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Linear and Nonlinear Multivariable Feedback Control: A Classical Approach



Linear and Nonlinear Multivariable Feedback Control: A Classical Approach

Oleg Gasparyan

ISBN: 978-0-470-06104-6 March 2008 354 Pages


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

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Part I Linear Multivariable Control System.

1 Canonical representations and stability analysis of linear MIMO systems.

1.1 Introduction.

1.2 General linear square MIMO systems.

1.3 Uniform MIMO systems.

1.4 Normal MIMO systems.

1.5 Multivariable root loci.

2 Performance and design of linear MIMO systems.

2.1 Introduction.

2.2 Generalized frequency response characteristics and accuracy of linear MIMO systems under sinusoidal inputs.

2.3 Dynamical accuracy of MIMO systems under slowly changing deterministic signals.

2.4 Statistical accuracy of linear MIMO systems.

2.5 Design of linear MIMO systems.

Part II Nonlinear multivariable control systems.

3 Study of one-frequency self-oscillation in nonlinear harmonically linearized MIMO systems.

3.1 Introduction.

3.2 Mathematical foundations of the harmonic linearization method for one-frequency periodical processes in nonlinear MIMO systems.

3.3 One-frequency limit cycles in general MIMO systems.

3.4 Limit cycles in uniform MIMO systems.

3.5 Limit cycles in circulant and anticirculant MIMO systems.

4 Forced oscillation and generalized frequency response characteristics of nonlinear MIMO systems.

4.1 Introduction.

4.2 Nonlinear general MIMO systems.

4.3 Nonlinear uniform MIMO systems.

4.4 Forced oscillations and frequency response characteristics along the canonical basis axes of nonlinear circulant and anticirculant systems.

4.5 Design of nonlinear MIMO systems.

5 Absolute stability of nonlinear MIMO systems.

5.1 Introduction.

5.2 Absolute stability of general and uniform MIMO systems.

5.3 Absolute stability of normal MIMO systems.

5.4 Off-axis circle and parabolic criteria of the absolute stability of mimo systems.

5.5 Multidimensional circle criteria of absolute stability.

5.6 Multidimensional circle criteria of the absolute stability of forced motions.