Jeffrey Burl,
Jeffrey B. Burl
Pearson Education
e druk, 1999
9780201808681
Linear Optimal Control
Specificaties
Paperback, blz.
|
Engels
Pearson Education |
e druk, 1999
ISBN13: 9780201808681
Rubricering
Verwachte levertijd ongeveer 9 werkdagen
Samenvatting
Linear Optimal Control: H2 and Hà Methods is a reader-friendly book that features recent research results on robustness, Hà control, and ...m- synthesis. Linear Optimal Control combines these new results with previous work on optimal control to form a complete picture of control system design and analysis.
A comprehensive book, Linear Optimal Control covers the analysis of control systems, H2 (linear quadratic Gaussian), and Hà to a degree not found in many similar books. Its logical organization and its focus on establishing a solid grounding in the basics be fore tackling mathematical subtleties make Linear Optimal Control an ideal learning tool.
Back Cover
A comprehensive book, Linear Optimal Control covers the analysis of control systems, H2 (linear quadratic Gaussian), and to a degree not found in many texts. Its logical organization and its focus on establishing a solid grounding in the basics before tackling mathematical subtleties make Linear Optimal Control an ideal teaching text. The book's structure also makes it suitable for two-semester, one-semester, and two-quarter courses, as well as for professional use.
Features:
Provides computer projects in each chapter to challenge readers with "what if" questions concerning the choice of cost functions and specifications. Simplifies results and derivations by treating special cases whenever possible without compromising the clarity of the results and methods. Familiarizes readers with the use of CAD tools for robust optimal controller design; software use is integrated throughout the book, and is included in almost every example. Offers a case study that compares the LQG and the µ-synthesis design methodologies and provides guidelines on when to apply which method. Presents LQG and control within a common framework— uses variational methods for both solutions.
Specificaties
Inhoudsopgave
<br> <br> List of Symbols. <br> <br> <br> 1. Introduction. <br> <p> </p> <div style="margin-left: 0.2in;"> The Fundamental Objectives of Feedback Control. A Brief History of Modern Controller Design. Scope and Objectives. Organization. References </div> <p></p> <p> 1. ANALYSIS OF CONTROL SYSTEMS. </p> <div style="margin-left: 0.2in;"> 2. Multivariable Linear Systems. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> The Continuous-Time State Model. The Discrete-Time State Model and Simulation. Transfer Functions. Frequency Response. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Frequency Response for SISO Systems. Frequency Response for MIMO Systems. The Singular Value Decomposition. The Principle Gains. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Poles, Zeros, and Modes. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Polesand Zeros for Siso Systems. Poles and Zeros for Mimo Systems. Modes. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Stability. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Internal Stability. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Change of Basis: Similarity Transformations. Controllability and Observability. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Controllability. Observability. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Observer Feedback. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> State Feedback. Observers. The Deterministic Separation Principle. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 3. Vector Random Processes. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> The Description of Vector Random Processes. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Second Moment Analysis. Two Random Processes. Wide Sense Stationarity. The Spectral Density. Gaussian Random Processes. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> White Noise. Linear Systems with Random Inputs. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Output Correlation Function. The Output Spectral Density. Approximation of Real Inputs by White Noise. Simulation of Systems with White Noise Inputs. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Colored Noise via Shaping Filters. Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 4. Performance. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> General Models of Feedback Control Systems. Transient Performance Analysis. Tracking Performance Analysis. Disturbance Rejection Analysis. Cost Functions and Norms. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Norms. Quadratic Cost Functions. Cost Functions for Systems with Random Inputs. The System 2-Norm Cost Function. The System Cost Function. Weighting Functions for System Norms. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 5. Robustness. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Internal Stability of Feedback Systems. The SISO Nyquist Stability Criterion. Gain and Phase Margins for SISO Systems. Unstructured Uncertainty. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Unstructured Uncertainty Models. Stability Robustness Analysis. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Structured Uncertainty. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Structured Uncertainty Model. The Structured Singular Value and Stability Robustness. Bounds on the Structured Singular Value. Additional Properties of the Structured Singular Value. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Performance Robustness Analysis Using The SSV. Summary. References. Exercises. Computer Exercises. </div> <p></p> <p> 2. H2 CONTROL. </p> <div style="margin-left: 0.2in;"> 6. The Linear Quadratic Regulator. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Optimization. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Variations. Lagrange Multipliers. