Control Systems Theory and Applications for Linear Repetitive Processes

Transcription

1 Eric Rogers, Krzysztof Galkowski, David H. Owens Control Systems Theory and Applications for Linear Repetitive Processes Springer

2 Contents 1 Examples and Representations Examples and Control Problems Long-wall Coal Cutting Metal Rolling as a Repetitive Process A General Abstract Representation D and 1D Discrete Linear Systems Equivalent Models D Transfer-Function and Related Representations 33 2 Stability Theory, Tests and Performance Bounds Asymptotic Stability Stability Along the Pass Stability Tests and Performance Bounds Stability of Discrete Processes via 2D Spectral Methods 78 3 Lyapunov Equations for Discrete Processes The 1D Lyapunov Equation The 2D Lyapunov Equation Stability and the 2D Lyapunov Equation An Alternative 2D Lyapunov Equation Solving the 2D Lyapunov Equation Lyapunov Equations for Differential Processes The 1D Lyapunov Equation The 2D Lyapunov Equation Differential Processes with Dynamic Boundary Conditions Robustness Discrete Processes Background Methods for Exactly Calculating the Stable Perturbation Bound Nonnegative Matrix Theory Approach LMI Based Approaches Discrete Processes Differential Processes 168

3 XII Contents 6 Controllability, Observability, Poles and Zeros Controllability For Discrete Processes D Discrete Linear Systems The Transition Matrix Sequence for Discrete Linear Repetitive Processes The General Response Formula Local Reachability/Controllability Controllability of Discrete Processes with Dynamic Boundary Conditions Controllability and Observability of Differential Processes Controllability Point Controllability Sufficient Conditions for Approximate Reachability and Controllability Observability and Control Canonical Forms System Equivalence Poles and Zeros - A Behavioral Approach Behavioral Theory - Background Characteristic Varieties Generalized Characteristic Varieties Poles and Zeros in the Behavioral Setting Feedback and Optimal Control Control Objectives and Structures Control Objectives Control Laws Design of Memoryless Control Laws Fast Sampling Control of a Class of Differential Linear Repetitive Processes Discrete Multivariable First Order Lag based Control Law Design An Extension LMI based Control Law Design for Stability Along the Pass Discrete Processes Discrete Processes with Dynamic Boundary Conditions Differential Processes Design for Performance and Disturbance Rejection Asymptotic Stability with Performance Design Stability Along the Pass with Performance Design Design for Disturbance Rejection PI Control Laws Asymptotic Stability Using the 1D Equivalent Model for Discrete Processes Stability Along the Pass with Performance for Discrete Processes 282

4 Contents XIII Differential Processes Direct Application of Delay Differential Stability Theory to Differential Processes Linear Quadratic Control of Differential Processes Control Law Design for Robustness and Performance LMI Based Design Discrete Processes Differential Processes i/oo Control of Discrete Processes Hoc, Control with a Static Control Law Hoc Control of Uncertain Discrete Processes Hoc, Control with a Dynamic Pass Profile Controller Guaranteed Cost Control of Discrete Processes Guaranteed Cost Bound Guaranteed Cost Control Hoc Control of Differential Processes Hoc Control with a Static Control Law Hoc Control of Uncertain Differential Processes Hoc Control with a Dynamic Pass Profile Controller Guaranteed Cost Control of Differential Processes Guaranteed Cost Bound Guaranteed Cost Control H 2 and Mixed H 2 /Hoc Control of Differential Processes The H 2 Norm and Stability Along the Pass Static H 2 Control Law Design The Mixed H 2 /Hoc Control Problem H 2 Control of Uncertain Processes Application to Iterative Learning Control Stability and Convergence of ILC Schemes Norm Optimal ILC Norm Optimal ILC Applied to Chain Conveyor Systems Experimental Results Robust ILC Experimental Verification of Robust ILC on a Gantry Robot Model uncertainty - Case (i) Model uncertainty - Cases (ii) and (iii) Robustness to initial State error Long-term Performance 424

5 XIV Contents 10 Conclusions and Further Work Conclusions Further Research Repetitive Processes with Switching Dynamics Spatially Interconnected Systems - a Role for Repetitive Processes? 436 References 451 Index 463