Kite control systems

Kite types, kite mooring, and kite applications result in a wide variety of kite control systems. Contemporary manufacturers, kite athletes, kite pilots, scientists, and engineers are expanding the possibilities.
Single-line kite control systems.
High-altitude attempt single-line control systems.
On-board angle-of-attack mechanisms were used in the 2000 altitude record-making flight; the operators' designed adjuster limited kite line tension to not more than 100 pounds by altering the angle of attack of the kite's wing body. The kite's line had a control: a line payout meter that did not function in the record-setting flight. However, some special tether line lower end used bungee and pulley arrangements to lower the impact of gusts on the long tether. Control of a kite includes how other aircraft see the kite system; the team placed a radio beacon (using two-meter frequency detectable for 50 miles) on the kite; for sight visibility, strobe lights were hung from the kite's nose. Control via use of reels and pulleys become critical when tension is high; the team had to repair and replace parts during the flight session.
Auxiliary control.
Auxiliary devices have been invented and used for controlling single-line kites. Devices on board the kite's wing can react to the kite-line's tension or to the kite's angle of attack with the ambient stream in which the kite is flying. Special reel devices allow kite-line length and tension control. Moving the kite's line lower end left or right or windward or anti-windward forms part of the control system of single-line kites. Devices at the kite's bridle can be set to alter the relative lengths of sub-bridle lines in order to set the attitude of the kite so that the kite flies at a certain position of the potential positions; this can be done for one setting while the kite is readied for flight; but Kenneth C. Howard invited a device that can be operated on single-line kites during the flight session for variable settings:
Fighter-kite control systems.
The traditional fighter kiting with single-line control dominates kite fighting while multi-line kite fighting is yet a minor activity. The human operator of the single line aims to master movements (tugs, jerks, releases, directional movements) in order to have the unstable kite temporarily move in one direction or another. The intents of the controls are offensive and defensive; escape from an attack or position for an attack. The building of the kite so that motions by the kite's human operator or pilot allow a temporary limited stability takes special care.
Historical kite control systems.
A piano-wire based kite control system.
Medium-length-tethered power kites.
Power kites are controlled by two to five lines. The simplest systems provide steering by pulling either end of the kite. More lines can provide different functions. These are:
The lines attach to different controllers:
Control of high-altitude electricity-generating wind-power kite systems.
Human control of high altitude wind power systems is typically accomplished through servo mechanisms, as the tether tensions are too great for direct manual operation.
There are a number of patents in this area:
Other concepts include:
Control of kite rigs.
Kite rigs are systems for propelling a vehicle, such as a boat, buggy, or a vehicle with snow and ice runners. They may be as simple as a person flying a kite while standing on a specialized skateboard, or be complex systems fixed to the vehicle with powered and automated controls. They differ from conventional sails in that they are flown from lines, not supported by masts.
Commercial transport propulsion.
Ship-pulling kites run to hundreds of square meters of area and require a special attachment points, a launch and recovery system, and fly-by-wire controls.
The SkySails ship propulsion system consists of a large foil kite, an electronic control system for the kite, and an automatic system to retract the kite.
The kite, while over ten times larger, bears similarities to the arc kites used in kitesurfing. However, the kite is an inflatable rather than a ram-air kite. Additionally, a control pod is used rather than direct tension on multiple kite control lines; only one line runs the full distance from kite to ship, with the bridle lines running from kite to control pod. Power to the pod is provided by cables embedded in the line; the same line also carries commands to the control pod from the ship.
The kite is launched and recovered by an animated mast or arm, which grips the kite by its leading edge. The mast also inflates and deflates the kite. When not in use, mast and deflated kite fold away.
Target-kites.
The term "target kite" generally refers to the war-time kites used for shipboard anti-aircraft gunnery practice. These were the invention of Paul E. Garber, doing war work while on leave from the Smithsonian (where he was responsible for the acquisition of much of the Air and Space collection).
The kites were ordinary two-spar Eddy style kites with a height of about five feet. The sail was sky blue with the profile of a Japanese Zero or German aircraft painted in black. Attached at the lower end of the vertical spar is a small rudder, much like a boat's rudder. The rudder is controlled by two kite lines, which are also used to fly the kite. The two lines come down to earth and terminate at an either a "flying bar" (a bar with spools at either end) or a special two-spool reel which incorporated a ratchet mechanism to assist in equalizing line length. The spool was in the center of a wooden bar which held the lines a fixed distance apart.
Indoor.
A wand or pole with a string on the end is often used to lead indoor kites around.
Hang-gliders.
Unpowered short-tethered hang-gliders.
Unlike the long-lined power kites used in extreme kiting sport, the focus in this section is the short-lined framed large kite. The kite line or "hang line" for best controlling the flight of the hang glider kite needs to be carefully lengthened; then the line frequently splits to two, three, or four main tethers that connect to the hung kite operator's or pilot's harness. Mike Meier, kite glider author, wrote How "To Get The Right Hang Height". NASA used mass-shifting in the Paresev hung-pilot aircraft with a stiffened-frame kite. The hang tether was also stiffened, differently. In sport hang gliding kite systems using the short hang line, the hang loop or first section of the hanging kite line is a flexible webbing, then the main lines to the harness are cords and sometimes webbing that are flexible. Control of the attitude of the kite's wing is achieved frequently by the pilot's grabbing the kite's stiffened airframe part called the control frame and pushing or pulling the kite's airframe left or right or forward and aft in various combinations; this control system is most commonly called "weight-shifting" although mechanically the situation is altering positions of mass to alter the center of gravity of the entire system relative to the aerodynamic center of pressure in order to effect leveraging moments to control the flight.
The place on the kite airframe where the tether is tied is very important as in all kites; such connection or bridling takes into consideration the aerodynamic center of pressure and the system's center of gravity. A key article by Mike Meier, "Pitch Stability & Center of Mass" "Location", focuses on this concern of control.
While flying the kite hang glider, there are times during flight instruction that instructors will have the student fully release from holding the triangle control frame and simply and only hang. The hanging (gravity pulls the student's body downwards and results in a tensional tugging of the kite's wing) student experiences that the properly bridled and trimmed wing will fly stably. However, since gusts occur, the student learns that hands-off flying is not the normal status—rather the kite pilot is almost always handling the control frame. Light bar pressure.
Powered short-tethered hang-gliders.
Here the unpowered kite is tethered to a pilot who arranges to have a harness to which is attached a thrusting prime moving engine or motor; the total system is a powered aircraft while the kite itself remains unpowered (very differently is when an engine is mounted on a wing). The control system includes the control system of the similar system where the pilot is not thrust by a harnessed prime moving engine or motor; however, in controlling flight, adjustments for center of mass are respected. Further, while the pilot's thrust is on, the pilot positions so that the kite's kite line is angled so tugging of the wing is accomplished in the familiar kiting manner where the kite line begins upwind and angles upward downwind (relative wind is to be the wind in attention here).
Under static-line tow.
Here the tug kite line stays the same length during the kiting operation. The ground vehicle driver has special control duties. The kited hang glider person controls the kite in some ways different from other tow methods; careful distinctions are learned in professional instruction. Controlling things when unexpected events occur is a large part of instruction.
Under non-static-line tow.
 The complex control system includes the operator of the winch. The length of line starts long and then gets shorter as the winch reels the tug line; this alters the control decisions by the kited hang glider pilot. Instruction for controls is available for new winch operators and hang glider pilots who want to be so kited. Distinguish this method from static-line (tug line stays same length during the tow). The control system for the shortening-the-tug-line method of kiting is different.
Under bungee-line launch.
Bungee launch control systems for kited hang gliders has its own special details. The tug kite line is very elastic; when tensed, the line is long; during use for launch, the kite line shortens. Controlling the kite's wing attitudes is up to the pilot who frequently is hung from a short kite line while controlling a triangle control frame or other airframe part or even aerodynamic surface controls. Professional instruction is highly recommended. Inelastic portion of the bungee assembly is used to help guard against what can happen if the bungee breaks and snaps back toward the pilot; a tug-line parachute can be used to lower the speed that the released bungee will fall. Bungee launch is used most frequently for launch off slopes when free-foot-launch is not easy (site structure or pilots who have not the use of their legs), or for flatland short-flight demonstrations.
Paragliders.
The non-stiffened Francis Rogallo parawing, the Domina Jalbert founded parafoil wing, or other modified fully flexible wings (Barish sailwing, KiteShip wing, parasails, modified conical parachutes) do not lend themselves to a mounting of a prime moving engine or motor to them; rather the kiting lines to the unpowered wing terminate below the wing to a static or mobile anchoring; that anchoring itself may be with its own active thrusting engine or motor or the anchor (which could be payload, pilot, or both payload and pilot) may simply fall by gravity force—and thus by gravity tug the wing through the kite lines. When the payload or pilot is simply falling without adding a prime moving engine or motor, then the kited flexible wing is a paragliding wing; when the payload or pilot is additionally arranged with a thrust engine or motor, then the kited unpowered flexible wing with such thrust payload or pilot is a powered aircraft system or powered paragliding system. The control systems are varied for particular applications (ranging from lowering military payloads, autonomous powered paragliders or drones, sport paragliding, sport powered paragliding, scale-model paragliding, scale-model powered paragliding). All variations have in common the unpowered kite whether or not the payload and/or pilot is powered.
Governable gliding parachutes.
 These free-flight kites are governable parachutes and are used as payload delivery systems, sport gliding parachuting or skydiving, BASE jumping, scale-model parachuting. When used for delivery of sensitive payloads or carrying humans, the fast opening from packed format is damped by use of a slider. The wing remains unpowered and kited by bridle tethering lines; the lines attach to platforms or harnesses. The size and design of the kited wing is customized for the final type of use where packing, opening, and sink rate are important feature. Control systems are specialized for the specific use. Control systems sometimes include radio control from remote locations.
Kite aerial photography.
Kites used in kite aerial photography (KAP) are typically controlled using the same reels and spools as non-KAP kite flyers. The best KAP work seems be done at lower altitudes than expected (100–200'), so no special equipment is required. The most problematic KAP flights are when the best camera shot requires the kite to be flown amongst tall trees or buildings, so quick haul-in can be a plus.
The camera rig itself is attached to the kite line some distance beneath the kite, preferably with a pulley scheme that will permit the camera to float in a level attitude regardless of the kite's gyrations. The "Picavet" system is one such scheme.
Further sophistication in kite photography comes with live video and radio control features to control where the camera is pointing. This is superior to the minimal rig which simply clicks the camera every few minutes and must be hauled down to earth to change the direction in which the camera points. The penalty of the radio control rigs is weight, which requires higher winds to do photography. So in addition to clear skies, high winds are also necessary, which will limit opportunities for photography.
Solar sail and plasma kites.
Scientists on one type of solar kite take pride that there will be a minimum of moving parts to control the movement of the solar kite through space and around the Earth, Moon, comet, or other Solar System body. A collection of scientists and engineers are expanding the definition of what a kite is; the solar kite described by authors C. Jack and C. Welch has the inertia of the mass of the kite providing resistance against photonic flow. Also, the controlling of the kite to alter the kite's acceleration sets up a kiting scenario: causing the kite to deflect away from the pull of gravity to keep it flying on its intended path supports the inclusion of the solar sail as a kite in photonic flow. The kite is fed start data; the kite tracks the stars and operates three elements to control its attitude to effect its deflections to result in the flight path desired by the ground-directing kite operators. The position of the payload is changed to alter the relative positions of the kite's center of pressure and center of mass; this is done in part by piezoelectric actuators. Also, the struts that hold the centered payload are differentially heated; such causes one of the struts to become longer than the cooler struts and thereby changing the center of mass relative to the center of pressure of the kite. Further, to cause an attitude change, tiny photo thrusters (heated wire) tweak the attitude of the kite; such thrusters do not propel the kite, but are only used to change the attitude of the kite's sail. These mechanisms aim to give authoritative control at minimum power use for giving direction to the kite. Working solar kite groups are considering at least seventeen means of control of the solar kite/solar sail.


