Sample Rate Effects on Disturbance Rejection for Digital Control Systems

Sample rate effects on disturbance rejection are discussed through design examples of a double integrator plant and mass-spring-mass systems. Disturbance rejection is one of the key factors that influences the sample rate selection. The discrete nature of digital control systems contributes to performance degradation compared to continuous controllers. The results show that a sample rate has a significant effect on the performance of a discrete controller´s disturbance rejection. Based on the representative examples analyzed, the performance of systems, where the 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. However, for the class of systems where the controller adds a significant amount of damping to a lightly damped mode which is faster than the bandwidth, the open-loop frequency of that mode has a large impact on the sample rate selection. Such a lightly damped mode causes sensitive sample rates near integer fractions of twice the mode frequency, where the performance degrades significantly. For this class of systems, it may be necessary to increase the sample rate over that suggested above in order to maintain acceptable performance.