Linear and nonlinear multivariable feedback control : a classical approach

Automatic feedback control systems play crucial roles in many fields, including manufacturing industries, communications, naval and space systems. At its simplest, a control system represents a feedback loop in which the difference between the ideal (input) and actual (output) signals is used to modify the behaviour of the system. Control systems are in our homes, computers, cars and toys. Basic control principles can also be found in areas such as medicine, biology and economics, where feedback mechanisms are ever present. Linear and Nonlinear Multivariable Feedback Control presents a highly original, unified control theory of both linear and nonlinear multivariable (also known as multi-input multi-output (MIMO)) feedback systems as a straightforward extension of classical control theory. It shows how the classical engineering methods look in the multidimensional case and how practising engineers or researchers can apply them to the analysis and design of linear and nonlinear MIMO systems. This comprehensive book: uses a fresh approach, bridging the gap between classical and modern, linear and nonlinear multivariable control theories; includes vital nonlinear topics such as limit cycle prediction and forced oscillations analysis on the basis of the describing function method and absolute stability analysis by means of the primary classical frequency-domain criteria (e.g. Popov, circle or parabolic criteria); reinforces the main themes with practical worked examples solved by a special MATLAB-based graphical user interface, as well as with problems, questions and exercises on an accompanying website. The approaches presented in Linear and Nonlinear Multivariable Feedback Control form an invaluable resource for graduate and undergraduate students studying multivariable feedback control as well as those studying classical or modern control theories. The book also provides a useful reference for researchers, experts and practitioners working in industry Linear and Nonlinear Multivariable Feedback Control:......Page 4 Contents......Page 7 Preface......Page 10 Part I Linear Multivariable Control Systems......Page 12 1.1 INTRODUCTION......Page 13 1.3 UNIFORM MIMO SYSTEMS......Page 50 1.4 NORMAL MIMO SYSTEMS......Page 61 1.5 MULTIVARIABLE ROOT LOCI......Page 84 2.1 INTRODUCTION......Page 110 2.2 GENERALIZED FREQUENCY RESPONSE CHARACTERISTICS AND ACCURACY OF LINEAR MIMO SYSTEMS UNDER SINUSOIDAL INPUTS 2.2.1 Frequency c......Page 111 2.2.2 Frequency characteristics and oscillation index of normal MIMO systems......Page 127 2.2.3 Frequency characteristics and oscillation index of uniform MIMO systems......Page 131 2.3 DYNAMICAL ACCURACY OF MIMO SYSTEMS UNDER SLOWLY CHANGING DETERMINISTIC SIGNALS 2.3.1 Matrices of error coefficient of genera......Page 134 2.3.2 Dynamical accuracy of circulant, anticirculant and uniform MIMO systems......Page 139 2.3.3 Accuracy of MIMO systems with rigid cross-connections......Page 142 2.4 STATISTICAL ACCURACY OF LINEAR MIMO SYSTEMS 2.4.1 Accuracy of general MIMO systems under stationary stochastic signals......Page 145 2.4.2 Statistical accuracy of normal MIMO systems......Page 149 2.4.3 Statistical accuracy of uniform MIMO systems......Page 151 2.4.4 Formulae for mean square outputs of characteristic systems......Page 155 2.5 DESIGN OF LINEAR MIMO SYSTEMS......Page 161 Part II Nonlinear Multivariable Control Systems......Page 180 3.1 INTRODUCTION......Page 181 3.2 MATHEMATICAL FOUNDATIONS OF THE HARMONIC LINEARIZATION METHOD FOR ONE-FREQUENCY PERIODICAL PROCESSES IN NONLINEAR MIMO SYSTE......Page 189 3.3 ONE-FREQUENCY LIMIT CYCLES IN GENERAL MIMO SYSTEMS 3.3.1 Necessary conditions for the existence and investigation of the lim......Page 192 3.3.2 Stability of the limit cycle in MIMO systems......Page 202 3.4.1 Necessary conditions for the existence and investigation of limit cycles in uniform MIMO systems......Page 207 3.4.2 Analysis of the stability of limit cycles in uniform systems......Page 213 3.5.1 Necessary conditions for the existence and investigation of limit cycles in circulant and anticirculant systems......Page 222 3.5.2 Limit cycles in uniform circulant and anticirculant systems......Page 237 4.1 INTRODUCTION......Page 244 5.1 INTRODUCTION......Page 292 5.2 ABSOLUTE STABILITY OF GENERAL AND UNIFORM MIMO SYSTEMS 5.2.1 Multidimensional Popov’s criterion......Page 295 5.2.2 Application of the Bode diagrams and Nichols plots......Page 301 5.2.3 Degree of stability of nonlinear MIMO systems......Page 304 5.3 ABSOLUTE STABILITY OF NORMAL MIMO SYSTEMS......Page 307 5.3.1 Generalized Aizerman’s hypothesis......Page 309 5.4 OFF-AXIS CIRCLE AND PARABOLIC CRITERIA OF THE ABSOLUTE STABILITY OF MIMO SYSTEMS......Page 312 5.4.1 Off-axis circle criterion......Page 313 5.4.2 Logarithmic form of the off-axis criterion of absolute stability......Page 317 5.4.3 Parabolic criterion of absolute stability......Page 321 5.5 MULTIDIMENSIONAL CIRCLE CRITERIA OF ABSOLUTE STABILITY......Page 322 5.5.1 General and normal MIMO systems......Page 324 5.5.2 Inverse form of the circle criterion for uniform systems......Page 327 5.6 MULTIDIMENSIONAL CIRCLE CRITERIA OF THE ABSOLUTE STABILITY OF FORCED MOTIONS......Page 329 Bibliography......Page 335 Index......Page 342 "Automatic feedback control systems play crucial roles in many fields, including manufacturing industries, communications, naval and space systems. At its simplest, a control system represents a feedback loop in which the difference between the idea (input) and actual (output) signals is used to modify the behavior of the system. Control systems are in our homes, computers, cars and toys. Basic control principles can also be found in areas such as medicine, biology and economics, where feedback mechanisms are ever present." "Linear and Nonlinear Multivariable Feedback Control presents a highly original, unified control theory of both linear and nonlinear multivariable (also known as multi-input multi-output (MIMO)) feedback systems as a straightforward extension of classical control theory. It shows how the classical engineering methods look in the multidimensional case and how practising engineers or researchers can apply them to the analysis and design of linear and nonlinear MIMO systems."--Jacket