| The selection of optimal sample rates for digital control systems is always a compromise among many aspects of design. For this reason, the analysis of the influence of sample rates on system performance plays a crucial role in gaining insight for a systematic sample rate selection. Disturbance rejection, among many contributing factors, is an important aspect of any control system and, in many cases, is the most important one.;This research explores sample rate effects on disturbance rejection and suggests general guidelines for a systematic sample rate selection. The investigation includes many factors affecting the variation of the disturbance rejection, such as sensitivity to off-nominal plant parameters, effects of finite word length and analog prefilters as well as plant and controller design parameters. Two types of compensators are examined: one is an optimal discrete synthesis based on a continuous quadratic cost function and the other is a simpler first-order lead compensator. The principal example used is a mass-spring-mass system, which has a lightly damped mode, subject to a white noise disturbance.;It is shown here that sample rates have a significant effect on the performance of a discrete controller's disturbance rejection. Based on the representative examples analyzed, the performance of systems where process disturbance is dominant, approaches the performance of a continuous controller to within 10% when using a sample rate of 40 or more times the closed-loop bandwidth, provided that there are no significant dynamics faster than the bandwidth. If a 50% degradation of the discrete system performance is acceptable, this can usually be achieved with a sample rate which is 8 times the closed-loop bandwidth. For systems where controllers add significant amounts of damping to lightly damped modes which are faster than the bandwidth, the open-loop frequencies of those modes have a large impact on the sample rate selection. Such lightly damped modes cause sensitive sample rates near integer fractions of twice the mode frequency, where the performance degrades significantly. In these cases, it may be necessary to increase the sample rate over that suggested above in order to maintain acceptable performance. |
