Problem Of Disturbance Decoupling Research Articles

Conditioned invariant subspaces, disturbance decoupling and solutions of rational matrix equations

Conditioned invariant subspaces are introduced both in terms of output injection and in terms of state estimation. Various properties of these subspaces are explored and the problem of disturbance decoupling by output injection (OIP) is defined. It is then shown that OIP is equivalent to the problem of disturbance decoupled estimation as introduced in Willems (1982) and Willems and Commault (1980). Both solvability conditions and a description of solutions for a class of rational matrix equations of the form X(s)M(s) = Q(s) on several ways are given in state-space form. Finally, the problem of output stabilization with respect to a disturbance is briefly addressed.

Disturbance Decoupling by Feedforward and Preview Control

The problem of disturbance decoupling is formulated and solved for continuous-time linear systems in which feedforward of disturbance input and its derivatives is allowed. The problem of disturbance decoupling by preview control is also formulated for discrete-time linear systems and it is shown that these two problems are algebraically equivalent. The result is applied to the design of a disturbance absorber for an open bottom floating structure and a simulation study is carried out to demonstrate the effectiveness of the result.

Almost invariant subspaces: An approach to high gain feedback design--Part I: Almost controlled invariant subspaces

In Part I of this paper, almost controlled invariant subspaces were studied. In this part we will consider their duals, the almost conditionally invariant subspaces. These concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem. Finally, we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if: 1) almost disturbance decoupling by state feedback, and 2) almost disturbance decoupled estimation of the to-be-controlled output are both possible.

Compensator synthesis using (C,A,B)-pairs

This paper gives a general framework (in the geometric style) for the design of compensators for linear multivariable systems. Basic is the notion of a "( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C,A,B</tex> )-pair of subspaces." This concept is newly defined here, and we give its simplest application (to the problem of disturbance decoupling by observation feedback). We then formulate a general compensator synthesis principle and show how several well-known synthesis techniques can be derived from it. We also show that "almost all" compensators can be interpreted as observer-based compensators, and discuss the relation between the compensator problem and the stable cover problem.

Disturbance localization in linear systems with simultaneous decoupling, pole assignment, or stabilization

For a class of constant linear dynamic systems with unmeasurable disturbances, geometric necessary and sufficient conditions are derived for the existence of a state-feedback controller that localizes the disturbances and simultaneously assigns the closed-loop poles or decouples the closed-loop system. These conditions are simple, intuitively appealing, and closely related to the known necessary and sufficient conditions for the separate problems to be solvable alone. Furthermore, it is shown that for these combined problems and for simultaneous disturbance localization and stabilization problems no additional flexibility is afforded by using dynamic compensation instead of static compensation except for the combined problem of disturbance localization and decoupling where the additional flexibility is derived from that for the decoupling problem alone. Under a standard rank assumption, it is established that the combined problem of simultaneously localizing the disturbances, assigning the poles and decoupling the system has no solution. Separate necessary and sufficient conditions are given for the existence of a solution to the combined problem of disturbance localization, stabilization, and decoupling.