Loop Shaping Robust Control

The loop-shaping approach consists of obtaining a specification in relation to the open loop of the control from specifications regarding various closed loop transfers, because it is easier to work on a single transfer (in addition to the open loop) than on a multitude of transfers (various loopings such as set point/error, disturbance/error, disturbance/control, etc.). The simplicity and flexibility of the approach make it very well adapted to the industrial context. This book presents the loop-shaping approach in its entirety, starting with the declension of high-level specifications into a loop-shaping specification. It then shows how it is possible to fully integrate this approach for the calculation of robust and efficient correctors with the help of existing techniques, which have already been industrially tried and tested, such as H-infinity synthesis. The concept of a gap metric (or distance between models) is also presented along with its connection with the prime factors of a set of systems shaping a ball of models, as well as its connections with robust synthesis by loop-shaping, in order to calculate efficient and robust correctors. As H-infinity loop-shaping is often demanding in terms of the order of correctors, the author also looks at loop-shaping synthesis under an ordering constraint. Two further promising lines of research are presented, one using stochastic optimization, and the other non-smooth optimization. Finally, the book introduces the concept of correction with two degrees of freedom via the formalism of prime factorization. Avenues for future work are also opened up by the author as he discusses the main drawbacks to loop-shaping synthesis, and how these issues can be solved using modern optimization techniques in an increasingly competitive industrial context, in accordance with ever more complex sets of functional specifications, associated with increasingly broad conditions of usage. Contents Introduction 1. The Loop-shaping Approach 2. Loop-shaping H-infinity Synthesis 3. Two Degrees-of-Freedom Controllers 4. Extensions and Optimizations Appendix 1. Demonstrative Elements on the Optimization of Robust Stabilization with Order Constraint Appendix 2. Establishment of Real LMIs for the Quasi-Convex Problem of Optimization of the Weighting Functions About the Authors Philippe Feyel is an R&D Engineer for the high-tech company Sagem Défense Sécurité, part of the defence and security business of the SAFRAN group, in Paris, France.

Shows readers how to exploit the capabilities of the MATLAB® Robust Control and Control Systems Toolboxes to the fullest using practical robust control examples.

Tiivistelmä: Robusti säätö avoimen järjestelmän manipulointia hyödyntäen.

Reset Control Systems addresses the analysis for reset control treating both its basic form, and some useful variations of the reset action and reset condition. The issues regarding reset control – concepts and motivation; analysis tools; and the application of design methodologies to real-world examples – are given thorough coverage. The text opens with a historical perspective which moves from the seminal work of the Clegg integrator and Horowitz FORE to more recent approaches based on impulsive/hybrid control systems and explains the motivation for reset compensation. Preliminary material is also included. The focus then turns to stability analysis for systems using techniques which account for various time- and frequency-domain criteria. The final section of the book is centered on control systems design and application. The PI+CI compensator is detailed as are a proposed frequency domain approach using quantitative feedback theory and ideas for design improvement. Design examples are given.

The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H∞ loop-shaping is emerging as a powerful but straightforward method of designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The ν-gap metric is an attempt to resolve this paradox — by indicating in what sense a model should be accurate if it is to be useful for feedback design.This book develops in detail the H∞ loop-shaping design method, the ν-gap metric and the relationship between the two, showing how they can be used together for successful feedback design.

A study of the practical aspects in designing feedback control systems in which the plant may be non-minimum phase, unstable and also highly uncertain. Classical (QFT) and modern (Hoo) design approaches are explained side-by-side and are used to solve design examples.

The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H[infinity] loop-shaping is emerging as a powerful but straightforward method for designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The v-gap metric is an attempt to resolve this paradox - by indicating in what sense a model should be accurate if it is to be useful for feedback design. This book develops in detail the H[infinity] loop-shaping design method, the v-gap metric and the relationship between the two, showing how they can be used together for successful feedback design.

A flight control system with stability and performance robustness is designed using a pseudo-sliding mode synthesis technique. The technique is interpreted in the frequency domain and allows loop shaping principles to be used in creating the sliding manifolds for the controller. The design methodology is evaluated through a desk-top flight simulation program that allows tracking performance assessment and identification of human pilot dynamics in the two axes being controlled by the pilot. Robustness is demonstrated by considering two disparate flight conditions in which the pseudo-sliding mode controller is used with no gain scheduling.

Designed as a university textbook, this text on robust systems theory includes problems with every chapter, a solutions manual and Matlab files containing worked examples.