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Variable Structure Systems
A variable structure system, or VSS, is a discontinuous nonlinear system of the form :\dot = \varphi( \mathbf, t ) where \mathbf \triangleq _1, x_2, \ldots, x_n \in \mathbb^n is the state vector, t \in \mathbb is the time variable, and \varphi(\mathbf,t) \triangleq \varphi_1(\mathbf,t), \varphi_2(\mathbf,t), \ldots, \varphi_n(\mathbf,t) : \mathbb^ \mapsto \mathbb^n is a ''piecewise continuous'' function. Due to the ''piecewise'' continuity of these systems, they behave like different continuous nonlinear systems in different regions of their state space. At the boundaries of these regions, their dynamics switch abruptly. Hence, their ''structure'' ''varies'' over different parts of their state space. The development of variable structure control depends upon methods of analyzing variable structure systems, which are special cases of hybrid dynamical systems. See also *Variable structure control *Sliding mode control *Hybrid system *Nonlinear control *Robust control *Optimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classification Of Discontinuities
Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a limit point (also called "accumulation point" or "cluster point") of its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. The oscillation of a function at a point quantifies these discontinuities as follows: * in a removable discontinuity, the distance that the value of the function is off by is the oscillation; * in a jump discontinuity, the size of the jump is the oscillation (assuming that the value ''at'' the point lies between these limits of the two sides); * in an essential discontinuity (a.k.a. infinite discontinuity), oscillation measures the failure of a limit to exist. A special case is if the function diverges to infinity or minus infinity, in which case the oscillati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Systems
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was a major American publishing#Textbook_publishing, educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for Dash#Relationships and connections, coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse-width Modulation
Pulse-width modulation (PWM), also known as pulse-duration modulation (PDM) or pulse-length modulation (PLM), is any method of representing a signal as a rectangular wave with a varying duty cycle (and for some methods also a varying period). PWM is useful for controlling the average power or amplitude delivered by an electrical signal. The average value of voltage (and current) fed to the load is controlled by switching the supply between 0 and 100% at a rate faster than it takes the load to change significantly. The longer the switch is on, the higher the total power supplied to the load. Along with maximum power point tracking (MPPT), it is one of the primary methods of controlling the output of solar panels to that which can be utilized by a battery. PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching. The goal of PWM is to control a load; however, the PWM switching frequency must be sele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse-density Modulation
Pulse-density modulation (PDM) is a form of modulation used to represent an analog signal with a binary signal. In a PDM signal, specific amplitude values are not encoded into codewords of pulses of different weight as they would be in pulse-code modulation (PCM); rather, the relative density of the pulses corresponds to the analog signal's amplitude. The output of a 1-bit DAC is the same as the PDM encoding of the signal. Description In a pulse-density modulation bitstream, a 1 corresponds to a pulse of positive polarity (+''A''), and a 0 corresponds to a pulse of negative polarity (−''A''). Mathematically, this can be represented as : x = -A (-1)^, where ''x'' 'n''is the bipolar bitstream (either −''A'' or +''A''), and ''a'' 'n''is the corresponding binary bitstream (either 0 or 1). A run consisting of all 1s would correspond to the maximum (positive) amplitude value, all 0s would correspond to the minimum (negative) amplitude value, and alternating 1s and 0s wou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta-sigma Modulation
Delta-sigma (ΔΣ; or sigma-delta, ΣΔ) modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency as part of the process of delta-sigma analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Delta-sigma modulation achieves high quality by utilizing a negative feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies well above the original signal's bandwidth. Subsequent low-pass filtering for demodulation easily removes this high frequency noise and time averages to achieve high accuracy in amplitude, which can be ultimately encoded as pulse-code modulation (PCM). Both ADCs and DACs can employ delta-sigma modulation. A delta-sigma ADC (e.g. Figure 1 top) encodes an analog signal using high-frequency delta-sigma modulation and then applies a digital filter to demodulate it t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Switching Amplifier
A class-D amplifier, or switching amplifier, is an electronic amplifier in which the amplifying devices (transistors, usually MOSFETs) operate as electronic switches, and not as linear gain devices as in other amplifiers. They operate by rapidly switching back and forth between the supply rails, using pulse-width modulation, pulse-density modulation, or related techniques to produce a pulse train output. A simple low-pass filter may be used to attenuate their high-frequency content to provide analog output current and voltage. Little energy is dissipated in the amplifying transistors because they are always either fully on or fully off, so efficiency can exceed 90%. History The first class-D amplifier was invented by British scientist Alec Reeves in the 1950s and was first called by that name in 1955. The first commercial product was a kit module called the X-10 released by Sinclair Radionics in 1964. However, it had an output power of only 2.5 watts. The Sinclair X-20 in 196 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H-bridge
An H-bridge is an electronic circuit that switches the polarity of a voltage applied to a load. These circuits are often used in robotics and other applications to allow DC motors to run forwards or backwards. The name is derived from its common schematic diagram representation, with four switching elements configured as the branches of a letter "H" and the load connected as the cross-bar. Most DC-to-AC converters (power inverters), most AC/AC converters, the DC-to-DC push–pull converter, isolated DC-to-DC converter most motor controllers, and many other kinds of power electronics use H bridges. In particular, a bipolar stepper motor is almost always driven by a motor controller containing two H bridges. General H-bridges are available as integrated circuits, or can be built from discrete components. The term ''H-bridge'' is derived from the typical graphical representation of such a circuit. An H-bridge is built with four switches (solid-state or mechanical). When the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Control
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors. The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness, prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today. In contrast with an adaptive control policy, a robust control policy is static, rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown but bounded. (Section 1.5) In German; an English version is also available Criteria for robust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear System
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
