Aspects of subrate digital control systems

The paper suggests an original design procedure for subrate digital compensators, which is based on an approximate transfer function. Theoretical and experimental evidence is presented which justifies the design technique in practice. However, the main body of the paper is an extension of the authors´ previous work on quantisation effects to the case of a closed-loop linear subrate direct digital control system. A slide-rule calculation provides an upper bound for the loss of steady-state control-system performance for all computer word lengths and inputs. Furthermore, the actual increase in steady-state mean-square system error may be evaluated by a simple iterative computer program. An 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. These calculations can result in better utilisation of computer facilities, thereby implying an economic saving. As a means of verifying the analysis, the performance of two different subrate digital compensators for a practical system are each compared with a counterpart having negligible quantisation and roundoff errors.