Krylov subspace

In linear algebra, the order-"r" Krylov subspace generated by an "n"-by-"n" matrix "A" and a vector "b" of dimension "n" is the linear subspace spanned by the images of "b" under the first "r" powers of "A" (starting from formula_1), that is,
Background.
The concept is named after Russian applied mathematician and naval engineer Alexei Krylov, who published a paper about it in 1931.
Use.
Krylov subspaces are used in algorithms for finding approximate solutions to high-dimensional linear algebra problems. Many linear dynamical system tests in control theory, especially those related to controllability and observability, involve checking the rank of the Krylov subspace. These tests are equivalent to finding the span of the Gramians associated with the system/output maps so the uncontrollable and unobservable subspaces are simply the orthogonal complement to the Krylov subspace.
Modern iterative methods such as Arnoldi iteration can be used for finding one (or a few) eigenvalues of large sparse matrices or solving large systems of linear equations. They try to avoid matrix-matrix operations, but rather multiply vectors by the matrix and work with the resulting vectors. Starting with a vector formula_13, one computes formula_23, then one multiplies that vector by formula_12 to find formula_25 and so on. All algorithms that work this way are referred to as Krylov subspace methods; they are among the most successful methods currently available in numerical linear algebra. These methods can be used in situations where there is an algorithm to compute the matrix-vector multiplication without there being an explicit representation of formula_12, giving rise to Matrix-free methods.
Issues.
Because the vectors usually soon become almost linearly dependent due to the properties of power iteration, methods relying on Krylov subspace frequently involve some orthogonalization scheme, such as Lanczos iteration for Hermitian matrices or Arnoldi iteration for more general matrices.
Existing methods.
The best known Krylov subspace methods are the Conjugate gradient, IDR(s) (Induced dimension reduction), GMRES (generalized minimum residual), BiCGSTAB (biconjugate gradient stabilized), QMR (quasi minimal residual), TFQMR (transpose-free QMR) and MINRES (minimal residual method).


Coloured Petri net

Coloured Petri nets are a backward compatible extension of the mathematical concept of Petri nets.
Coloured Petri nets preserve useful properties of Petri nets and at the same time extend the initial formalism to allow the distinction between tokens.
Coloured Petri nets allow tokens to have a data value attached to them. This attached data value is called the token color. Although the color can be of arbitrarily complex type, places in coloured Petri nets usually contain tokens of one type. This type is called the color set of the place.
Definition 1. A "net" is a tuple "N" = ("P", "T", "A", Σ, "C", "N", "E", "G", "I" ) where:
In coloured Petri nets, sets of places, transitions and arcs are pairwise disjoint "P" ∩ "T" = "P" ∩ "A" = "T" ∩ "A" = ∅
Use of node function and arc expression function allows multiple arcs connect the same pair of nodes with different arc expressions.
A well-known program for working with coloured Petri nets is cpntools.


Application Level Events

Application Level Events (ALE) is a standard created by EPCglobal, an organization of industry leaders devoted to the development of standards for the Electronic Product Code (EPC) and Radio-frequency identification (RFID) technologies and standards. The ALE specification is a software specification indicating required functionality and behavior, as well as a common API expressed through XML Schema Definition (XSD) and Web Services Description Language (WSDL).


Maria Pia Fanti

Maria Pia Fanti (born 21 February 1957) is an Italian control theorist known for her research on topics that include discrete event dynamic systems, Petri nets, consensus, fault detection and isolation, agile manufacturing, and road traffic control. She is a professor in the Department of Electrical and Information Engineering at the Polytechnic University of Bari, where she heads the Laboratory for Control and Automation.
Education and career.
Fanti studied electronic engineering at the University of Pisa, and earned a laurea there in 1983. She has been a full professor at the Polytechnic University of Bari since 2012.
Recognition.
Fanti was named an IEEE Fellow in 2017 "for contributions to modeling and control of discrete event systems".


Kirsten Morris

Kirsten Anna Morris (born 1960) is a Canadian applied mathematician specializing in control theory, including work on flexible structures, smart materials, hysteresis, and infinite-dimensional optimization. She is a professor at the University of Waterloo, the former chair of the Society for Industrial and Applied Mathematics Activity Group on Control and Systems, the author of two books on control theory, and an IEEE Fellow.
Education and career.
Morris was motivated to study mathematical economics at Queen's University at Kingston by a job doing econometrics at a bank, but lost interest in the economic applications of mathematics after a year, instead switching into a program in mathematics and engineering, which she finished in 1982. She became interested in control theory while studying for a master's degree at the University of Waterloo. After completing the degree in 1984, she continued at Waterloo as a doctoral student, and earned her Ph.D. there in 1989. Her dissertation, "Finite-Dimensional Control of Infinite-Dimensional Systems", was supervised by Mathukumalli Vidyasagar.
After a year as a staff scientist at the NASA Langley Research Center, she returned to Waterloo as an assistant professor in the Department of Applied Mathematics in 1990. She became a full professor there in 2003, and also holds a cross-appointment in the Department of Mechanical and Mechatronics Engineering. She chaired the Society for Industrial and Applied Mathematics Activity Group on Control and Systems from 2018 to 2019, and has held leadership positions in the IEEE Control Systems Society and the International Federation of Automatic Control.
Books.
Morris is the author of the books "Introduction to Feedback Control" (Harcourt-Brace, 2001) and "Controller Design for Distributed Parameter Systems" (Springer, 2020). She is the editor of "Control of Flexible Structures: Papers from the Workshop on Problems in Sensing, Identification and Control of Flexible Structures held in Waterloo, Ontario, June 1992" (American Mathematical Society, 1993).
Recognition.
In 2020, Morris was named an IEEE Fellow, affiliated with the IEEE Control Systems Society, "for contributions to control and estimator design for infinite-dimensional systems". She was named a SIAM Fellow in the 2021 class of fellows, "for contributions to modeling, approximation, and control design for distributed parameter systems". She is also a Fellow of the International Federation of Automatic Control.


