Approximate loop transfer recovery method for designing fixed-order compensators

Abstract

An approach is outlined for designing fixed-order dynamic compensators for multivariable time-invariant linear systems, based on minimizing a linear quadratic performance index. The formulation is done in an output feedback setting that exploits an observer canonical form to represent the compensator dynamics. The formulation also precludes the use of direct feedback of the plant output. The main contribution lies in defining a method for penalizing the states of the plant and of the compensator, and for choosing the distribution on initial conditions so that the loop transfer matrix approximates that of a full-state feedback design. When linear quadratic regulator theory is used to do the full-state feedback design, the approach can result in good gain and phase margin characteristics. Two examples are given to illustrate the effectiveness of the approach. The first treats the problem of pointing a flexible structure, and the second is a helicopter flight control problem using a tenth-order model for the fuselage and rotor dynamics. Both of the examples considered in this paper are for nonsquare plants.