Decoupling linear multiinput multioutput plants by dynamic output feedback: An algebraic theory

Abstract

This paper presents an algebraic theory for the design of a decoupling Compensator for linear time-invariant multiinput multioutput systems. The design method uses a two-input one-output compensator, which gives a convenient parametrization of all diagonal input-output (I/ 0) maps and all disturbance-to-output (D/O) maps achievable by a stabilizing compensator for a given plant. It is shown that this method has two degrees of freedom: any achievable diagonal 110 map and any achievable D/O map can be realized simultaneously by a choice of an appropriate compensator. The difference between all achievable diagonal and nondiagonal I/O maps and the "cost" of decoupling is discussed for some particular algebraic settings. recommended bv Associate Editor. S. P. Bhattacharvva. This work was Manuscript received April 29, 1985; revised February 14, 1986. Paper supported by~thgNationa1 Science Foundation under Grant ECS-8119763, Comuuter Sciences and the Electronics Research Laboraton;. Universih, of The authors are with the Department of Electrical Engineering and ~~ G i h n i a , Berkeley, CA 94720. IEEE Log Number 8609227.

Input/Output Decoupling of Square Linear Systems by Dynamic Two‐Parameter Stabilizing Control

“…In [10] it is shown that any achievable diagonal I/O map and any achievable disturbance to output map can be realized simultaneously by a choice of an appropriate TPSC.…”

An optimal H 2 decoupling design for non-square plant systems based on the two-degree-of-freedom standard model

“…Solving the problem of developing a decoupling design for linear multivariable control systems has been studied in past decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14]21]. Vardulakis [1] presented a sufficient condition for the existence of a decoupling controller: There is no coincidence of plant poles and zeros in the unstable region.…”

“…These cited papers, however, adopted a 1DOF (one-degree-of-freedom) controller structure that imposed restrictions on both performance and stability margin when a decoupling constraint was invoked. An efficient way to overcome this restriction is to exploit a 2DOF controller configuration [9][10][11]. In [9], all decoupling input-output maps were parameterized by stabilizing controllers for a 2DOF controller configuration.…”

Decoupling Controller Design for H∞Performance Condition

“…Park and Choi [10] recently proposed a set of necessary and sufficient conditions for the existence of decoupling controllers in the generalized plant model. Another efficient approach to overcome 1-DOF restrictions is by exploiting a two-degree-of-freedom controller configuration [11][12][13]. The literature review suggests that attempts to design a decoupling controller using the norm have been done.…”