Margin-infused relaxed algorithm

Margin-infused relaxed algorithm (MIRA) is a machine learning algorithm, an online algorithm for multiclass classification problems. It is designed to learn a set of parameters (vector or matrix) by processing all the given training examples one-by-one and updating the parameters according to each training example, so that the current training example is classified correctly with a margin against incorrect classifications at least as large as their loss. The change of the parameters is kept as small as possible.
A two-class version called binary MIRA simplifies the algorithm by not requiring the solution of a quadratic programming problem (see below). When used in a one-vs-all configuration, binary MIRA can be extended to a multiclass learner that approximates full MIRA, but may be faster to train.
The flow of the algorithm looks as follows:
 Input: Training examples formula_1
 Output: Set of parameters formula_2
 formula_3 ← 0, formula_4 ← 0
 for formula_5 ← 1 to formula_6
 for formula_7 ← 1 to formula_8
 formula_9 ← update formula_10 according to formula_11
 formula_3 ← formula_13
 end for
 end for
 return formula_14
The update step is then formalized as a quadratic programming problem: Find formula_15, so that formula_16, i.e. the score of the current correct training formula_17 must be greater than the score of any other possible formula_18 by at least the loss (number of errors) of that formula_18 in comparison to formula_17.


Tensor product model transformation

In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition of functions. It transforms a function (which can be given via closed formulas or neural networks, fuzzy logic, etc.) into TP function form if such a transformation is possible. If an exact transformation is not possible, then the method determines a TP function that is an approximation of the given function. Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity.
A free MATLAB implementation of the TP model transformation can be downloaded at or an old version of the toolbox is available at MATLAB Central . A key underpinning of the transformation is the higher-order singular value decomposition.
Besides being a transformation of functions, the TP model transformation is also a new concept in qLPV based control which plays a central role in the providing a valuable means of bridging between identification and polytopic systems theories. The TP model transformation is uniquely effective in manipulating the convex hull of polytopic forms, and, as a result has revealed and proved the fact that convex hull manipulation is a necessary and crucial step in achieving optimal solutions and decreasing conservativeness in modern LMI based control theory. Thus, although it is a transformation in a mathematical sense, it has established a conceptually new direction in control theory and has laid the ground for further new approaches towards optimality. Further details on the control theoretical aspects of the TP model transformation can be found here: TP model transformation in control theory.
The TP model transformation motivated the definition of the "HOSVD canonical form of TP functions", on which further information can be found here. It has been proved that the TP model transformation is capable of numerically reconstructing this HOSVD based canonical form. Thus, the TP model transformation can be viewed as a numerical method to compute the HOSVD of functions, which provides exact results if the given function has a TP function structure and approximative results otherwise.
The TP model transformation has recently been extended in order to derive various types of convex TP functions and to manipulate them. This feature has led to new optimization approaches in qLPV system analysis and design, as described at TP model transformation in control theory.
Definitions.
that is, using compact tensor notation (using the tensor product operation formula_4 of ):
where core tensor formula_6 is constructed from formula_7, and row vector formula_8 contains continuous univariate weighting functions formula_9. The function formula_10 is the formula_11-th weighting function defined on the formula_12-th dimension, and formula_13 is the formula_12-the element of vector formula_15. Finite element means that formula_16 is bounded for all formula_17. For qLPV modelling and control applications a higher structure of TP functions are referred to as TP model.
Here formula_19 is a tensor as formula_20, thus the size of the core tensor is formula_21. The product operator formula_22 has the same role as formula_23, but expresses the fact that the tensor product is applied on the formula_24 sized tensor elements of the core tensor formula_25. Vector formula_26 is an element of the closed hypercube formula_27.
This means that formula_30 is inside the convex hull defined by the core tensor for all formula_31.
namely it generates the core tensor formula_35 and the weighting functions formula_36 for all formula_37. Its free MATLAB implementation is downloadable at or at MATLAB Central .
If the given formula_38 does not have TP structure (i.e. it is not in the class of TP models), then the TP model transformation determines its approximation:
where trade-off is offered by the TP model transformation between complexity (number of components in the core tensor or the number of weighting functions) and the approximation accuracy. The TP model can be generated according to various constrains. Typical TP models generated by the TP model transformation are:
References.
Baranyi, P. (2018). Extension of the Multi-TP Model Transformation to Functions with Different Numbers of Variables. Complexity, 2018.


Temper mill

A temper mill is a steel sheet or steel plate processing line composed of a horizontal pass cold rolling mill stand, entry and exit conveyor tables and upstream and downstream equipment depending on the design and nature of the processing system.
The primary purpose of a temper mill is to improve the surface finish on steel products.
Components.
A typical type of temper mill installation includes entry equipment for staging and accepting hot rolled coils of steel which have been hot wound at the end of a hot strip mill or hot rolled plate mill. Also included in a typical temper mill installation are pinch rolls, a leveler (sometimes two levelers), a shear for cutting the finished product to pre-determined lengths, a stacker for accumulating cut lengths of product
Sometimes a temper mill installation includes a re-coil line where the finished product is a coil instead of bundles of cut lengths of product. Maximum product flexibility capability could be attained if the installation was arranged to produce both coils and bundles of cut to length product.
The heart of the temper mill is the cold rolling mill stand which produces the temper pass. It will include electric powered drive motors and speed reduction gearing suited to the process desired. The design of the rolling mill can be a 2-high or 4-high (even 6-high in some cases). The mill stand can be work roll driven or back up roll driven. The mill can be designed with hydraulic work roll bending or back up roll bending. Installations typically have a single rolling mill stand, but may have two. Pinch rolls provide back tension for the pay off reel in the entry section and entry and exit tension for the temper pass.
Function.
The process goal is physical property enhancement through cold forming of the steel product in the bite of the work rolls. The physical properties that are enhanced by the temper pass due to elongation of the product include:
Typical elongation produced in the product is 0.5% to 2%. Product dimensions vary. Thicknesses include typical sheet metal gauges up to 1.00" thick plate. Widths vary from 36" to 125".
The finish of the rolled product is controlled by using rolls having a variety of surface finishes designed to impart the desired finish to the product. Roll finishes range from ground and polished rolls to impart a bright finish, to shot-blasted or electric-discharged textured rolls that produce a dull, velvety finish on the steel surface.
Typical auxiliary equipment includes PLC based controls, overhead traveling cranes, roll changing equipment, roll grinding equipment, hydraulic power unit(s), bundle lifting devices, Coil handling devices, etc.


