Role of sample period in transients, robustness and sensitivity in optimally designed digital control systems

Abstract

A simulation-based study of the influence of sample period on the performance of a general sample data servomechanism problem is presented. The digital controller consists of an error-driven internal model, which duplicates the reference and disturbance signals, and a state-feedback stabilizer obtained by minimizing a quadratic measure which penalizes both the continuous system states and the digital controller states. To ensure a unified approach is used for comparison, the structure of the internal model and performance measure are chosen such that as the sample period approaches zero, the optimal sample data control system converges to an optimal continuous control system. Simulation results show that the quadratic performance measure increases monotonically with the sample period, the norms of the controller gains decrease monotonically with the sample period, robustness tends to decrease with increasing sample period and sensitivity tends to increase with the sample period.