Digital Controller Implementation and Fragility

1 Finite-precision Computing for Digital Control Systems: Current Status and Future Paradigms.- 1.1 Introduction.- 1.2 Finite-precision Control and Fragility.- 1.3 Hardware Issues and Development of Control System Process ing Structures.- 1.4 Future Paradigms and Relevant Research Problems.- References.- 2 Stability Margins and Digital Implementation of Controllers.- 2.1 Introduction.- 2.2 Digital Implementation.- 2.3 Simulation Setup.- 2.4 Examples.- 2.5 Concluding Remarks.- Acknowledgements.- References.- 3 Finite Word-length Effects in Systems with Fast Sampling.- 3.1 Introduction.- 3.2 The Case of Small Sampling Periods.- 3.3 A Reformulated Aström’s Theorem.- 3.4 Estimation of the Word-length.- 3.5 Examples.- 3.6 Remarks about Regulator Design and Implementation.- 3.7 Problems with Model Identification.- 3.8 Conclusions and Notes.- References.- 4 Implementation of a Class of Low Complexity, Low Sensitivity Digital Controllers Using Adaptive Fixed-point Arithmetic.- 4.1 Introduction.- 4.2 Digital Feedback Controller.- 4.3 Q-Parameterized Controller.- 4.4 Dynamically Scaled Controllers.- 5 Convexity and Diagonal Stability: an LMI Approach to Digital Filter Implementation.- 5.1 Introduction.- 5.2 Convex Approach to the Diagonal Stability Issue.- 5.3 Application to Digital Filter Implementations.- 5.4 Concluding Remarks.- 6 The Determination of Optimal Finite-precision Controller Realisations Using a Global Optimisation Strategy: a Pole-sensitivity Approach.- 6.1 Introduction.- 6.2 Problem Formulation.- 6.3 A New Pole-sensitivity Stability Related Measure.- 6.4 Optimisation Procedure.- 6.5 A Numerical Example.- 6.6 Conclusions.- References.- 6.A Appendix - Theorem Proof.- 6.B Appendix - Adaptive Simulated Annealing.- 7 Computational Algorithms For Sparse Optimal Digital Controller Realisations.- 7.1 Introduction.- 7.2 Digital Controller Coefficient Quantisation.- 7.3 Stability-optimal Controller Realisations.- 7.4 Numerical Issues.- 7.5 Concluding Remarks.- References.- 8 On the Structure of Digital Controllers in Sampled-data Systems with Stability Consideration.- 8.1 Introduction.- 8.2 Digital Controller State Space Implementation.- 8.3 A Stability Robustness Related Measure.- 8.4 Optimal Controller Structures.- 8.5 Sparse Structures.- 8.6 A Design Example.- References.- 9 An Evolutionary Algorithm Approach to the Design of Finite Word-length Controller Structures.- 9.1 Introduction.- 9.2 Multi-objective Optimisation.- 9.3 Evolutionary Algorithms and the Multi-objective Genetic Algorithm.- 9.4 A Linear System Equivalence Completion Problem.- 9.5 FWL Controller Structure Design using Evolutionary Computation.- 9.6 Application Example.- 9.7 Concluding Remarks.- References.- 10 Non-fragile Robust Controller Design.- 10.1 Introduction.- 10.2 Robustness and Fragility Analysis.- 10.3 Another View on Robustness and Fragility.- 10.4 Factored Controller Form.- 10.5 Partial Fraction Controller Form.- 10.6 Conclusions.- Acknowledgements.- References.- 11 Robust Resilient Controller Design.- 11.1 Introduction.- 11.2 Robust Stability and Performance.- 11.3 Sufficient Conditions for Robust Stability and Performance.- 11.4 Multiplicative Controller Uncertainty Structure and Guaranteed Cost Bound.- 11.5 Decentralised Static Output Feedback Formulation.- 11.6 Sufficient Conditions for Fixed-order Resilient Compensation with Multiplicative Uncertainty.- 11.7 Additive Controller Uncertainty Structure and Guaranteed Cost Bound.- 11.8 Decentralised Static Output Feedback Formulation.- 11.9 Sufficient Conditions for Fixed-order Resilient Compensation with Additive Uncertainty.- 11.10 Quasi-Newton Optimisation Algorithm.- 11.11 Illustrative Numerical Examples.- 11.12 Conclusion.- References.- 12 Robust Non-fragile Controller Design for Discrete Time Systems with FWL Consideration.- 12.1 Introduction.- 12.2 Problem Statement and Preliminaries.- 12.3 Robust Non-fragile H2 Control with Additive Controller Uncertainty.- 12.4 Robust Non-fragile H2 control with Multiplicative Controller Uncertainty.- 12.5 Example.- 12.6 Conclusion.- Acknowledgements.- References.- 13 Synthesis of Controllers with Finite-precision Considerations.- 13.1 Introduction.- 13.2 A Model for Finite-precision Controller Design.- 13.3 The Noise Model.- 13.4 Finite-precision Effects on Closed-loop Performance.- 13.5 Optimal Controller Coordinates.- 13.6 Optimal Controller Design.- 13.7 Skewed Sampling.- 13.8 A Numerical Example.- Acknowledgements.- References.- 13.A Proof of Lemma 13.1.- 13.B Proof of Lemma 13.2.- 13.C Proof of Lemma 13.3.- 14 Quantisation Errors in Digital Implementations of Fuzzy Controllers.- 14.1 Introduction.- 14.2 Fuzzy Systems.- 14.3 Sources of Quantisation Errors.- 14.4 Digitised FLCs.- 14.5 Consequences of the Digitisation in Feedback Fuzzy Systems.- 14.6 Conclusions.- References.