Perceptron

In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.
History.
The perceptron was invented in 1943 by Warren McCulloch and Walter Pitts. The first implementation was a machine built in 1958 at the Cornell Aeronautical Laboratory by Frank Rosenblatt, funded by the United States Office of Naval Research.
The perceptron was intended to be a machine, rather than a program, and while its first implementation was in software for the IBM 704, it was subsequently implemented in custom-built hardware as the "Mark 1 perceptron". This machine was designed for image recognition: it had an array of 400 photocells, randomly connected to the "neurons". Weights were encoded in potentiometers, and weight updates during learning were performed by electric motors.
In a 1958 press conference organized by the US Navy, Rosenblatt made statements about the perceptron that caused a heated controversy among the fledgling AI community; based on Rosenblatt's statements, "The New York Times" reported the perceptron to be "the embryo of an electronic computer that [the Navy] expects will be able to walk, talk, see, write, reproduce itself and be conscious of its existence."
Although the perceptron initially seemed promising, it was quickly proved that perceptrons could not be trained to recognise many classes of patterns. This caused the field of neural network research to stagnate for many years, before it was recognised that a feedforward neural network with two or more layers (also called a multilayer perceptron) had greater processing power than perceptrons with one layer (also called a single-layer perceptron).
Single-layer perceptrons are only capable of learning linearly separable patterns. For a classification task with some step activation function, a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve many otherwise non-separable problems.
In 1969, a famous book entitled "Perceptrons" by Marvin Minsky and Seymour Papert showed that it was impossible for these classes of network to learn an XOR function. It is often believed (incorrectly) that they also conjectured that a similar result would hold for a multi-layer perceptron network. However, this is not true, as both Minsky and Papert already knew that multi-layer perceptrons were capable of producing an XOR function. (See the page on "Perceptrons (book)" for more information.) Nevertheless, the often-miscited Minsky/Papert text caused a significant decline in interest and funding of neural network research. It took ten more years until neural network research experienced a resurgence in the 1980s. This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected.
A 2022 article states that the Mark 1 Perceptron was "part of a previously secret four-year NPIC [the US' National Photographic Interpretation Center] effort from 1963 through 1966 to develop this algorithm into a useful tool for photo-interpreters".
The kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by Freund and Schapire (1998), and more recently by Mohri and Rostamizadeh (2013) who extend previous results and give new L1 bounds.
The perceptron is a simplified model of a biological neuron. While the complexity of biological neuron models is often required to fully understand neural behavior, research suggests a perceptron-like linear model can produce some behavior seen in real neurons.
Definition.
In the modern sense, the perceptron is an algorithm for learning a binary classifier called a threshold function: a function that maps its input formula_1 (a real-valued vector) to an output value formula_2 (a single binary value):
where formula_4 is a vector of real-valued weights, formula_5 is the dot product formula_6, where is the number of inputs to the perceptron, and is the "bias". The bias shifts the decision boundary away from the origin and does not depend on any input value.
The value of formula_2 (0 or 1) is used to classify formula_1 as either a positive or a negative instance, in the case of a binary classification problem. If is negative, then the weighted combination of inputs must produce a positive value greater than formula_9 in order to push the classifier neuron over the 0 threshold. Spatially, the bias alters the position (though not the orientation) of the decision boundary. The perceptron learning algorithm does not terminate if the learning set is not linearly separable. If the vectors are not linearly separable learning will never reach a point where all vectors are classified properly. The most famous example of the perceptron's inability to solve problems with linearly nonseparable vectors is the Boolean exclusive-or problem. The solution spaces of decision boundaries for all binary functions and learning behaviors are studied in the reference.
Rosenblatt described the details of the perceptron in a 1958 paper. His organization of a perceptron is constructed of three kinds of cells ("units"): AI, AII, R, which stand for "projection", "association" and "response".
In the context of neural networks, a perceptron is an artificial neuron using the Heaviside step function as the activation function. The perceptron algorithm is also termed the single-layer perceptron, to distinguish it from a multilayer perceptron, which is a misnomer for a more complicated neural network. As a linear classifier, the single-layer perceptron is the simplest feedforward neural network.
Learning algorithm.
Below is an example of a learning algorithm for a single-layer perceptron. For multilayer perceptrons, where a hidden layer exists, more sophisticated algorithms such as backpropagation must be used. If the activation function or the underlying process being modeled by the perceptron is nonlinear, alternative learning algorithms such as the delta rule can be used as long as the activation function is differentiable. Nonetheless, the learning algorithm described in the steps below will often work, even for multilayer perceptrons with nonlinear activation functions.
When multiple perceptrons are combined in an artificial neural network, each output neuron operates independently of all the others; thus, learning each output can be considered in isolation.
Definitions.
We first define some variables:
We show the values of the features as follows:
To represent the weights:
To show the time-dependence of formula_4, we use:
Steps.
The algorithm updates the weights after every training sample in step 2b.
Convergence.
The perceptron is a linear classifier, therefore it will never get to the state with all the input vectors classified correctly if the training set is not linearly separable, i.e. if the positive examples cannot be separated from the negative examples by a hyperplane. In this case, no "approximate" solution will be gradually approached under the standard learning algorithm, but instead, learning will fail completely. Hence, if linear separability of the training set is not known a priori, one of the training variants below should be used.
If the training set "is" linearly separable, then the perceptron is guaranteed to converge. Furthermore, there is an upper bound on the number of times the perceptron will adjust its weights during the training.
Suppose that the input vectors from the two classes can be separated by a hyperplane with a margin formula_31, i.e. there exists a weight vector formula_32, and a bias term such that formula_33 for all formula_19 with formula_35 and formula_36 for all formula_19 with formula_38, where formula_39 is the desired output value of the perceptron for input formula_19. Also, let denote the maximum norm of an input vector. Novikoff (1962) proved that in this case the perceptron algorithm converges after making formula_41 updates. The idea of the proof is that the weight vector is always adjusted by a bounded amount in a direction with which it has a negative dot product, and thus can be bounded above by , where is the number of changes to the weight vector. However, it can also be bounded below by because if there exists an (unknown) satisfactory weight vector, then every change makes progress in this (unknown) direction by a positive amount that depends only on the input vector.
While the perceptron algorithm is guaranteed to converge on "some" solution in the case of a linearly separable training set, it may still pick "any" solution and problems may admit many solutions of varying quality. The "perceptron of optimal stability", nowadays better known as the linear support-vector machine, was designed to solve this problem (Krauth and Mezard, 1987).
Variants.
The pocket algorithm with ratchet (Gallant, 1990) solves the stability problem of perceptron learning by keeping the best solution seen so far "in its pocket". The pocket algorithm then returns the solution in the pocket, rather than the last solution. It can be used also for non-separable data sets, where the aim is to find a perceptron with a small number of misclassifications. However, these solutions appear purely stochastically and hence the pocket algorithm neither approaches them gradually in the course of learning, nor are they guaranteed to show up within a given number of learning steps.
The Maxover algorithm (Wendemuth, 1995) is "robust" in the sense that it will converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal stability (maximum margin between the classes). For non-separable data sets, it will return a solution with a small number of misclassifications. In all cases, the algorithm gradually approaches the solution in the course of learning, without memorizing previous states and without stochastic jumps. Convergence is to global optimality for separable data sets and to local optimality for non-separable data sets.
The Voted Perceptron (Freund and Schapire, 1999), is a variant using multiple weighted perceptrons. The algorithm starts a new perceptron every time an example is wrongly classified, initializing the weights vector with the final weights of the last perceptron. Each perceptron will also be given another weight corresponding to how many examples do they correctly classify before wrongly classifying one, and at the end the output will be a weighted vote on all perceptrons.
In separable problems, perceptron training can also aim at finding the largest separating margin between the classes. The so-called perceptron of optimal stability can be determined by means of iterative training and optimization schemes, such as the Min-Over algorithm (Krauth and Mezard, 1987) or the AdaTron (Anlauf and Biehl, 1989)). AdaTron uses the fact that the corresponding quadratic optimization problem is convex. The perceptron of optimal stability, together with the kernel trick, are the conceptual foundations of the support-vector machine.
The formula_42-perceptron further used a pre-processing layer of fixed random weights, with thresholded output units. This enabled the perceptron to classify analogue patterns, by projecting them into a binary space. In fact, for a projection space of sufficiently high dimension, patterns can become linearly separable.
Another way to solve nonlinear problems without using multiple layers is to use higher order networks (sigma-pi unit). In this type of network, each element in the input vector is extended with each pairwise combination of multiplied inputs (second order). This can be extended to an "n"-order network.
It should be kept in mind, however, that the best classifier is not necessarily that which classifies all the training data perfectly. Indeed, if we had the prior constraint that the data come from equi-variant Gaussian distributions, the linear separation in the input space is optimal, and the nonlinear solution is overfitted.
Other linear classification algorithms include Winnow, support-vector machine, and logistic regression.
Multiclass perceptron.
Like most other techniques for training linear classifiers, the perceptron generalizes naturally to multiclass classification. Here, the input formula_43 and the output formula_44 are drawn from arbitrary sets. A feature representation function formula_45 maps each possible input/output pair to a finite-dimensional real-valued feature vector. As before, the feature vector is multiplied by a weight vector formula_46, but now the resulting score is used to choose among many possible outputs:
Learning again iterates over the examples, predicting an output for each, leaving the weights unchanged when the predicted output matches the target, and changing them when it does not. The update becomes:
This multiclass feedback formulation reduces to the original perceptron when formula_43 is a real-valued vector, formula_44 is chosen from formula_51, and formula_52.
For certain problems, input/output representations and features can be chosen so that formula_53 can be found efficiently even though formula_44 is chosen from a very large or even infinite set.
Since 2002, perceptron training has become popular in the field of natural language processing for such tasks as part-of-speech tagging and syntactic parsing (Collins, 2002). It has also been applied to large-scale machine learning problems in a distributed computing setting.


Roll-to-roll processing

In the field of electronic devices, roll-to-roll processing, also known as web processing, reel-to-reel processing or R2R, is the process of creating electronic devices on a roll of flexible plastic, metal foil, or flexible glass. In other fields predating this use, it can refer to any process of applying coating, printing, or performing other processes starting with a roll of a flexible material and re-reeling after the process to create an output roll. These processes, and others such as sheeting, can be grouped together under the general term converting. When the rolls of material have been coated, laminated or printed they can be subsequently slit to their finished size on a slitter rewinder.
In electronic devices.
Large circuits made with thin-film transistors and other devices can be patterned onto these large substrates, which can be up to a few meters wide and long. Some of the devices can be patterned directly, much like an inkjet printer deposits ink. For most semiconductors, however, the devices must be patterned using photolithography techniques.
Roll-to-roll processing of large-area electronic devices reduces manufacturing cost. Most notable would be solar cells, which are still prohibitively expensive for most markets due to the high cost per unit area of traditional bulk (mono- or polycrystalline) silicon manufacturing. Other applications could arise which take advantage of the flexible nature of the substrates, such as electronics embedded into clothing, large-area flexible displays, and roll-up portable displays.
Thin-film cells.
A crucial issue for a roll-to-roll thin-film cell production system is the deposition rate of the microcrystalline layer, and this can be tackled using four approaches:
In electrochemical devices.
The roll-to-roll processing has been used in the manufacture of electrochemical devices such as batteries, supercapacitors, fuel cells, and water electrolyzers. Here, the roll-to-roll processing is utilized for electrode manufacturing and is the key to reducing manufacturing cost through stable production of electrodes on various film substrates such as metal foils, membranes, diffusion media, and separators.


