1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

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Essentials of Robust Control

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

Performance enhancement stabilizing controllers design environment off-line controller design iterated and nested (S, Q) design direct adaptive-Q control indirect (S, Q) adaptive control adaptive-Q application to non-linear systems real-time implementation laboratory case studies.

High Performance Control

A different aspect of using the parameterisation of all systems stabilised by a given controller, i.e. the dual Youla parameterisation, is considered. The relation between system change and the dual Youla parameter is derived in explicit form. A number of standard uncertain model descriptions are considered and the relation with the dual Youla parameter given. Some applications of the dual Youla parameterisation are considered in connection with the design of controllers and model/performance validation

Dual Youla parameterisation

SUMMARY A concept for implementation of multivariable controllers is presented in this paper. The concept is based on the Youla–Jabr–Bongiorno–Kucera (YJBK) parameterization of all stabilizing controllers. Using this scheme for implementation of multivariable controllers, it is shown how it is possible to smoothly switch between multivariable controllers with guaranteed closed-loop stability. This includes also the case where one or more controllers are unstable. The concept for smooth on-line changes of multivariable controllers based on the YJBK architecture can also handle the start-up and shut down of multivariable systems. Furthermore, the start-up of unstable multivariable controllers can be handled as well. Finally, implementation of (unstable) controllers as a stable Q parameter in a Q-parameterized controller can also be achieved. Copyright # 2004 John Wiley & Sons, Ltd.

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Switching between multivariable controllers

It is shown that the class of all strictly proper stabilizing controllers for proper linear plants can be structured as state estimate feedback with frequency shaping in the state estimates and/or in the state estimate feedback law. The selection of where the frequency shaping takes place is at the designer's discretion. The parameterization of the controller class can be in terms of an arbitrary proper stable transfer function, with the closed-loop system transfer functions affine in the transfer function. With constant output feedback permitted in addition to the state estimate feedback, the class of all proper stabilizing controllers can be generated in a like manner. >

http://users.rsise.anu.edu.au/~john/papers/JOUR/098.PDF

All stabilizing controllers as frequency-shaped state estimate feedback

Doubly coprime factorizations of the transfer function of a lumped linear time-invariant system are a starting point for many of the results in the factorization approach to multivariabie control system analysis and synthesis. In work by Nett et al. (1984), explicit state-space realizations of these factorizations are derived using results from state estimation/state feedback theory. Here new doubly coprime factorizations are developed based on minimal-order observers. Following on from this, various extensions are noted, and it is proved that the class of all proper stabilizing controllers for a given plant can be generated by dynamic feedback of the reduced-order state estimate.

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Doubly coprime factorizations, reduced-order observers, and dynamic state estimate feedback

Standard balanced-truncation or Hankel-norm model approximation methods are applied to augmentations of the controller which emerge when characterizing the class of all stabilizing controllers in terms of an arbitrary proper stable transfer function. In the method, scaling parameters are at the disposal of the engineer to achieve an appropriate compromise between preserving performance for the nominal plant and a certain type of robustness of plant variations. There are a number of unique features of the approach. One feature is that a straightforward reoptimization of a reduced-order controller is possible within the framework of the method. A second feature is that for controllers designed for simultaneous stabilization of a number of plants, the method seeks to preserve the performance/robustness of the reduced-order controller for each plant. >

/pdf/controller-reduction-methods-maintaining-performance-and-mtf7o5uyc0.pdf

Controller reduction methods maintaining performance and robustness

This paper shows that the class of all strictly proper stabilizing controllers for proper linear plants can be structured as state estimate feedback with frequency shaping in the state estimates and/or in the state estimate feedback law. The selection of where the frequency shaping takes place is at the designers discretion. The parameterization of the controller class can be in terms of an arbitrary proper stable transfer function, with the closed loop system transfer functions affine in this transfer function. With constant output feedback permitted in addition to the state estimate feedback, the class of all proper stabilizing controllers can be generated in like manner.

On the class of all stabilizing controllers

Control systems can drift into instability or, less catastrophically, exhibit resonance behaviour. One role for adaptive controllers is to learn sufficient information concerning the dominant closed-loop system mode so as to apply effective feedback to dampen these modes. In such situations the adaptive loop augments the fixed controller feedback loop. This paper presents an algorithm for adaptive resonance suppression and provides simulation results to study its behaviour in the presence of high-order unmodelled dynamics. The algorithm appears particularly useful for enhancing existing fixed controller designs.

http://users.cecs.anu.edu.au/~john/papers/JOUR/102.PDF

Andrew J. Telford

Papers

All stabilizing controllers as frequency-shaped state estimate feedback

Doubly coprime factorizations, reduced-order observers, and dynamic state estimate feedback

Controller reduction methods maintaining performance and robustness

On the class of all stabilizing controllers

Adaptive stabilization and resonance suppression