Matched Pole-Zero State-Space Model and Continuous-Time Properties

Abstract

The matched pole-zero (MPZ) model is a widely used technique for discrete-

time approximation of continuous-time controllers. In this article a new state-

space representation for the (MPZ) model is presented. The new formulation

can be used for direct discretization of state-space controllers, and can be eas-

ily automated on a digital computer. The most important advantage of the

proposed representation is that it preserves the dynamic structure of the orig-

inal continuous-time realization, i.e., the physical meaning of the states and

the direction of eigenvectors remain unchanged. In fact, the new method pro-

vides, exactly, the same dynamic state equations as the step-invariant model,

together with some modifications on the static output state equation.

Up to now, due to the lack of such an eigenstructure-preserving state-

space representations, most of the time domain studies on the effects of dis-

crete approximation of analog controllers were mostly performed using the

step-invariant model, although that method is seldom used for actual dis-

cretization of controllers. The new formulation, paves the way for extending

those studies to the case of the more widely used MPZ method.