Punching machine

A punching machine is a machine tool for punching and embossing flat sheet-materials to produce form-features needed as mechanical element and/or to extend static stability of a sheet section.
CNC punching.
Punch presses are developed for high flexibility and efficient processing of metal stampings. The main areas of application are for small and medium runs. Those machines are typically equipped with a linear die carrier (tool carrier) and quick change tools. Today the method is used where the application of lasers are inefficient or technically impractical. CNC is the abbreviation of Computer Numerically Controlled.
Principle of operation.
After programming the work pieces and entering length of bars the control automatically calculates the maximum number of pieces to be punched (for example, 18 pieces of a bar of 6000 mm). Once the desired number of work pieces is entered, the bar is pushed toward the stop. The machine is fully automated once the production process is launched.
The third CNC axis always moves the cylinder exactly over the tool, which keeps the wear on the bearings and tools to a minimum. All pieces are sent down a slat conveyor and are pushed sideways on a table. Any scrap is carried to the end of the conveyor and dropped into a bin. Different workpieces can be produced within one work cycle to optimize production.
Programming.
Programming is done on a PC equipped with appropriate software that can be part of the machine or a connected external workstation. For generating a new program engineering data can be imported or pasted per mouse and keyboard. Through a graphic and menu-driven user interface previous CNC programming skills are not required. All the punches in a work piece are shown on the screen making programming mistakes easily detected. Ideally each program is stored in one database, so it is easy to recover them by search and sort functions. When selecting a new piece, all the necessary tooling changes are displayed. Before transferring it to the control unit the software scans each program for possible collisions. This eliminates most handling errors.
Tool change system.
The linear tool carrier (y-axis) has several stations that hold the punching tools and one cutting tool. Especially for flexibility and efficient processing are set up times a crucial cost factor. Downtimes should be reduced to a minimum. Therefore, recent tool systems are designed for fast and convenient change of punches and dies. They are equipped with a special plug-in system for a quick and easy change of tools.
There is no need to screw anything together. The punch and die plate are adjusted to each other automatically Punches and dies can be changed rapidly meaning less machine downtime.
Networking with the whole production line.
A lot of organizational effort and interface management is saved, if the CNC punch press is connected to the previous and subsequent process. For a connection to other machines and external workstations corporate interfaces have to be established.
Integration of further production steps.
Besides punching, machines of the high end class can be equipped with special functions. For example:


Configuration design

Configuration design is a kind of design where a fixed set of predefined components that can be interfaced (connected) in predefined ways is given, and an assembly (i.e. designed artifact) of components selected from this fixed set is sought that satisfies a set of requirements and obeys a set of constraints.
The associated "design configuration problem" consists of the following three constituent tasks:
Types of knowledge involved in configuration design include:


Hall circles

Hall circles (also known as M-circles and N-circles) are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis.
Construction.
Consider a closed-loop linear control system with open-loop transfer function given by transfer function formula_1 and with a unit gain in the feedback loop. The closed-loop transfer function is given by formula_2.
To check the stability of "T"("s"), it is possible to use the Nyquist stability criterion with the Nyquist plot of the open-loop transfer function "G"("s"). Note, however, that only the Nyquist plot of "G"("s") does not give the actual values of "T"("s"). To get this information from the G(s)-plane, Hall proposed to construct the locus of points in the "G"("s")-plane such that "T"("s") has constant magnitude and the also the locus of points in the "G"("s")-plane such that "T"("s") has constant phase angle.
Given a positive real value "M" representing a fixed magnitude, and denoting G(s) by "z", the points satisfying formula_3are given by the points "z" in the "G"("s")-plane such that the ratio of the distance between "z" and 0 and the distance between "z" and -1 is equal to "M". The points "z" satisfying this locus condition are circles of Apollonius, and this locus is known in the context of control systems as "M-circles".
Given a positive real value "N" representing a phase angle, the points satisfying formula_4are given by the points z in the "G"("s")-plane such that the angle between -1 and z and the angle between 0 and z is constant. In other words, the angle opposed to the line segment between -1 and 0 must be constant. This implies that the points z satisfying this locus condition are arcs of circles, and this locus is known in the context of control systems as "N-circles".
Usage.
To use the Hall circles, a plot of M and N circles is done over the Nyquist plot of the open-loop transfer function. The points of the intersection between these graphics give the corresponding value of the closed-loop transfer function.
Hall circles are also used with the Nichols plot and in this setting, are also known as Nichols chart. Rather than overlaying directly the Hall circles over the Nichols plot, the points of the circles are transferred to a new coordinate system where the ordinate is given by formula_5 and the abscissa is given by formula_6. The advantage of using Nichols chart is that adjusting the gain of the open loop transfer function directly reflects in up and down translation of the Nichols plot in the chart.


Lamp rerating

Lamp rerating is modelling the predicted properties of a filament lamp when running the lamp at a voltage other than its specified rating, using a power law function of voltage. The following equations can be used to estimate the new operating point. The exact value of the exponent parameters will typically vary slightly with the particular lamp design.


Industrial dryer

Industrial dryers are used to efficiently process large quantities of bulk materials that need reduced moisture levels. Depending on the amount and the makeup of material needing to be dried, industrial dryers come in many different models constructed specifically for the type and quantity of material to be processed. The most common types of industrial dryers are fluidized bed dryers, rotary dryers, rolling bed dryers, conduction dryers, convection dryers, pharmaceutical dryers, suspension/paste dryers, toroidal bed or TORBED dryers and dispersion dryers. Various factors are considered in determining the correct type of dryer for any given application, including the material to be dried, drying process requirements, production requirements, final product quality requirements and available facility space.


Timer coalescing

Timer coalescing is a computer system energy-saving technique that reduces central processing unit (CPU) power consumption by reducing the precision of software timers used for synchronization of process wake-ups, minimizing the number of times the CPU is forced to perform the relatively power-costly operation of entering and exiting idle states.


Semi-automation

Semi-automation is a process or procedure that is performed by the combined activities of man and machine with both human and machine steps typically orchestrated by a centralized computer controller.
Within manufacturing, production processes may be fully manual, semi-automated, or fully automated. In this case, semi-automation may vary in its degree of manual and automated steps.
Semi-automated manufacturing processes are typically orchestrated by a computer controller which sends messages to the worker at the time in which he/she should perform a step. The controller typically waits for feedback that the human performed step has been completed via either a human-machine interface or via electronic sensors distributed within the process. Controllers within semi-automated processes may either directly control machinery or send signals to machinery distributed within the process. Centralized computer controllers within semi-automated processes orchestrate processes by instructing the worker, providing electronic communication and control to process equipment, tools, or machines, as well as perform data management to record and ensure that the process meets established process criteria.
Many manufacturers choose not to fully automate a process, and instead implement semi-automation due to the complexity of the task, or the number of products produced is too low to justify the investment in full automation. Other processes may not be fully automated because it may reduce the flexibility to easily adapt the processes to reflect production needs.


Tipped tool

A tipped tool is any cutting tool in which the cutting edge consists of a separate piece of material that is brazed, welded, or clamped onto a body made of another material. In the types in which the cutter portion is an indexable part clamped by a screw, the cutters are called inserts (because they are inserted into the tool body). Tipped tools allow each part of the tool, the shank and the cutter(s), to be made of the material with the best properties for its job. Common materials for the cutters (brazed tips or clamped inserts) include cemented carbide, polycrystalline diamond, and cubic boron nitride. Tools that are commonly tipped include milling cutters (such as end mills, face mills, and fly cutters), tool bits, router bits, and saw blades (especially the metal-cutting ones).
Advantages and disadvantages.
The advantage of tipped tools is only a small insert of the cutting material is needed to provide the cutting ability. The small size makes manufacturing of the insert easier than making a solid tool of the same material. This also reduces cost because the tool holder can be made of a less-expensive and tougher material. In some situations a tipped tool is better than its solid counterpart because it combines the toughness of the tool holder with the hardness of the insert.
In other situations this is less than optimal, because the joint between the tool holder and the insert reduces rigidity. However, these tools may still be used because the overall cost savings is still greater.
In industry today, insert tools are perhaps slightly more common than solid tools, but solid tools are still used in many applications. Entire catalogs of solid–high-speed steel (HSS) and solid-carbide end mills, for example, play prominent parts in some areas of milling practice, including diesinking, moldmaking, and aerospace job or batch production. Most machine shops with lathes have many solid-HSS and solid-carbide tool bits as well as many insert-tipped tool bits, and most commercial operations that involve routers (such as cabinetry and furniture shops) use plenty of solid-HSS and solid-carbide router bits as well as some tipped bits.
Indexable inserts.
Inserts are removable cutting tips, which means they are not brazed or welded to the tool body. They are usually indexable, meaning that they can be exchanged, and often also rotated or flipped, without disturbing the overall geometry of the tool (effective diameter, tool length offset, etc.). This saves time in manufacturing by allowing fresh cutting edges to be presented periodically without the need for tool grinding, setup changes, or entering of new values into a CNC program.
Wiper insert.
A "wiper insert" is an insert used in a milling machine or a lathe. It is designed for finished cutting, to give a smooth surface on the surface being cut. It uses special geometry to give a good finish on the workpiece at a higher-than-normal feedrate. Wiper inserts generally have a larger area in contact with the workpiece, so they exert higher force on the workpiece. This makes them unsuitable for fragile workpieces.
ISO insert coding.
"Inserts used for turning and milling" are often numbered according to ISO standard 1832. This standard aims to make the naming, specifying and ordering of inserts a simple, consistent and traceable process. This standard takes into account both metric and imperial systems of units, although certain elements differ for each unit system. The code consists of up to 13 symbols with the first 12 of them being compulsory for inserts composed of cubic boron or poly-crystalline diamond and the first 7 being compulsory for all other types of composition.


