This website uses cookies to ensure you have the best experience. Learn more

Real Dynamical Systems Essay

2855 words - 11 pages

A time lag between a change of an input and the corresponding change of the output that real dynamical systems often show has a whole range of causes. For needs of mathematical modelling, it is aggregated into a total phenomenon called time delay or dead time [3]. In process control, one often encounters systems that can be described by transfer functions with time delays [1]. If a dynamical system with time delay is modelled as a time invariant linear system, its transfer function (rational function) becomes due to time delay a transcendental function [3]. For design and analysis purposes, these delays are usually approximated by rational transfer functions [2]. This is usually carried out using delay approximation methods Viz. Taylor series expansion, Padé.
PI and PID controllers have been at the heart of control engineering practice for seven decades [4]. The use of the PI or PID controller is ubiquitous in industry. It has been stated, for example, that in process control applications, and more than 95% of the controllers are of PI or PID type [1, 4, 5]. PID controllers can assure satisfactory performances with a simple algorithm for a wide range of processes [6, 7].
The Internal Model Control (IMC) provides a progressive, effective, natural, generic, unique, powerful, and simple framework for analysis and synthesis of control system performance [8-11]. The easiness and enhanced performance of the IMC based tuning rule, and the analytically derived IMC-PID tuning techniques have appealed the attention of the industrial users, in the past decade [10, 11]. The well-known IMC-PID tuning rule provides a clear compromise in the midst of closed loop performance and robustness to model uncertainties, and is achieved by only one user-defined tuning parameter, which is directly related to the closed-loop time constant[3, 8, 10 - 13].
IMC – PID Design:
The widely used approximate or predictive models of the process, more specifically chemical processes are the FOPTD, Equation (1). Garcia and Morari [12, 14] introduced internal model control; IMC it is characterized as a controller where the process model is explicitly an integral part of the controller. The Design process of IMC involves factorizing the predictive plant model as invertible and non-invertible parts depicted in Equation (2) by simple factorization or all pass factorization [8, 12, 13, 15, 16]. The Internal model controller in Equation (3) is the inverse of the invertible portion of the plant model , IMC filter , Equation (4) is used to realize the controller.
(1)
(2)
The design of the IMC controller is
(3)
...

Find Another Essay On Real Dynamical Systems

The Acquired Immune Deficiency Syndrome Essay

2480 words - 10 pages , Fernando Gomide et al.,(2004) Fuzzy Modeling in Symptomatic HIV Virus Infected Population: Bulletin of Mathematical Biology 66, 1597–1620 SwarnaliSharma ,G. P. Samanta, (2013)Dynamical Behaviour of an HIV/AIDS Epidemic Model : Differential Equations and Dynamical Systems

Design and Simulation of an Intelligent Traffic Control System

1589 words - 7 pages this paper. We have taken idea through current traffic control system through which we identified problem at ‘+’ junction and then we implemented our own system to solve the problem. Their approach was based on embedded system based methodology. Our new system, we have designed in such a way that it has pulled out some problems that were there in current traffic control systems. In order to get in detail to the current traffic control system

Chaos Theory Explained

2928 words - 12 pages , Princeton, 1987 The Physical Universe, Konrad B. Krauskoph, Arthur Beiser, 1997, WCB/McGraw hill Chaos in Dynamical Systems, Edward Ott, Cambridge University Press, 1993. www.lib.rmit.edu.au/fractals/exploring.html -Understanding Chaos and Fractals www-chaos.umd.edu - the Maryland chaos page, magazine publications and articles + diagrams and explanations The Meaning of Quantum Theory - Jim Baggot, Oxford, 1992 Chaos in Wonderland

Philanthropy and Elite Social Stratification in America

4099 words - 16 pages = 1/(1-ε), then a slight perturbation to ε will make one of the above cases true. Once that is the case, either pure philanthropy or pure miserliness will always be optimal. This concludes the derivation. Bibliography Aldrich, Nelson W., Jr. Old Money: The Mythology of America’s Upper Class. New York: Vintage, 1989. Hofbauer, Josef and Sigmund, Karl. The Theory of Evolution and Dynamical Systems. Cambridge: Cambridge UP

