Synthesis of multivariable, basically non-interacting systems with significant plant uncertainty

Abstract

This paper presents a synthesis technique for basically non-interacting, time-invariant, linear, minimum-phase, multi-variable feedback control systems with significant plant uncertainty. The technique permits precise design to specifications in the frequency domain, of the form k i 1( ω)⩽| τ ii ( jω)|⩽ k i 2( ω), | τ ij ( jω)|⩽ k ij ( ω), i/ n= j, to be satisfied over the range of plant parameter uncertainty, where T = [ τ αβ ] is the matrix of transfer functions of the closed-loop system, and the k's are a priori specified. The specifications are achieved with loop transmission elements of minimum ‘bandwidth’. A computerized iteration scheme is developed. At each iteration the problem is one of designing separate, single input-output systems with parameter uncertainty. An exact synthesis technique exists for this problem. Two detailed examples are given: one, a rotating d.c. to a.c. converter, in which parameter uncertainty is by a factor of 10 (1000%) and the second with parameter uncertainty factors up to 100.