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Linear Quadratic Regulator. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Hamiltonian Equations. The Riccati Equation. Computation of the Optimal Cost. Selection of the Weighting Matrices. Perspective. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Steady-State Linear Quadratic Regulator. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Computation of the Feedback Gain Matrix. Existence and Uniqueness. Robustness. The Closed Loop Poles. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Stochastic Regulator. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Cost Computation. H2 Optimal Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 7. The Kalman Filter. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Linear Minimum Mean Square Estimation. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Orthogonality Principle. The Optimal Estimation Error. Updating an Estimate Given New Data. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Kalman Filter. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Kalman Filter Equation. The Kalman Gain Equations. Application Notes. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Steady-State Kalman Filter. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> H2 Optimal Estimation. Duality. Computation of the Kalman Gain. Existence and Uniqueness. Robustness. The Kalman Filter Poles. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Non White Noise Inputs. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Non White Plant Noise. Non White Measurement Noise. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Exercises. Computer Exercises </div> <p></p> <div style="margin-left: 0.2in;"> 8. Linear Quadratic Gaussian Control. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Combined Estimation and Control: LQG Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Performance. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Steady-State LQG Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Performance. Robustness. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Loop Transfer Recovery. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Asymptotic Properties. Robustness to Output Multiplicative Perturbations. Frequency Shaped LTR. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Tracking System Design. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Tracking Constant Reference Inputs. Tracking Time-Varying Reference Inputs. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Designing for Disturbance Rejection. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Feedforward Disturbance Cancellation. Integral Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Frequency Shaped Control via LQG Methods. Equivalence of LQG and H2 Optimal Control. Summary. References. Exercises. Computer Exercises. </div> <p></p> <p> 3. CONTROL. </p> <div style="margin-left: 0.2in;"> 9. Full Information Control and Estimation. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Differential games. Full Information Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Hamiltonian Equations. The Riccati Equation. The Value of the Objective Function. Steady-State Full Information Control. Generalizations. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Estimation. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Adjoint System. Finite-Time Optimal Estimation. Steady-State Optimal Estimation. Generalizations. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 10. Output Feedback. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Controller Structure. Finite-Time Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> An Alternative Estimator Riccati Equation. Summary. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Steady-State Control. Application of Control. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Performance Limitations. Integral Control. Designing for Robustness. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> µ-Synthesis. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> D-Scaling and the Structured Singular Value. D-K- Iteration. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Comparison of Design Methodologies. Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> 11. Controller Order Reduction. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Perturbation Analysis. Frequency Weighting. Removing Poles and Zeros from SISO Controllers. Balanced Truncation. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Balanced Realization. Balanced Truncation. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Summary. References. Exercises. Computer Exercises. </div> <p></p> <div style="margin-left: 0.2in;"> Appendix: Mathematical Notes. </div> <br> <p> </p> <div style="margin-left: 0.4in;"> Calculus of Vectors and Matrices. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Calculus of Vector-Matrix Functions of a Scalar. Derivatives of Vector-Matrix Products. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Useful Relations from Linear Algebra. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Positive Definite and Positive Semidefinite Matrices. Relations Involving the Trace. Determinants of Block Matrices. The Matrix Inversion Lemma. Block Matrix Inversion. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> The Singular Value Decomposition. Spectral Theory of Matrices. L2 Stability. Change of Basis (Time-Varying Transformations). Controllability and Observability Grammians. Useful Relations Involving (I+GK) and (I+KG). </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Equivalence of the Determinants. The Push Through Theorem. Miscellaneous. </div> <p></p> <p> </p> <div style="margin-left: 0.4in;"> Properties of the System. Bound on the System. The Adjoint System. The Kalman Filter Innovations. The Phase-Gain Relationship. References. </div> <p></p>