The History of Math

4801 words - 19 pages algebra in England by George Peacock. Another was the discovery of algebraic systems that have many, but not all, of the properties of the real numbers. Such systems include the quaternions of the Irish mathematician William Rowan Hamilton, the vector analysis of the American mathematician and physicist J. Willard Gibbs, and the ordered n-dimensional spaces of the German mathematician Hermann Günther Grassmann. A third major step was the

MATHEMATICS -ARA

4768 words - 19 pages subject during the 19th century from a study of polynomials to a study of the structure of algebraic systems. A major step in this direction was the invention of symbolic algebra in England by George Peacock. Another was the discovery of algebraic systems that have many, but not all, of the properties of the real numbers. Such systems include the quaternions of the Irish mathematician William Rowan Hamilton, the vector analysis of the American

Black Holes

3355 words - 13 pages accretion can occur onto supermassive black holes at the center of galaxies and in binary systems between a black hole (not necessarily supermassive) and a supermassive star. The accretion disk of a rotating black hole, is, by the black hole, driven into the equatorial plane of the rotation. The force on the disk is gravitational. Black holes are not really black, because they can radiate matter and energy. As they do this, they slowly

Black Holes

3065 words - 12 pages hole and the area near it, the accretion disk (a region of force-free fields), and an acceleration region outside the plasma.Disk accretion can occur onto supermassive black holes at the center of galaxies and in binary systems between a black hole (not necessarily supermassive) and a supermassive star. The accretion disk of a rotating black hole, is, by the black hole, driven into the equatorial plane of the rotation. The force on the disk is

Black holes in space. If

3089 words - 12 pages being the rotating black hole and the area near it, the accretion disk (a region of force-free fields), and an acceleration region outside the plasma. Disk accretion can occur onto supermassive black holes at the center of galaxies and in binary systems between a black hole (not necessarily supermassive) and a supermassive star. The accretion disk of a rotating black hole, is, by the black hole, driven into the equatorial plane of the rotation

Understanding Black Holes

3433 words - 14 pages black holes at the center of galaxies and in binary systems between a black hole (not necessarily super massive) and a super massive star (Caidin, The Book of Knowledge pp. 33). The accretion disk of a rotating black hole is, by the black hole, driven into the equatorial plane of the rotation. The force on the disk is gravitational. Black holes are not really black, because they can radiate matter and energy. As they do this, they slowly lose

When the Bubble Burst

1539 words - 6 pages By the time I arrived state side from my second tour in the Middle East the housing bubble had already burst. I noticed a drastic change in the way that many of my friends and family were living. Several of my friends that worked in real estate had sold their boats and seconds houses. My own stock portfolio had lost a third of its value. My sister and her husband had defaulted on their home mortgage leaving them scrambling for a place to live. I

Similar Essays

Lexical Development From The Perspectives Of Artificial Neural Network Models And Dynamical Systems Theory

2355 words - 9 pages , 2004). The aim of the present essay is to evaluate the ability of two theories, namely the Artificial Neural Network (ANN) and Dynamical Systems theory (DST), to explain the issues underlying the lexical development and vocabulary spurt. This essay provides an overview of both theories and compares their strengths and weaknesses in their explanation of lexical development supported by empirical evidence. Both ANN and DST were formed in opposition

Explaining The Chaos Theory Essay

1177 words - 5 pages an erratic behavior of the chaos theory. To understand the chaos theory’s principles of that underlie pattern of all real systems; they research from the ecosystems to the social systems to the universe as a whole. It is defined to show sensitivity to initial conditions. When the initial conditions started out small, it will rapidly lead to growing error in any effort to predict the future’s behavior. Measurement is not indefinitely precise but

Algorithms In Engineering Control Systems Essay

1526 words - 7 pages Increasing requirements for design of system with increased fault tolerance is the current trend in design of control systems. Since the majority of real control systems are non- linear, algorithms dealing with a class of non-linear systems use the approach of Takagi-Sugeno fuzzy models. These algorithms deals with fault diagnosis, reconfiguration of the system and solve problems related to the constraints of the system and the time delay that

Basic Limitations In Modern Sciences Essay

1112 words - 4 pages pure theory request nature to manifest itself in terms of predictable forces", the linear systems' results are considered as determinant, predictable, absolute in modern sciences. So, in linear systems a small error in input will lead to a small error in the result,as the results are determinant, predictable, absolute and therefore not contain any chaos.However, in the real life there is chaos because it is non linear. We can apply to Williams' view