Multivariable Feedback Control: Analysis and Design – Sigurd Skogestad, Ian Postlethwaite – 2nd Edition

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.

APPENDIX 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.

APPENDIX B: PROJECTWORK and SAMPLE EXAM.
B.1 Project work.
B.2 Sample exam.