Multivariable Feedback Control: Analysis and Design, Second Editionpresents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems.  Focusing on practical feedback control and not on system theory in general, this book provides the reader with insights into the opportunities and limitations of feedback control.

Taking into account the latest developments in the field, this fully revised and updated second edition:

• features a new chapter devoted to the use of linear matrix inequalities (LMIs);
• presents current results on fundamental performance limitations introduced by RHP-poles and RHP-zeros;
• introduces updated material on the selection of controlled variables and self-optimizing control;
• provides simple IMC tuning rules for PID control;
• covers additional material including unstable plants, the feedback amplifier, the lower gain margin and a clear strategy for incorporating integral action into LQG control;
• includes numerous worked examples, exercises and case studies, which make frequent use of Matlab and the new Robust Control toolbox.

Multivariable Feedback Control: Analysis and Design, Second Editionis an excellent resource for advanced undergraduate and graduate courses studying multivariable control. It is also an invaluable tool for engineers who want to understand multivariable control, its limitations, and how it can be applied in practice. The analysis techniques and the material on control structure design should prove very useful in the new emerging area of systems biology.

Reviews of the first edition:

“Being rich in insights and practical tips on controller design, the book should also prove to be very beneficial to industrial control engineers, both as a reference book and as an educational tool.” Applied Mechanics Reviews

“In summary, this book can be strongly recommended not only as a basic text in multivariable control techniques for graduate and undergraduate students, but also as a valuable source of information for control engineers.” International Journal of Adaptive Control and Signal Processing

Intended to serve as a textbook for an introductory graduate or advanced undergraduate course in multivariable control, this work by Skogestad (Norwegian U. of Science and Technology, Norway) and Posthlewaite (U. of Leicester, UK) provides treatment for linear systems in order to keep the theory and mathematics at a relatively simple level. Important topics covered include classical frequency domain methods, analysis of directions in multivariable systems using the singular value decomposition, input-output controllability (inherent control limitations in the plant), model uncertainty and robustness, performance requirements, methods for controller design and model reduction, control structure selection and decentralized control, and linear matrix inequalities. Prerequisite are an introductory course in classical single-input single-output control and some elementary knowledge of matrices and linear algebra. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Thoroughly updated, this second edition of Multivariable Feedback Control provides an ideal introduction to the analysis and design of robust multivariable control. Model uncertainty, multivariable systems, robustness, interactions between design and control, decentralized control, control structures, model reduction, and an overview of techniques for controller design are among the topics discussed. Parts of the book can be used for self-study and provide an appropriate background for a number of linear control courses at both undergraduate and graduate levels. The book includes numerous worked examples.

PREFACE.