Recursive Bayesian estimation

In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model. The process relies heavily upon mathematical concepts and models that are theorized within a study of prior and posterior probabilities known as Bayesian statistics.
In robotics.
A Bayes filter is an algorithm used in computer science for calculating the probabilities of multiple beliefs to allow a robot to infer its position and orientation. Essentially, Bayes filters allow robots to continuously update their most likely position within a coordinate system, based on the most recently acquired sensor data. This is a recursive algorithm. It consists of two parts: prediction and innovation. If the variables are normally distributed and the transitions are linear, the Bayes filter becomes equal to the Kalman filter.
In a simple example, a robot moving throughout a grid may have several different sensors that provide it with information about its surroundings. The robot may start out with certainty that it is at position (0,0). However, as it moves farther and farther from its original position, the robot has continuously less certainty about its position; using a Bayes filter, a probability can be assigned to the robot's belief about its current position, and that probability can be continuously updated from additional sensor information.
Model.
The measurements formula_1 are the manifestations of a hidden Markov model (HMM), which means the true state formula_2 is assumed to be an unobserved Markov process. The following picture presents a Bayesian network of a HMM.
Because of the Markov assumption, the probability of the current true state given the immediately previous one is conditionally independent of the other earlier states.
Similarly, the measurement at the "k"-th timestep is dependent only upon the current state, so is conditionally independent of all other states given the current state.
Using these assumptions the probability distribution over all states of the HMM can be written simply as:
However, when using the Kalman filter to estimate the state x, the probability distribution of interest is associated with the current states conditioned on the measurements up to the current timestep. (This is achieved by marginalising out the previous states and dividing by the probability of the measurement set.)
This leads to the "predict" and "update" steps of the Kalman filter written probabilistically. The probability distribution associated with the predicted state is the sum (integral) of the products of the probability distribution associated with the transition from the ("k" - 1)-th timestep to the "k"-th and the probability distribution associated with the previous state, over all possible formula_6.
The probability distribution of update is proportional to the product of the measurement likelihood and the predicted state.
The denominator
is constant relative to formula_2, so we can always substitute it for a coefficient formula_11, which can usually be ignored in practice. The numerator can be calculated and then simply normalized, since its integral must be unity.
Sequential Bayesian filtering.
Sequential Bayesian filtering is the extension of the Bayesian estimation for the case when the observed value changes in time. It is a method to estimate the real value of an observed variable that evolves in time.
The method is named:
The notion of Sequential Bayesian filtering is extensively used in control and robotics.


Strict-feedback form

In control theory, dynamical systems are in strict-feedback form when they can be expressed as
where
Here, "strict feedback" refers to the fact that the nonlinear functions formula_11 and formula_12 in the formula_13 equation only depend on states formula_14 that are "fed back" to that subsystem. That is, the system has a kind of lower triangular form.
Stabilization.
Systems in strict-feedback form can be stabilized by recursive application of backstepping. That is,
This process is known as backstepping because it starts with the requirements on some internal subsystem for stability and progressively "steps back" out of the system, maintaining stability at each step. Because
then the resulting system has an equilibrium at the origin (i.e., where formula_58, formula_59, formula_60, ... , formula_61, and formula_62) that is globally asymptotically stable.


Bellman pseudospectral method

The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. The method is named after Richard E. Bellman. It was introduced by Ross et al.
first as a means to solve multiscale optimal control problems, and later expanded to obtain suboptimal solutions for general optimal control problems.
Theoretical foundations.
The multiscale version of the Bellman pseudospectral method is based on the spectral convergence property of the Ross–Fahroo pseudospectral methods. That is, because the Ross–Fahroo pseudospectral method converges at an exponentially fast rate, pointwise convergence to a solution is obtained at very low number of nodes even when the solution has high-frequency components. This aliasing phenomenon in optimal control was first discovered by Ross et al. Rather than use signal processing techniques to anti-alias the solution, Ross et al. proposed that Bellman's principle of optimality can be applied to the converged solution to extract information between the nodes. Because the Gauss–Lobatto nodes cluster at the boundary points, Ross et al. suggested that if the node density around the initial conditions satisfy the Nyquist–Shannon sampling theorem, then the complete solution can be recovered by solving the optimal control problem in a recursive fashion over piecewise segments known as Bellman segments.
In an expanded version of the method, Ross et al., proposed that method could also be used to generate feasible solutions that were not necessarily optimal. In this version, one can apply the Bellman pseudospectral method at even lower number of nodes even under the knowledge that the solution may not have converged to the optimal one. In this situation, one obtains a feasible solution.
A remarkable feature of the Bellman pseudospectral method is that it automatically determines several measures of suboptimality based on the original pseudospectral cost and the cost generated by the sum of the Bellman segments.
Computational efficiency.
One of the computational advantages of the Bellman pseudospectral method is that it allows one to escape Gaussian rules in the distribution of node points. That is, in a standard pseudospectral method, the distribution of node points are Gaussian (typically Gauss-Lobatto for finite horizon and Gauss-Radau for infinite horizon). The Gaussian points are sparse in the middle of the interval (middle is defined in a shifted sense for infinite-horizon problems) and dense at the boundaries. The second-order accumulation of points near the boundaries have the effect of wasting nodes. The Bellman pseudospectral method takes advantage of the node accumulation at the initial point to anti-alias the solution and discards the remainder of the nodes. Thus the final distribution of nodes is non-Gaussian and dense while the computational method retains a sparse structure.
Applications.
The Bellman pseudospectral method was first applied by Ross et al. to solve the challenging problem of very low thrust trajectory optimization. It has been successfully applied to solve a practical problem of generating very high accuracy solutions to a trans-Earth-injection problem of bringing a space capsule from a lunar orbit to a pin-pointed Earth-interface condition for successful reentry.
The Bellman pseudospectral method is most commonly used as an additional check on the optimality of a pseudospectral solution generated by the Ross–Fahroo pseudospectral methods. That is, in addition to the use of Pontryagin's minimum principle in conjunction with the solutions obtained by the Ross–Fahroo pseudospectral methods, the Bellman pseudospectral method is used as a primal-only test on the optimality of the computed solution.


SpaceAge Control

SpaceAge Control is a design, manufacturing, and service company focused on 3D displacement sensing and measurement.
The company has supplied precision displacement sensors to industries worldwide since 1969. During its history, the company created ongoing displacement sensing innovations starting with miniature and subminiature string potentiometers (1968) and 2D and 3D cable-actuated displacement sensors (1974).
History.
SpaceAge Control was established in 1968 to design, develop, and manufacture pilot protection devices in support of space-based and high-performance test aircraft programs. In 1970, the company was awarded a NASA contract to produce precision, small-format position transducers for aircraft flight control testing. The successful completion of this contract led to the development and production of a complete line of innovative, small-size position transducers.
In 1974, the company was tasked with producing a multi-dimensional "swivel head" air data probe to enhance total and static pressure accuracy at the high angles of attack associated with rotary wing aircraft. The resulting product, the 100510 air data boom, is used for flight test air data sensing requirements to include STOL, VSTOL, rotary wing, business jet, military transport, and general aviation aircraft.
Through the 1970s, 1980s, and 1990s, significantly all U.S., Canadian, and European aerospace companies have used the company's air data products and position transducers in their research, development, and test activities. Often, these products were designed and manufactured to custom specifications.
In 1989, the company began its focus on unmanned aerial vehicles (UAVs) with the development and introduction of the 100400 miniature air data boom. That product use led to the adoption of SpaceAge Control air data products on a broad range of unmanned aircraft to include aerial targets, autonomous vehicles, and experimental vehicles.
Also in 1989, a single auto racing team began using these position transducers to monitor throttle movement and suspension travel. This use resulted in the adoption of the products in automotive test and measurement projects including anthropomorphic dummy instrumentation, impact testing, and control verification.


