The delay approximation of discrete control in higher-order systems

Abstract

Physical machinery of high mathematical order operating in industry increasingly nowadays requires the replacement of early analog controllers by imbedded digital systems. Using a 7 th-order longwall shearer as the motivating case-study, the paper examines the possibility of easing the digital control system design process by substituting a continuous transport-delay for the digital sample-hold operation. Based on first- and second-order models, this is shown to produce a design procedure that is pessimistic (i.e., safe) in the main and to a practically acceptable degree. Similar response speeds are generated by the discrete- and delay-models. By simulation, the technique is shown to carry over well to the higher-order case study aforementioned. This provides confidence in the delay-for-sampler substitution, the advantages of which are that the need to generate multiple z-transform models for a range of sampling intervals and the difficulties of interpreting z-plane plots (compared to those of familiar Nyquist diagrams and root loci) are avoided.