The influence of rate limit on proportional-integral controller for first-order plus time-delay systems

The control performance can be worsened by actuator rate limit, which can result in amplitude attenuation and phase delay in process control. In some extreme situations, actuator rate limit may bring about the system non-convergence. This paper focuses on the control difficulties and solutions of first-order plus time-delay (FOPTD) systems caused by rate limit. The influence of rate limit on stability regions of proportional-integral (PI) controller is analysed. Results show that a small rate limit value can reduce stability regions of PI parameters greatly. The negative correlation between the integral gain and the onset frequency, and the positive correlation between the proportional gain and the onset frequency are conducted. Moreover, the control performance of different PI tuning rules such as Skogestad internal model control, integral gain maximization, delay robustness-constrained optimization and Tyreus-Luyben​ tuning rules is evidently affected by rate limit. Simulation and experiment results verify that the PI controller tuned by Skogestad internal model control (SIMC) method is less sensitive to the rate limit variation and is more suitable for processes (the normalized dead-time is from 0.03 to 1) which have severe actuator rate limit. Tyreus-Luyben tuning rule is another optional method. In addition, the reasons why SIMC is not sensitive to rate limit variation are analysed. These analytical results can offer a guideline for practical applications.