Gu D-W., Petkov P.H., Konstantinov M.M. Robust Control Design with MatLAB

2nd ed. London: Springer-Verlag, 2005, 2013. 472 p. — ISBN: 978-1-4471-4681-0, ISBN: 978-1-4471-4682-7 (eBook).Robust Control Design with MatLAB (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MatLAB Robust Control Toolbox 3, Control System Toolbox and Simulink. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; new Part II forming a tutorial on Robust Control Toolbox 3; fresh design problems including the control of a two-rotor dynamic system; and end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/ISBN: include: M-files developed with MatLAB help in understanding the essence of robust control system design portrayed in text-based examples; MDL-files for simulation of open- and closed-loop systems in Simulink; and a solutions manual available free of charge to those adopting Robust Control Design with MatLAB as a textbook for courses. Robust Control Design with MatLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.Basic Methods and Theory.Control-System Representations.
System Stabilities.
Coprime Factorization and Stabilizing Controllers.
Signals and System Norms.
Vector Norms and Signal Norms.
System Norms.
Modeling of Uncertain Systems.
Unstructured Uncertainties.
Parametric Uncertainty.
Linear Fractional Transformations.
Structured Uncertainties.
Robust Design Specifications.
Small-Gain Theorem and Robust Stabilization.
Performance Considerations.
Structured Singular Values.
H∞ Design.
Mixed Sensitivity H∞ Optimization.
Degree-of-Freedom H∞ Design.
H∞ Suboptimal Solutions.
Solution Formulas for Normalized Systems.
Solution to S-over-KS Design.
The Case of D22 =.
Normalization Transformations.
Direct Formulas for H∞ Suboptimal Central Controller.
Formulas for Discrete-Time Cases.
H∞ Loop-Shaping Design Procedures.
Robust Stabilization Against Normalized Coprime Factor Perturbations.
Loop-Shaping Design Procedures.
Formulas for the Discrete-Time Case.
Normalized Coprime Factorization of Discrete-Time Plant.
Robust Controller Formulas.
The Strictly Proper Case.
OntheThreeDARESolutions.
A Mixed Optimization Design Method with LSDP.
μ-Analysis and Synthesis.
Consideration of Robust Performance.
μ-Synthesis: D–K Iteration Method.
μ-Synthesis: μ–K Iteration Method.
Lower-Order Controllers.
Absolute-Error Approximation Methods.
Balanced Truncation Method.
Singular Perturbation Approximation.
Hankel-Norm Approximation.
Reduction via Fractional Factors.
Fractional Balanced Truncation (FBT) Method.
Fractional Singular Perturbation Approximation (FSPA) Method.
Relative-Error Approximation Methods.
Frequency-Weighted Approximation Methods.
Frequency-Weighted Balanced Truncation (FWBT).
Frequency-Weighted Singular Perturbation Approximation(FWSPA).
Frequency-Weighted Moduli Truncation Method (FWMT).
LMI Approach.
Basics About LMI.
Control Problems Using LMI.
Lyapunov Stability Criterion.
Stabilization by State Feedback.
Computation of L2 Norm.
Computation of H∞ Norm.
Formulation of LQR in LMI.
A Few More Properties Concerning LMI.
Congruence Transformation.
Schur Complements for Nonstrict Inequalities.
Projection and Finsler’s Lemmas.
The S-Procedure for Quadratic Functions.
Dualization Lemma.
Introduction to Robust Control Toolbox v3.
Building Uncertain Models.
LTI Models.
Structured Uncertainty Models.
Uncertain Real Parameters.
Uncertain State-Space Systems.
Properties of Uncertain Systems.
Other Functions to Build Uncertain Models.
Decomposing Uncertain Objects.
Building Uncertain Models Using iconnect and sysic.
Unstructured Uncertainty Models.
Models with Additive Uncertainty.
Models with Multiplicative Uncertainty.
Unmodeled Dynamics.
Multivariable Plants with Unstructured Uncertainty.
Exercises.
Robust Stability and Performance.
Robust Stability Analysis.
Robust Performance Analysis.
Worst-Case Gain.
Exercises.
H∞ Design.
H∞ Loop-Shaping Design.
Mixed Sensitivity Design.
Other Versions of H∞ Design.
H∞ Control with Models.
Two-Degree-of-Freedom H∞ Control.
Exercises.
μ-Synthesis.
The μ-Synthesis Problem.
μ-Synthesis by D–K Iterations.
Versions of μ-Synthesis.
μ-Synthesis with Model.
μ-Synthesis of 2-Degree-of-Freedom Controller.
Practical Aspects of μ-Analysis and μ-Synthesis.
Exercises.
Analysis and Design of Parameter-Dependent Systems.
Representation of Parameter-Dependent Systems.
SYSTEM Matrix.
Affine Parameter-Dependent Models.
Polytopic Models.
Analysis of Parameter-Dependent Systems.
Gain Scheduling Design for Parameter-Dependent Systems.
Exercises.
Design Examples.
Robust Control of a Hard Disk Drive.
Hard Disk Drive Servo System.
Derivation of Uncertainty Model.
Closed-Loop System Design Specifications.
Nominal Performance.
Robust Stability.
Robust Performance.
System Interconnections.
Controller Design in Continuous-Time.
μ-Design.
H∞ Design.
H∞ Loop-Shaping Design.
Comparison of Designed Controllers.
Controller-Order Reduction.
Design of Discrete-Time Controller.
Nonlinear System Simulation.
Conclusions.
Notes and References.
A Triple Inverted Pendulum Control System Design.
System Description.
Modeling of Uncertainties.
Design Specifications.
Robust Stability.
Nominal Performance.
Robust Performance.
System Interconnections.
H∞ Design.
μ-Synthesis.
Nonlinear System Simulation.
Conclusions.
Notes and References.
Robust Control of a Distillation Column.Dynamic Model of the Distillation Column.
Uncertainty Modeling.
Closed-Loop System Performance Specifications.
Open-Loop and Closed-Loop System Interconnections.
Controller Design.
Loop-Shaping Design.
μ-Synthesis.
Nonlinear System Simulation.
Conclusions.
Notes and References.
Robust Control of a Flexible-Link Manipulator.
Dynamic Model of the Flexible Manipulator.
A Linear Model of the Uncertain System.
System Performance Specifications.
System Interconnections.
Controller Design and Analysis.
Nonlinear System Simulations.
Conclusions.
Notes and References.
Robust Control of a Twin-Rotor Aerodynamic System.
Twin-Rotor Aerodynamic System.
Nonlinear System Model.
Linearized System Model.
Uncertainty Modeling.
Closed-Loop System Performance Requirements.
Robust Stability.
Nominal Performance.
Robust Performance.
System Interconnections.
μ-Synthesis.
Nonlinear System Simulation.
Experimental Results.
Conclusions.
Notes and References.
Robust Control of Self-balancing Two-Wheeled Robot.Uncertain Model of the Two-Wheeled Robot.
Design of Robust Controller.
Closed-Loop System Properties.
Experimental Results.
Conclusions.
Notes and References.