Relay Feedback : Analysis, Identification and Control (Hardcover)

I. Analysis of Relay Feedback Systems.- 1. Existence of Solutions.- 1.1 Introduction.- 1.2 System Formulation.- 1.3 Existence of Solutions.- 1.4 Delay-free Case.- 2. Existence of Limit Cycles.- 2.1 Introduction.- 2.2 Sufficient Condition.- 2.2.1 Supporting Lemmas.- 2.2.2 Existence of Limit Cycles.- 2.3 A Simple Existence Condition.- 2.4 Limit Cycle Location.- 3. Local Stability of Limit Cycles.- 3.1 Introduction.- 3.2 Problem Formulation and Preliminaries.- 3.3 Local Stability of Limit Cycles.- 3.4 Extension.- 4. Global Stability of Limit Cycles.- 4.1 Introduction.- 4.2 Problem Formulation.- 4.3 Supporting Lemmas.- 4.4 Global Stability of Limit Cycles.- 4.5 Extensions.- 4.6 Existence of Globally Stable Limit Cycles.- 4.6.1 Preliminaries.- 4.6.2 Sufficient Conditions.- II. Process Identification from Relay Feedback Test.- 5. Relay Feedback and its Variations.- 5.1 Fundamentals.- 5.2 First-order Modelling.- 5.3 Robustness Enhancement.- 5.4 Parasitic Relay.- 5.5 Cascade Relay.- 5.6 Extension to MIMO Case.- 6. Use of Relay Transient Responses.- 6.1 Signal Analysis.- 6.2 Decomposition Method.- 6.3 Weighting Method.- 6.4 Testing on Pilot Plants.- 6.5 Extension to the MIMO case.- 7. Transfer Function Modelling.- 7.1 From Frequency Response.- 7.2 From Step Response.- 7.2.1 Second-order Modelling.- 7.2.2 nth-order Modelling.- 7.2.3 Implementation Issues.- 7.2.4 Simulation and Real-time Test.- 7.3 A Hybrid Approach.- 8. A General Identification Approach.- 8.1 SISO Systems.- 8.1.1 The Method.- 8.1.2 Simulation.- 8.2 MIMO Systems.- 8.2.1 The Method.- 8.2.2 Simulation.- 8.3 Unstable Processes.- III. Controller Design.- 9. Single-variable Systems.- 9.1 Design Methodology.- 9.2 PID Controller.- 9.3 High-order Controller.- 9.4 Stability Analysis.- 9.5 Unstable Processes.- 9.5.1 PID Controller.- 9.5.2 High-order Controller.- 10. Multivariable Systems.- 10.1 IMC Scheme.- 10.1.1 Decoupling.- 10.1.2 Analysis.- 10.1.3 Design.- 10.1.4 Simulation.- 10.2 Unity Feedback System.- 10.2.1 Design Methodology.- 10.2.2 PID Controller.- 10.2.3 High-order Controller.- 10.2.4 Stability Analysis.- 11. Partial Internal Model Control.- 11.1 Review of the IMC.- 11.2 The Proposed PIMC Scheme.- 11.3 Internal Stability Analysis.- 11.4 Asymptotic Tracking and Regulation.- 11.5 Primary Control Design.- 11.5.1 PIMC Primary Controller Design.- 11.5.2 MPIMC Primary Controller Design.- 11.6 Robustness Analysis.- 11.6.1 Robust Stability.- 11.6.2 Practical Stability.- 11.7 Practical Aspects.- 11.7.1 Pre-filter Design.- 11.7.2 Determination of G?.- 11.7.3 Dead Time.- 11.8 Simulation Results.- 11.9 Real-time Implementation.- Appendix A: Controller Design for Processes with Two Unstable Poles.- Appendix B: Formulas for Decomposition of some Typical Unstable Processes.- 12. Decentralized Control.- 12.1 The Proposed Independent Design Strategy.- 12.2 Choice of Solutions to Controller Gain Equations.- 12.3 Rational Approximation of the Irrational Solutions.- 12.4 Controller Reduction and Performance Trade-off.- 12.5 Stability Analysis.- 12.6 Extension to the m × m Case.- References.