S.Skogestad and I.Postlethwaite, "Multivariable feedback control", Wiley, 1996.

Comments about the chapters

1. INTRODUCTION

   Chapter 1 is mainly intended as background material. Important topics are notation and scaling (!!).

2. CLASSICAL FEEDBACK CONTROL

   Chapter 2 is mainly intended to provide a refresher of classical SISO control, including understanding loopshaping in the frequency domain. I Section 2.7 on weighted sensitivity should be read carefully as it provides a background for some of the later chapters.

3. INTRODUCTION TO MULTIVARIABLE CONTROL

   Chapter 3 is important and gives a tutorial introduction to MIMO control systems.

4. ELEMENTS OF LINEAR SYSTEM THEORY

   Covers Coprime factorization, State controllability and observability, Stability, Zeros, Internal stability, Nyquist stability

   Norms. H2-norm. H-infinity-norm. Hankel norm.

   It is recommended to do the exercises in this chapters so you are sure you have a working knowledge of these topics.

5. LIMITATIONS ON PERFORMANCE IN SISO SYSTEMS

   Chapter 5 and 6 discusses inherent control limitations imposed by the plan G(s) which cannot be overcome by any controller.

6. LIMITATIONS ON PERFORMANCE IN MIMO SYSTEMS

   Note the similarity with Chapter 6. This is important material, but again try not to get lost in the details. Try to make a table of the main results in the two chapters - also to highlight the difference between MIMO and SISO. It is recommended that each reader makes such a table (you probably the learn the most from doing it yourself).

7. UNCERTAINTY AND ROBUSTNESS FOR SISO SYSTEMS

8. ROBUST STABILITY AND PERFORMANCE ANALYSIS

   Chapters 7 and 8 discuss uncertainty (how to model) and how to test if the system is robust with respect to the uncertainty. An important tool is the structured singular value. Most of the material in this chapter will be covered.

   Note that there are two main approaches to get a robust design:

   1. Make it robust to some general class of uncertainty. For SISO systems one may consider GM and PM or the peak of S or T. For MIMO systems the normalized coprime uncertainty provides a good general class, and the corresponding Glover-McFarlane H-infinity loopshaping design has proved useful in many applications.
   2. Model the uncertainty in detail and make the system robust with respect to it. This may require a large effort both in terms if uncertainty modelling (in particular for parametric uncertainty) and in terms of analysis and design (which involves the structured singular value).
   In pratice, one will therefore often start with approach 1, and switch to approach 2 if the resulting control performance is not satisfactory.

9. CONTROLLER DESIGN

   Chapter 9 discusses controller design, includimng tradtional LQG and various H-infinity methods.

10. CONTROL STRUCTURE DESIGN

    Chapter 10 discusses control structure design and decentralized control.

11. MODEL REDUCTION

    Chapter 11 discusses model reduction.

12. CASE STUDIES

    Chapter 12 provides three case studies.

13. APPENDIX A: MATRIX THEORY AND NORMS

    Appendix A gives an overview of matrix theory.

14. APPENDIX B: PROJECT WORK and SAMPLE EXAM

    Appendix B gives the text for the project work.