a branch potential difference formula_3 and a branch current formula_4 for formula_5, and suppose that they are measured with respect to arbitrarily picked "associated" reference directions. If the branch potential differences formula_6 satisfy all the constraints imposed by KVL and if the branch currents formula_7 satisfy all the constraints imposed by KCL, then
Tellegen's theorem is extremely general; it is valid for any lumped network that contains any elements, "linear or nonlinear", "passive or active", "time-varying or time-invariant". The generality is extended when formula_3 and formula_4 are linear operations on the set of potential differences and on the set of branch currents (respectively) since linear operations don't affect KVL and KCL. For instance, the linear operation may be the average or the Laplace transform. More generally, operators that preserve KVL are called Kirchhoff voltage operators, operators that preserve KCL are called Kirchhoff current operators, and operators that preserve both are simply called Kirchhoff operators. These operators need not necessarily be linear for Tellegen's theorem to hold.
The set of currents can also be sampled at a different time from the set of potential differences since KVL and KCL are true at all instants of time. Another extension is when the set of potential differences formula_3 is from one network and the set of currents formula_4 is from an entirely different network, so long as the two networks have the same topology (same incidence matrix) Tellegen's theorem remains true. This extension of Tellegen's Theorem leads to many theorems relating to two-port networks.
Definitions.
We need to introduce a few necessary network definitions to provide a compact proof.
Incidence matrix:
The formula_13 matrix formula_14 is called node-to-branch incidence matrix for the matrix elements formula_15 being
A reference or datum node formula_17 is introduced to represent the environment and connected to all dynamic nodes and terminals. The formula_18 matrix formula_19, where the row that contains the elements formula_20 of the reference node formula_21 is eliminated, is called reduced incidence matrix.
The conservation laws (KCL) in vector-matrix form:
The uniqueness condition for the potentials (KVL) in vector-matrix form:
where formula_24 are the absolute potentials at the nodes to the reference node formula_21.
Proof.
Using KVL:
because formula_27 by KCL. So:
Applications.
Network analogs have been constructed for a wide variety of physical systems, and have proven extremely useful in analyzing their dynamic behavior. The classical application area for network theory and Tellegen's theorem is electrical circuit theory. It is mainly in use to design filters in signal processing applications.
A more recent application of Tellegen's theorem is in the area of chemical and biological processes. The assumptions for electrical circuits (Kirchhoff laws) are generalized for dynamic systems obeying the laws of irreversible thermodynamics. Topology and structure of reaction networks (reaction mechanisms, metabolic networks) can be analyzed using the Tellegen theorem.
Another application of Tellegen's theorem is to determine stability and optimality of complex process systems such as chemical plants or oil production systems. The Tellegen theorem can be formulated for process systems using process nodes, terminals, flow connections and allowing sinks and sources for production or destruction of extensive quantities.
A formulation for Tellegen's theorem of process systems:
where formula_30 are the production terms, formula_31 are the terminal connections, and formula_32 are the dynamic storage terms for the extensive variables.


ApertusVR

ApertusVR is an embeddable, open-source (MIT), framework-independent, platform-independent, network-topology-independent, distributed, augmented reality/virtual reality/mixed reality engine.
It is written in C++, with JavaScript and HTTP Rest API (in Node.js). ApertusVR creates a new abstraction layer over the hardware in order to integrate the virtual and augmented reality technologies into any developments or products.


Artstein's theorem

Artstein's theorem states that a nonlinear dynamical system in the control-affine form
formula_1
has a differentiable control-Lyapunov function if and only if it admits a regular stabilizing feedback "u"("x"), that is a locally Lipschitz function on Rn\{0}.
The original 1983 proof by Zvi Artstein proceeds by a nonconstructive argument. In 1989 Eduardo D. Sontag provided a constructive version of this theorem explicitly exhibiting the feedback.


Sprog (software)

Sprog is a graphical tool to build Perl programs by plugging parts (called "gears" in Sprog terminology) together. Given the available gears are mostly for reading and processing data, this program can be classified as an ETL (Extract-Transform-Load) tool.


LINDO

LINDO (Linear, Interactive, and Discrete Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization.
Lindo also creates "What'sBest!" which is an add-in for linear, integer and nonlinear optimization. First released for Lotus 1-2-3 and later also for Microsoft Excel.


Active valve lift system

The I-Active Valve Lift System (i stands for intelligence) or i-AVLS is a valvetrain technology implemented by Subaru in the 2.5L naturally aspirated engines SOHC to improve emissions, efficiency and performance. Note that AVLS is different from AVCS used on other Subaru engines. AVLS improves performance and efficiency by changing which camshaft is operating which of the two intake valves. The camshafts on all AVLS Subaru engines have specially designed lobes for intake valves. They feature two different cam profiles: a low/mid lift profile or a high lift profile. The two intake valves in each cylinder are operated by a rocker arm with its own cam lobe. The cam utilized is selected by the Engine Control Unit (ECU). To select different valve lift modes, oil pressure generated by the engine moves a pin which locks the two lobes together. At low engine speeds the low/mid lift camshafts increases the speed of air rushing into the engine thereby increasing torque and efficiency. At higher engine speeds the high lift camshafts fully open the intake valves, reducing resistance to incoming air and improving power. AVLS only operates one of the intake valves in each cylinder as the other is always open to promote swirl.