Full Description
New results, fresh ideas and new applications in automotive and flight control systems are presented in this second edition of Robust Control. The book presents parametric methods and tools for the simultaneous design of several representative operating conditions and several design specifications in the time and frequency domains. It also covers methods for robustness analysis that guarantee the desired properties for all possible values of the plant uncertainty. A lot of practical application experience enters into the case studies of driver support systems that avoid skidding and rollover of cars, automatic car steering systems, flight controllers for unstable aircraft and engine-out controllers. The book also shows the historic roots of the methods, their limitations and research needs in robust control.
Contents
1 Parametric Plants and Controllers.- 1.1 State Space Model, Linearization, Eigenvalues.- 1.2 The Leverrier-Faddejew Algorithm.- 1.3 Transfer Function.- 1.4 Robust Controllability, Observability, Feedback Structures.- 1.5 Output Feedback, Closed-loop Characteristic Polynomial.- 1.6 Hurwitz-stability, Stabilizing Controller Parameters.- 1.7 Controller Structures for Partially Known Inputs.- 2 Hurwitz-stability Boundary Crossing and Parameter Space Approach.- 2.1 Critical Stability Conditions.- 2.2 The Parameter Space Approach.- 2.3 Pole Placement.- 2.4 Sequential Pole Shifting.- 2.5 Singular Frequencies.- 2.6 Hurwitz-stability Regions for PID-controllers.- 2.7 Hurwitz-stability Regions for a Compensator or Plant Subpolynomial.- 3 Eigenvalue Specifications.- 3.1 Poles, Zeros and Step Responses.- 3.2 Root Sets, Gamma-stability.- 3.3 Physical Meaning of Closed-loop Poles.- 3.4 Remarks on Existence of Robust Controllers.- 3.5 Further Potential of the Parameter Space Approach.- 4 Gamma-boundary Mapping into Parameter Space.- 4.1 Algebraic Problem Formulation.- 4.2 Parameter Space Mapping.- 4.3 Generalized Singular Frequencies.- 4.4 Gamma-stable PID-control.- 4.5 Non-linear Coefficient Functions.- 5 Frequency Domain Analysis and Design.- 5.1 Frequency Loci Specifications (Theta-stability).- 5.2 Mapping of Frequency Loci Margins into Parameter Space.- 5.3 Frequency Response Magnitude Specifications (Beta-stability).- 5.4 Mapping of Frequency Response Magnitude Specifications into Parameter Space.- 5.5 MIMO Systems.- 6 Case Studies in Car Steering.- 6.1 Tires, Braking, and Steering.- 6.2 The Two Steering Tasks.- 6.3 The Non-linear Single-track Model and its Robust Unilateral Decoupling.- 6.4 The Linearized Single-track Model.- 6.5 Linear Analysis of Robust Decoupling.- 6.6 Skidding Avoidance Based on Robust Decoupling.- 6.7 Skidding Avoidance Based on the Disturbance Observer.- 6.8 Rollover Avoidance.- 6.9 Patents.- 6.10 Automatic Car Steering.- 7 Case Studies in Flight Control.- 7.1 Aircraft Load Alleviation in case of an Engine Out by Robust Yaw-lateral Decoupling.- 7.2 Robust and Fault-tolerant Gamma-stabilization of an F4-E.- 7.3 Large Envelope Flight Control of a High Performance Aircraft.- 8 Robustness Analysis by Value Sets.- 8.1 Mikhailov Plot.- 8.2 Value Sets and Zero Exclusion.- 8.3 Interval Polynomials, Kharitonov Theorem.- 8.4 Affine Coefficients: Edge Theorem.- 8.5 Edge Theorem for Gamma-stability.- 8.6 Singularity of Value Sets.- 9 Value Sets for Non-linear Coefficient Functions.- 9.1 A Warning Example.- 9.2 Desoer Mapping Theorem.- 9.3 Tree-structured Value Set Construction.- 9.4 Computer-aided Execution of Value Set Operations.- 9.5 Tree-structured Transfer Functions.- 9.6 The Stability Profile.- 9.7 Synopsis of Parametric Robustness Analysis.- 10 The Stability Radius.- 10.1 Tsypkin-Polyak Loci.- 10.2 Affine Dependence: The Largest Hypersphere in Parameter Space.- 10.3 Polynomial Dependence.- 11 Robustness of Sampled-data Control Systems.- 11.1 Plant and Controller Discretization.- 11.2 Discrete-time Controllers.- 11.3 Eigenvalue Specifications.- 11.4 Classical Stability Tests.- 11.5 Edge Test.- 11.6 Construction of Value Sets.- 11.7 Real Radius of Stability.- 11.8 Single-loop Feedback Structures.- 11.9 Circle Stability.- A Polynomials and Polynomial Equations.- B PARADISE: Parametric Robustness Analysis and Design Interactive Software Environment.
