Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >

State-space solutions to standard H/sub 2/ and H/sub infinity / control problems

Model predictive control: theory and practice—a survey

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.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results.

/pdf/multivariable-feedback-design-concepts-for-a-classical-3ynzpf9dn5.pdf

Multivariable feedback design: Concepts for a classical/modern synthesis

In many modern-day control problems encountered in the fluid, petroleum, power, gas and paper industries, cross coupling (interaction) between controlled and manipulated variables can be so severe that any attempt to employ single-loop controllers results in unacceptable performance. In all these situations, any workable control strategy most take into account the true multivariable nature of the plant and address itself directly to the design of a compatible multivariable controller. Any practical design technique most be able to cope with load disturbance, plant saturation, measurement noise, process lag, sensitivity and also incorporate suitable criteria delimiting transient behavior and steady-state performance. These difficulties, when compounded by the fact that many plants (such as chemical reactors) are inherently open-loop unstable have hindered the development of an inclusive frequency-domain analytic design methodology. However, a solution based on a least-square Wiener-Hopf minimization of an appropriately chosen cost functional is now available. The optimal controller obtained by this method guarantees an asymptotically stable and dynamical closed-loop configuration irrespective of whether or not the plant is proper, stable, or minimum-phase and also permits the stability margin of the optimal design to be ascertained in advance. The main purpose of this paper is to lay bare the physical assumptions underlying the choice of model and to present an explicit formula for the optimal controller.

Modern Wiener-Hopf design of optimal controllers--Part II: The multivariable case

The design of linear two-degree-of-freedom stabilizing controllers is treated in a quadratic-cost setting. The class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance, tracking-cost sensitivity, and stability margins is discussed.

A feedback theory of two-degree-of-freedom optimal Wiener-Hopf design

Multivariable control system design in a quadratic cost setting is treated for a completely general configuration. The class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite. This controller class is parameterized in terms of an arbitrary real rational strictly-proper matrix Z(s), which is analytic in the closed right-hand side of the s-plane. The choice Z identical to 0 gives the controller which minimizes the quadratic cost functional. >

A general theory for the Wiener-Hopf design of multivariable control systems

The design of linear two-degree-of-freedom stabilizing controllers in a quadratic-cost setting is treated The class of all such controllers which give finite cost is established and the trade-off possible between optimum performance, tracking-cost sensitivity, and stability margins is discussed

A Feedback Theory of Two-Degree-of-Freedom Optimal Wiener-Hopf Design

An important consideration in the design of many control systems is decoupling (each command input controlling only one output). The two-degree-of-freedom or three-degree-of-freedom controller structure is ideally suited to this task since only one of the degrees of freedom is affected by the decoupling requirement. The decoupling constraint on this degree of freedom, however, can lead to some deterioration in achievable system performance. A Wiener-Hopf design procedure which minimizes this performance deterioration is described here for plants with non-square transfer matrices. Moreover, the parametrization of the class of all decoupled systems is given for which the cost functional representing system performance remains finite.

Joseph J. Bongiorno

Papers

Modern Wiener-Hopf design of optimal controllers--Part II: The multivariable case

A feedback theory of two-degree-of-freedom optimal Wiener-Hopf design

A general theory for the Wiener-Hopf design of multivariable control systems

A Feedback Theory of Two-Degree-of-Freedom Optimal Wiener-Hopf Design

Wiener-Hopf design of optimal decoupling controllers for plants with non-square transfer matrices†