1 INTRODUCTION.

1.1 The process of control system design.

1.2 The control problem.

1.3 Transfer functions.

1.4 Scaling.

1.5 Deriving linear models.

1.6 Notation.

2 CLASSICAL FEEDBACK CONTROL.

2.1 Frequency response.

2.2 Feedback control.

2.3 Closed-loop stability.

2.4 Evaluating closed-loop performance.

2.5 Controller design.

2.6 Loop shaping.

2.7 IMC design procedure and PID control for stable plants.

2.8 Shaping closed-loop transfer functions.

2.9 Conclusion.

3 INTRODUCTION TO MULTIVARIABLE CONTROL.

3.1 Introduction.

3.2 Transfer functions for MIMO systems.

3.3 Multivariable frequency response analysis.

3.4 Relative Gain Array(RGA).

3.5 Control of multivariable plants.

3.6 Introduction to multivariable RHP-zeros.

3.7 Introduction to MIMO robustness.

3.8 General control problem formulation.

3.9 Additional exercises.

3.10 Conclusion.

4 ELEMENTS OF LINEAR SYSTEM THEORY.

4.1 System descriptions.

4.2 State controllability and state observability.

4.3 Stability.

4.4 Poles.

4.5 Zeros.

4.6 Some important remarks on poles and zeros.

4.7 Internal stability of feedback systems.

4.8 Stabilizing controllers.

4.9 Stability analysis in the frequency domain.

4.10 System norms.

4.11 Conclusion.

5 LIMITATIONS ON PERFORMANCE IN SISO SYSTEMS.

5.1 Input-Output Controllability.

5.2 Fundamental limitations on sensitivity.

5.3 Fundamental limitations: Bounds on peaks.

5.4 Perfect control and plant inversion.

5.5 Ideal ISE optimal control.

5.6 Limitations imposed by time delays.

5.7 Limitations imposed by RHP-zeros.

5.8 Limitations imposed b y phase lag.

5.9 Limitations imposed by unstable(RHP) poles.

5.10 Performance requirements imposed by disturbances and commands.

5.11 Limitations imposed by input constraints.

5.12 Limitations imposed by uncertainty.

5.13 Summary: Controllability analysis with feedback control.

5.14 Summary: Controllability analysis with feed forward control.

5.15 Applications of controllability analysis.

5.16 Conclusion.

6 LIMITATIONS ON PERFORMANCE IN MIMO SYSTEMS.

6.1 Introduction.

6.2 Fundamental limitations on sensitivity.

6.3 Fundamental limitations: Bounds on peaks.

6.4 Functional controllability.

6.5 Limitations imposed by time delays.

6.6 Limitations imposed by RHP-zeros.

6.7 Limitations imposed by unstable(RHP) poles.

6.8 Performance requirements imposed by disturbances.

6.9 Limitations imposed by input constraints.

6.10 Limitations imposed by uncertainty.

6.11 MIMO Input-output controllability.

6.12 Conclusion.

7 UNCERTAINTY AND ROBUSTNESS FOR SISO SYSTEMS.

7.1 Introduction to robustness.

7.2 Representing uncertainty.

7.3 Parametric uncertainty.

7.4 Representing uncertainty in the frequency domain.

7.5 SISO Robust stability.

7.6 SISO Robust performance.

7.7 Additional exercises.

7.8 Conclusion.

8 ROBUST STABILITY AND PERFORMANCE ANALYSIS FOR MIMO

SYSTEMS.

8.1 General control configuration with uncertainty.

8.2 Representing uncertainty.

8.3 Obtaining _, _ and _ .

8.4 Definitions of robust stability and robust performance.

8.5 Robust stability of the__-structure.

8.6 RS for complex unstructured uncertainty.

8.7 Rs with structured uncertainty : Motivation.

8.8 The structured singular value.

8.9 Robust stability with structured uncertainty.

8.10 Robust performance.

8.11 Application: RP with input uncertainty.

8.12 _-synthesis and __-iteration.

8.13 Further remarks on _.

8.14 Conclusion.

9 CONTROLLER DESIGN.

9.1 Trade-offs in MIMO feedback design.

9.2 LQG control.

9.3 __ and __ control.

9.4 __ loop-shaping design.

9.5 Conclusion.

10 CONTROL STRUCTURE DESIGN.

10.1 Introduction.

10.2 Optimal operation and control.

10.3 Selection of primary controlled outputs.

10.4 Regulatory control layer.

10.5 Control configuration elements.

10.6 Control configurations: Decentralized feedback control.

10.7 Conclusion.

11 MODEL REDUCTION.

11.1 Introduction.

11.2 Truncation and residualization.

11.3 Balanced realizations.

11.4 Balanced truncation and balanced residualization.

11.5 Optimal Hankel norm approximation.

11.6 Reduction of unstable models.

11.7 Model reduction using Matlab.

11.8 Two practical examples.

11.9 Conclusion.

12 LINEAR MATRIX INEQUALITIES.

12.1 Introduction to LMI problems.

12.2 Types of LMI problems.

12.3 Tricks in LMI problems.

12.4 Case study: anti-windup compensator synthesis.

12.5 Conclusion.

13 CASE STUDIES.

13.1 Introduction.

13.2 Helicopter control.

13.3 Aero-engine control.

13.4 Distillation process.

13.5 Conclusion.

A MATRIX THEORY AND NORMS.

A.1 Basics.

A.2 Eigen values and eigen vectors.

A.3 Singular Value Decomposition.

A.4 Relative Gain Array.

A.5 Norms.

A.6 All pass factorization of transfer function matrices.

A.7 Factorization of the sensitivity function.

A.8 Linear fractional transformations.

B PROJECTWORK and SAMPLE EXAM.

B.1 Project work.

B.2 Sample exam.

BIBLIOGRAPHY.

INDEX.