IEC 63119

IEC 63119 is an international standard defining a protocol for information exchange for electric vehicle charging roaming services, which is currently under development. IEC 63119 is one of the International Electrotechnical Commission's group of standards for electric road vehicles and electric industrial trucks, and is the responsibility of Working Group 9 (WG9) of IEC Technical Committee 69 (TC69).
Standard documents.
IEC 63119 consists of the following parts, detailed in separate IEC 63119 standard documents:


Transfer stamping

Sheet metal forming in medium-high volume production environments is often completed through the use of a Transfer Press operating a number of dies as a complete system. Each die in the system is responsible for adding more shape to the part until the metal work piece attains its final shape. What makes transfer stamping unique is that a single press operates a number of tools, the movement of the sheet metal work piece from one operation to the next is performed by automation either built into the press or onto the dies. With each closing of the press the entire system of tools will close, each performing its designed work to the sheet metal. Upon opening the built in transfer mechanism moves the workpiece from one operation to the next in the sequence.
In the past these operations may have been performed using individual presses and the workpieces may have been moved from press to press, and die to die, by hand. As Automation improved hand loading was replaced by pick and place automation and by robots. The transfer press is a natural extension of this practice, simplifying the operation by having all tools in a single large press and using automation which is specifically designed for the press operations.
Transfer mechanisms.
Tri-axis transfer.
Named for the movement of the transfer mechanism, tri-axis transfer mechanisms motion is defined by the three (3) axes of movement made by the part manipulators each press stroke. On the press downstroke the automation which will likely be holding the work piece will lower the work piece to the tool and retract to leave the part on the tool. At the bottom of the stroke the automation mechanism in the retracted state will cycle backward one pitch to position itself adjacent to the next workpiece. As the press cycles upward the part manipulators will index inward to pick up the next work piece, continuing upward following the press ram, then indexing forward to next station. As the press reaches the top of its stroke, the process repeats. The three axes of motion are up-down, in-out, and forward-back.
Cross-bar transfer.
With a cross bar transfer mechanism, the in-out axes of movement is constrained by an automation bar spanning the die space. Commonly mounted with suction cups, this cross bar will pick the workpiece up from above and release the part, dropping it into place at the next station. With only two axes of motion and the automation spanning the die space, the cross bar transfer mechanism must "dwell" between adjacent tools between each press stroke.


Jet mill

A jet mill grinds materials by using a high speed jet of compressed air or inert gas to impact particles into each other. Jet mills can be designed to output particles below a certain size while continuing to mill particles above that size, resulting in a narrow size distribution of the resulting product. Particles leaving the mill can be separated from the gas stream by cyclonic separation.
Particle size.
A jet mill consists of a short cylinder, meaning the cylinder's height is less than its diameter. Compressed gas is forced into the mill through nozzles tangent to the cylinder wall, creating a vortex. The gas leaves the mill through a tube along the axis of the cylinder. Solid particles in the mill are subject to two competing forces:
The drag on small particles is less than large particles, according to the formula derived from Stokes' law,
where "V" is the flow settling velocity (m/s) (vertically downwards if "ρp" > "ρf", upwards if "ρp" gravitational acceleration (m/s2), "ρp" is the mass density of the particles (kg/m3), "ρf" is the mass density of the fluid (kg/m3), "μ" is the dynamic viscosity (kg /m*s), and "R" is the radius of the spherical particle (m).
The formula shows that particles will be pulled toward the wall of the mill according to the square of their radius or diameter. Large particles will continue the comminution process, until they are small enough to stay in the center of the mill where the discharge port is located.


Raster passes

Raster passes are the most basic of all machining strategies for the finishing or semi-finishing of a part during computer-aided manufacturing (CAM). In raster passes machining the milling cutter moves along curves on the cutter location surface (CL surface) obtained by intersecting the CL surface with vertical, parallel planes. Many CAM systems implement this strategy by sampling cutter location points on these curves by calculating intersection points of the CL surface and as many vertical lines as needed to approximate the curve to the desired accuracy.


Observability

Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs.
In control theory, the observability and controllability of a linear system are mathematical duals.
The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system.
Definition.
Consider a physical system modeled in state-space representation. A system is said to be observable if, for every possible evolution of state and control vectors, the current state can be estimated using only the information from outputs (physically, this generally corresponds to information obtained by sensors). In other words, one can determine the behavior of the entire system from the system's outputs. On the other hand, if the system is not observable, there are state trajectories that are not distinguishable by only measuring the outputs.
Linear time-invariant systems.
For time-invariant linear systems in the state space representation, there are convenient tests to check whether a system is observable. Consider a SISO system with formula_1 state variables (see state space for details about MIMO systems) given by
Observability matrix.
If and only if the column rank of the "observability matrix", defined as
is equal to formula_1, then the system is observable. The rationale for this test is that if formula_1 columns are linearly independent, then each of the formula_1 state variables is viewable through linear combinations of the output variables formula_8.
Related concepts.
Observability index.
The "observability index" formula_9 of a linear time-invariant discrete system is the smallest natural number for which the following is satisfied: formula_10, where
Unobservable subspace.
The "unobservable subspace" formula_12 of the linear system is the kernel of the linear map formula_13 given byformula_14where formula_15 is the set of continuous functions from formula_16 to formula_17. formula_12 can also be written as
Since the system is observable if and only if formula_20, the system is observable if and only if formula_12 is the zero subspace.
The following properties for the unobservable subspace are valid:
Detectability.
A slightly weaker notion than observability is "detectability". A system is detectable if all the unobservable states are stable.
Detectability conditions are important in the context of sensor networks.
Linear time-varying systems.
Consider the continuous linear time-variant system
Suppose that the matrices formula_27, formula_28 and formula_29 are given as well as inputs and outputs formula_30 and formula_8 for all formula_32 then it is possible to determine formula_33 to within an additive constant vector which lies in the null space of formula_34 defined by
where formula_36 is the state-transition matrix.
It is possible to determine a unique formula_33 if formula_34 is nonsingular. In fact, it is not possible to distinguish the initial state for formula_39 from that of formula_40 if formula_41 is in the null space of formula_34.
Note that the matrix formula_43 defined as above has the following properties:
Observability matrix generalization.
The system is observable in formula_51 if and only if there exists an interval formula_51 in formula_16 such that the matrix formula_34 is nonsingular.
If formula_55 are analytic, then the system is observable in the interval [formula_56,formula_57] if there exists formula_58 and a positive integer "k" such that
where formula_60 and formula_61 is defined recursively as
Example.
Consider a system varying analytically in formula_63 and matricesformula_64 Then formula_65 , and since this matrix has rank = 3, the system is observable on every nontrivial interval of formula_16.
Nonlinear systems.
Given the system formula_67, formula_68. Where formula_69 the state vector, formula_70 the input vector and formula_71 the output vector. formula_72 are to be smooth vector fields.
Define the observation space formula_73 to be the space containing all repeated Lie derivatives, then the system is observable in formula_74 if and only if formula_75, where
Early criteria for observability in nonlinear dynamic systems were discovered by Griffith and Kumar, Kou, Elliot and Tarn, and Singh.
There also exist an observability criteria for nonlinear time-varying systems.
Static systems and general topological spaces.
Observability may also be characterized for steady state systems (systems typically defined in terms of algebraic equations and inequalities), or more generally, for sets in formula_77. Just as observability criteria are used to predict the behavior of Kalman filters or other observers in the dynamic system case, observability criteria for sets in formula_77 are used to predict the behavior of data reconciliation and other static estimators. In the nonlinear case, observability can be characterized for individual variables, and also for local estimator behavior rather than just global behavior.


Pneumatic tool

A pneumatic tool, air tool, air-powered tool or pneumatic-powered tool is a type of power tool, driven by compressed air supplied by an air compressor. Pneumatic tools can also be driven by compressed carbon dioxide  stored in small cylinders allowing for portability.
Most pneumatic tools convert the compressed air to work using a pneumatic motor. Compared to electric power tool equivalents, pneumatic tools are safer to run and maintain, without risk of sparks, short-circuiting or electrocution, and have a higher power to weight ratio, allowing a smaller, lighter tool to accomplish the same task. Furthermore, they are less likely to self-destruct in case the tool is jammed or overloaded.
General grade pneumatic tools with a short life span are commonly less expensive and considered “disposable tools” in tooling industries, while industrial grade pneumatic tools with long life span are more expensive. In general, pneumatic tools are cheaper than the equivalent electric-powered tools. Regular lubrication of the tools is still needed however.
Most pneumatic tools are to be supplied with compressed air at 4 to 6 bar.
Advantages and disadvantages.
Pneumatic tools have many benefits which have contributed to their rise in popularity. The benefits of using compressed air to power tools are:
The primary disadvantage of pneumatic tools is the need for an air compressor, which can be expensive. Pneumatic tools also need to be properly maintained and oiled regularly. Failing to maintain tools can lead to deterioration, due to a build up residual oil and water.
Technical terms.
Pneumatic tools are rated using several metrics: Free Speed (rpm), Air Pressure (psi/bar), Air Consumption (cfm/scfm or m3/min), Horse Power (hp), and spindle size. Each individual tool has its own specific requirements which determine their compatibility with air compressor systems.
Flow or airflow, related to air consumption in pneumatic tools, represents the quantity of compressed air that passes through a section over a unit of time. It is represented in l/min, m3, at the equivalent value in free air in conditions of standard reference atmosphere (SRA). For example: +20 c, 65% of relative humidity, 1013 mbar, in accordance with norms NFE.
Types of pneumatic tools.
Pneumatic tools come in many shapes and form, including small and large-sized hand tools.
The most common types of pneumatic tools include:


