Analysis of multi-loop multi-rate digital control systems

A multi-rate multi-loop digital control system is a special class of a time varying system which contains two or more sampling switches operating at different data rates and two or more signal flow loops. When the ratio of the different rates are integers (i. e,, in practice most often powers of two) it is possible to analyze a multi-rate multi-loop system by reducing it to an equivalent signal rate multiloop time invariant system. Three different modeling procedures for this class of systems are: (i) sampler decomposition in time domain, (ii) sampler decomposition in frequency domain, and (iii) hybrid state transition. In the first and the third methods, the multi-rate system is reduced to an equivalent single rate system with the largest sampling period, whereas in the second method, the multi-rate system is reduced to an equivalent single rate system with the smallest sampling period. In this paper, a methodology is developed to apply the frequency domain decomposition technique to large scale digital systems. Three assertions are given which provide methods to compute multi-rate system with state space techniques. The developed algorithm which has been incorporated in the DIGIKON-II program is applied to the Space Shuttle flight control system. The multi-rate results are developed for 2:1 and 4:1 sampling ratios.