Optimum structures of digital controllers in sampled-data systems: a roundoff noise analysis

Abstract

In this paper, the effect of roundoff noise in a digital controller is analyzed for a sampled-data system in which the digital controller is implemented in a state-space realization. A new measure, called averaged roundoff noise gain, is derived. Unlike the traditionally used measure, where the analysis is done based on an equivalent digital control system, this newly defined averaged roundoff noise gain allows us to take consideration of the inter-sample behavior. It is shown that this measure is a function of the state-space realization. Noting the fact that the state-space realizations of a digital controller are not unique, the problem of optimum controller structure is to identify those realizations that minimize the averaged roundoff noise gain subject to the $l_2$-scaling constraint which is for preventing the signals in the controller from overflow. An analytical solution to the problem is presented and a design example is given. Both theoretical analysis and simulation results show that the optimum controller realizations obtained with the proposed approach are superior to those obtained with the traditional analysis based on a digital control system.