Robust Control Design: A Polynomial Approach

To a large extent, our lives on this earth depend on systems that operate auto­ matically. Manysuchsystems can be found in nature and others are man made. These systems can be biological, electrical, mechanical, chemical, or ecological, to namejust a few categories. Our human body is full ofsystems whose conti­ nued automatic operation is vital for our existence. On a daily basis we come in contact with man made systems whose automatic operation ensures increa­ sed productivity, promotes economic development and improves the quality of life. A primary component that is responsible for the automatic operation of a system is a device or mechanism called the controller. In man made systems one must first design and then implement such a controller either as a piece of hardware or as software code in a computer. The safe and efficient automatic operation of such systems is testimony to the success of control theorists and practitioners over the years. This book presents new methods {or controller design. The process ofdeveloping a controller or control strategy can be dramatically improved if one can generate an appropriate dynamic model for the system under consideration. Robust control design deals with the question of how to develop such controllers for system models with uncertainty. In many cases dynamic models can be expressed in terms oflinear, time invariant differential equations or transfer functions.

Table of Contents:
1 Introduction.- 1.1 The Control Problem.- 1.2 Book Outline.- 2 System Dynamics.- 2.1 System Representations.- 2.2 Feedback Configurations.- 2.3 Stability.- 2.4 Stability of Interconnected Systems.- 2.5 D-Stability.- 2.6 Performance.- 3 Stability Tests.- 3.1 Polynomial Stability.- 3.2 The Routh-Hurwitz Stability Criterion.- 3.3 The Nyquist Stability Theorem.- 3.4 The Finite Nyquist Theorem.- 4 Uncertainty and Robust Stability.- 4.1 Uncertainty in System Models.- 4.2 Robust Stability.- 4.3 Performance as Robust Polynomial Stability.- 4.4 Robust Performance as Robust Polynomial Stability.- 4.5 Value Sets of Uncertain Polynomials.- 4.6 Rectangular Value Set Overbound.- 4.7 The Need for Robust Analysis and Design Tools.- 5 Some Robust Stability Tests.- 5.1 Polynomial Family Stability.- 5.2 Zero Exclusion Condition.- 5.3 Interval Polynomials.- 5.4 Edge Theorem.- 5.5 A Finite Frequency Test.- 5.6 The Finite Matched Phase Theorem.- 5.7 Simultaneous Polynomial Stability.- 6 The Finite Inclusions Theorem.- 6.1 Robust D-Stability.- 6.2 A Finite Number of Polynomial Families.- 6.3 Application of FIT to Robust Analysis.- 6.4 Relationship with Simultaneous Polynomial Stability.- 7 Fit Based D-Stabilization.- 7.1 FIT for Synthesis.- 7.2 FIT Based Algorithm for D-Stabilization.- 7.3 Example 1: Mass-Spring-Mass System.- 7.4 Example 2: Automatic Bus Steering System.- 7.5 Example 3: A FIT Software Package.- 7.6 Simultaneous Plant Family Stabilization.- 7.7 An SSFIT Software Package.- 7.8 Other SSFIT Synthesis Algorithms.- 8 Fit Synthesis for Robust Performance.- 8.1 Robust Performance Synthesis as Robust Polynomial Stabilization.- 8.2 A FIT based Robust Performance Synthesis Algorithm.- 8.3 Example: FIT Robust Performance Synthesis.- 9 Fit Synthesis for Robust Multiobjective Performance.- 9.1 Robust Performance Synthesis as Simultaneous Polynomial Family Stabilization.- 9.2 An SSFIT Based Robust Performance Synthesis Algorithm.- 9.3 Example: Seeker Stabilization Loop.- 10 Robust Design Via Simultaneous Polynomial Stabilization.- 10.1 Robust Stabilization as Simultaneous Polynomial Stabilization.- 10.2 Single Parameter Uncertainty.- 10.3 Multiple Parameter Uncertainty.- 10.4 The Interval Plant Family.- 10.5 Nominal Performance Synthesis via Simultaneous Polynomial Stabilization.- 10.6 Robust Performance Synthesis via Simultaneous Polynomial Stabilization.- 11 Fit for Robust Multivariable Design.- 11.1 System Representations.- 11.2 Feedback Configurations.- 11.3 Stability.- 11.4 Performance.- 11.5 Parameter Uncertainty.- 11.6 A Robust Pole Assignment Scheme.- 11.7 FIT Based Robust D-Stabilization.- 11.8 FIT Based Synthesis for Robust Performance.- 11.9 Robust Decoupling.- References.