Design of digital high-gain PD control systems using analytical approach

It is known that a continuous stable high-gain PD control system may become unstable when the controller is implemented digitally. Recent works consider this problem and determine the stability regions of such systems. In most cases the stability regions are obtained numerically. This work introduces a new analytical approach for obtaining the stability criteria for digital systems. The approach is based on the critical constraints of simplified version of Jury test and makes use of the capabilities of MATLAB software. The approach is applied to digital PD control systems. Here, the effect of computation time in addition to that of sampling period are considered. The resulting stability criteria are presented in closed forms that are suitable for design purposes and make it possible to map the stability region for various control design parameters. This versatile capability is illustrated via design examples. To the contrary of previous knowledge, the results show that, in certain cases, the stability is obtained through increasing the proportional gain or computation time rather than by decreasing them. A comparison with the literature shows that this approach is straightforward, versatile and even corrects some of the stability regions that have been reported.