High Performance Control

The engineering objective of high performance control using the tools of optimal control theory, robust control theory, and adaptive control theory is more achiev­ able now than ever before, and the need has never been greater. Of course, when we use the term high peiformance control we are thinking of achieving this in the real world with all its complexity, uncertainty and variability. Since we do not expect to always achieve our desires, a more complete title for this book could be "Towards High Performance Control". To illustrate our task, consider as an example a disk drive tracking system for a portable computer. The better the controller performance in the presence of eccen­ tricity uncertainties and external disturbances, such as vibrations when operated in a moving vehicle, the more tracks can be used on the disk and the more memory it has. Many systems today are control system limited and the quest is for high performance in the real world.

1 Performance Enhancement.- 1.1 Introduction.- 1.2 Beyond Classical Control.- 1.3 Robustness and Performance.- 1.4 Implementation Aspects and Case Studies.- 1.5 Book Outline.- 1.6 Study Guide.- 1.7 Main Points of Chapter.- 1.8 Notes and References.- 2 Stabilizing Controllers.- 2.1 Introduction.- 2.2 The Nominal Plant Model.- 2.3 The Stabilizing Controller.- 2.4 Coprime Factorization.- 2.5 All Stabilizing Feedback Controllers.- 2.6 All Stabilizing Regulators.- 2.7 Notes and References.- 3 Design Environment.- 3.1 Introduction.- 3.2 Signals and Disturbances.- 3.3 Plant Uncertainties.- 3.4 Plants Stabilized by a Controller.- 3.5 State Space Representation.- 3.6 Notes and References.- 4 Off-line Controller Design.- 4.1 Introduction.- 4.2 Selection of Performance Index.- 4.3 An LQG/LTR Design.- 4.4 H? Optimal Design.- 4.5 An ?1 Design Approach.- 4.6 Notes and References.- 5 Iterated and Nested (Q, S) Design.- 5.1 Introduction.- 5.2 Iterated (Q, S) Design.- 5.3 Nested (Q, S) Design.- 5.4 Notes and References.- 6 Direct Adaptive- Q Control.- 6.1 Introduction.- 6.2 Q-Augmented Controller Structure: Ideal Model Case.- 6.3 Adaptive-Q Algorithm.- 6.4 Analysis of the Adaptive-Q Algorithm. Ideal Case.- 6.5 Q-augmented Controller Structure: Plant-model Mismatch.- 6.6 Adaptive Algorithm.- 6.7 Analysis of the Adaptive-Q Algorithm: Unmodeled Dynamics Situation.- 6.8 Notes and References.- 7 Indirect (Q, S) Adaptive Control.- 7.1 Introduction.- 7.2 System Description and Control Problem Formulation.- 7.3 Adaptive Algorithms.- 7.4 Adaptive Algorithm Analysis: Ideal case.- 7.5 Adaptive Algorithm Analysis: Nonideal Case.- 7.6 Notes and References.- 8 Adaptive-Q Application to Nonlinear Systems.- 8.1 Introduction.- 8.2 Adaptive-Q Method for Nonlinear Control.- 8.3 Stability Properties.-8.4 Learning-Q Schemes.- 8.5 Notes and References.- 9 Real-time Implementation.- 9.1 Introduction.- 9.2 Algorithms for Continuous-time Plant.- 9.3 Hardware Platform.- 9.4 Software Platform.- 9.5 Other Issues.- 9.6 Notes and References.- 10 Laboratory Case Studies.- 10.1 Introduction.- 10.2 Control of Hard-disk Drives.- 10.3 Control of a Heat Exchanger.- 10.4 Aerospace Resonance Suppression.- 10.5 Notes and References.- A Linear Algebra.- A.1 Matrices and Vectors.- A.2 Addition and Multiplication of Matrices.- A.3 Determinant and Rank of a Matrix.- A.4 Range Space, Kernel and Inverses.- A.5 Eigenvalues, Eigenvectors and Trace.- A.6 Similar Matrices.- A.7 Positive Definite Matrices and Matrix Decompositions.- A.8 Norms of Vectors and Matrices.- A.9 Differentiation and Integration.- A.10 Lemma of Lyapunov.- A.11 Vector Spaces and Subspaces.- A.12 Basis and Dimension.- A.13 Mappings and Linear Mappings.- B Dynamical Systems.- B.1 Linear Dynamical Systems.- B.2 Norms, Spaces and Stability Concepts.- B.3 Nonlinear Systems Stability.- C Averaging Analysis For Adaptive Systems.- C.1 Introduction.- C.2 Averaging.- C.3 Transforming an adaptive system into standard form.- C.4 Averaging Approximation.- References.