Effect of a finite-word-length computer in a sampled-data feedback system

When a digital computer acts as the compensating element of a sampled-data feedback system, the system performance is degenerated by the computational errors inherent in the finite-word-length machine. The statistical analysis presented in this paper enables the increase in the mean-square system error due to quantisation and computer roundoff errors to be assessed for a closed-loop linear sampled-data system. In fact, the loss in overall performance can be determined by slide-rule calculation for all computer word lengths. A further advantage of the present approach over previous work is that the necessary computations are performed on the conventional block diagram of the system, rather than its matrix equivalent. One application of the analysis is to specify the precision required in the digital compensator and peripheral equipment for consistency with the overall accuracy demanded of the closed-loop system. It also enables the selection of the programming technique which requires the shortest computer word length for this accuracy. As a means of verifying the analysis, the performance of two different digital compensators for a practical system are each compared with a counterpart having negligible quantisation and roundoff errors.