Mechatronics

Mechatronics engineering also called mechatronics, is an interdisciplinary branch of engineering that focuses on the integration of mechanical, electrical and electronic engineering systems, and also includes a combination of robotics, electronics, computer science, telecommunications, systems, control, and product engineering.
As technology advances over time, various subfields of engineering have succeeded in both adapting and multiplying. The intention of mechatronics is to produce a design solution that unifies each of these various subfields. Originally, the field of mechatronics was intended to be nothing more than a combination of mechanics, electrical and electronics, hence the name being a portmanteau of the words "mechanics" and "electronics"; however, as the complexity of technical systems continued to evolve, the definition had been broadened to include more technical areas.
The word "mechatronics" originated in Japanese-English and was created by Tetsuro Mori, an engineer of Yaskawa Electric Corporation. The word "mechatronics" was registered as trademark by the company in Japan with the registration number of "46-32714" in 1971. The company later released the right to use the word to the public, and the word began being used globally. Currently the word is translated into many languages and is considered an essential term for advanced automated industry.
Many people treat "mechatronics" as a modern buzzword synonymous with automation, robotics and electromechanical engineering.
French standard NF E 01-010 gives the following definition: "approach aiming at the synergistic integration of mechanics, electronics, control theory, and computer science within product design and manufacturing, in order to improve and/or optimize its functionality".
History.
The word "mechatronics" was registered as trademark by the company in Japan with the registration number of "46-32714" in 1971. The company later released the right to use the word to the public, and the word began being used globally.
With the advent of information technology in the 1980s, microprocessors were introduced into mechanical systems, improving performance significantly. By the 1990s, advances in computational intelligence were applied to mechatronics in ways that revolutionized the field.
Description.
A mechatronics engineer unites the principles of mechanics, electrical, electronics, and computing to generate a simpler, more economical and reliable system.
Engineering cybernetics deals with the question of control engineering of mechatronic systems. It is used to control or regulate such a system (see control theory). Through collaboration, the mechatronic modules perform the production goals and inherit flexible and agile manufacturing properties in the production scheme. Modern production equipment consists of mechatronic modules that are integrated according to a control architecture. The most known architectures involve hierarchy, polyarchy, heterarchy, and hybrid. The methods for achieving a technical effect are described by control algorithms, which might or might not utilize formal methods in their design. Hybrid systems important to mechatronics include production systems, synergy drives,
exploration rovers, automotive subsystems such as anti-lock braking systems and spin-assist, and everyday equipment such as autofocus cameras, video, hard disks, CD players and phones.
Course structure.
Mechatronics students take courses in various fields:
Applications.
Physical implementations.
Mechanical modeling calls for modeling and simulating physical complex phenomena in the scope of a multi-scale and multi-physical approach. This implies to implement and to manage modeling and optimization methods and tools, which are integrated in a systemic approach.
The specialty is aimed for students in mechanics who want to open their mind to systems engineering, and able to integrate different physics or technologies, as well as students in mechatronics who want to increase their knowledge in optimization and multidisciplinary simulation techniques.
The specialty educates students in robust and/or optimized conception methods for structures or many technological systems, and to the main modeling and simulation tools used in R&D. Special courses are also proposed for original applications (multi-materials composites, innovating transducers and actuators, integrated systems, …) to prepare the students to the coming breakthrough in the domains covering the materials and the systems.
For some mechatronic systems, the main issue is no longer how to implement a control system, but how to implement actuators. Within the mechatronic field, mainly two technologies are used to produce movement/motion.
Subdisciplines.
Mechanical.
Mechanical engineering is an important part of mechatronics engineering. It includes the study of mechanical nature of how an object works. Mechanical elements refer to mechanical structure, mechanism, thermo-fluid, and hydraulic aspects of a mechatronics system. The study of thermodynamics, dynamics, fluid mechanics, pneumatics and hydraulics. Mechatronics engineer who works a mechanical engineer can specialize in hydraulics and pneumatics systems, where they can be found working in automobile industries. A mechatronics engineer can also design a vehicle since they have strong mechanical and electronical background. Knowledge of software applications such as computer-aided design and computer aided manufacturing is essential for designing products. Mechatronics covers a part of mechanical syllabus which is widely applied in automobile industry.
Mechatronic systems represent a large part of the functions of an automobile. The control loop formed by sensor—information processing—actuator—mechanical (physical) change is found in many systems. The system size can be very different. The Anti-lock braking system (ABS) is a mechatronic system. The brake itself is also one. And the control loop formed by driving control (for example cruise control), engine, vehicle driving speed in the real world and speed measurement is a mechatronic system, too. The great importance of mechatronics for automotive engineering is also evident from the fact that vehicle manufacturers often have development departments with "Mechatronics" in their names.
Electronics and Electricals.
Electronics and Telecommunication engineering specializes in electronics devices and telecom devices of a mechatronics system. A mechatronics engineer specialized in electronics and telecommunications have knowledge of computer hardware devices. The transmission of signal is the main application of this subfield of mechatronics. Where digital and analog systems also forms an important part of mechatronics systems. Telecommunications engineering deals with the transmission of information across a medium.
Electronics engineering is related to computer engineering and electrical engineering. Control engineering has a wide range of electronic applications from the flight and propulsion systems of commercial airplanes to the cruise control present in many modern cars. VLSI designing is important for creating integrated circuits. Mechatronics engineers have deep knowledge of microprocessors, microcontrollers, microchips and semiconductors. The application of mechatronics in electronics manufacturing industry can conduct research and development on consumer electronic devices such as mobile phones, computers, cameras etc. For mechatronics engineers it is necessary to learn operating computer applications such as MATLAB and Simulink for designing and developing electronic products.
Mechatronics engineering is a interdisciplinary course, it includes concepts of both electrical and mechanical systems. A mechatronics engineer engages in designing high power transformers or radio-frequency module transmitters.
Avionics.
Avionics is also considered a variant of mechatronics as it combines several fields such as electronics and telecom with Aerospace engineering. It is the subdiscipline of mechatronics engineering and aerospace engineering which is engineering branch focusing on electronics systems of aircraft. The word avionics is a blend of aviation and electronics. The electronics system of aircraft includes aircraft communication addressing and reporting system, air navigation, aircraft flight control system, aircraft collision avoidance systems, flight recorder, weather radar and lightning detector. These can be as simple as a searchlight for a police helicopter or as complicated as the tactical system for an airborne early warning platform.
Advanced Mechatronics.
Another variant is Motion control for Advanced Mechatronics, presently recognized as a key technology in mechatronics. The robustness of motion control will be represented as a function of stiffness and a basis for practical realization. Target of motion is parameterized by control stiffness which could be variable according to the task reference. The system robustness of motion always requires very high stiffness in the controller.
Industrial.
The branch of industrial engineer includes the design of machinery, assembly and process lines of various manufacturing industries. This branch can be said somewhat similar to automation and robotics. Mechatronics engineers who works as industrial engineers design and develop infrastructure of a manufacturing plant. Also it can be said that they are architect of machines. One can work as an industrial designer to design the industrial layout and plan for setting up of a manufacturing industry or as an industrial technician to lookover the technical requirements and repairing of the particular factory.
Robotics.
Robotics is one of the newest emerging subfield of mechatronics. It is the study of robots that how they are manufactured and operated. Since 2000, this branch of mechatronics is attracting a number of aspirants. Robotics is interrelated with automation because here also not much human intervention is required. A large number of factories especially in automobile factories, robots are founds in assembly lines where they perform the job of drilling, installation and fitting. Programming skills are necessary for specialization in robotics. Knowledge of programming language —ROBOTC is important for functioning robots. An industrial robot is a prime example of a mechatronics system; it includes aspects of electronics, mechanics, and computing to do its day-to-day jobs.
Computer.
The Internet of things (IoT) is the inter-networking of physical devices, embedded with electronics, software, sensors, actuators, and network connectivity which enable these objects to collect and exchange data. IoT and mechatronics are complementary. Many of the smart components associated with the Internet of Things will be essentially mechatronic. The development of the IoT is forcing mechatronics engineers, designers, practitioners and educators to research the ways in which mechatronic systems and components are perceived, designed and manufactured. This allows them to face up to new issues such as data security, machine ethics and the human-machine interface.
Knowledge of programming is very important. A mechatronics engineer has to do programming in different levels example.—PLC programming, drone programming, hardware programming, CNC programming etc. Due to combination of electronics engineering, soft skills from computer side is important. Important programming languages for mechatronics engineer to learn is Java, Python, C++ and C programming language.


Rudder ratio

Rudder ratio refers to a value that is monitored by the computerized flight control systems in modern aircraft. The ratio relates the aircraft airspeed to the rudder deflection setting that is in effect at the time. As an aircraft accelerates, the deflection of the rudder needs to be reduced proportionately within the range of the rudder pedal depression by the pilot. This automatic reduction process is needed because if the rudder is fully deflected when the aircraft is in high-speed flight, it will cause the plane to sharply and violently yaw, or swing from side to side, leading to loss of control and rudder, tail and other damages, even causing the aircraft to crash.