Analysis of Actuator Rate Limit Effects on First-Order Plus Time-Delay Systems under Fractional-Order Proportional-Integral Control

Abstract

Actuator rate limit deteriorates control performance, and may even lead to system instability in precision process control. In this paper, a first-order plus time-delay (FOPTD) system class with actuator rate limit is considered. The describing function (DF) of the rate limiter is derived to obtain the describing functions of the closed-loop and open-loop systems, and the onset frequency in the Nichols chart is used to analyze the rate limit effects in frequency domain. A fractional-order proportional-integral (FOPI) controller is first designed based on the flat phase constraint, crossover frequency, and phase margin specifications. Then a traditional integer-order PID (IOPID) controller is designed based on the same specifications to compare with the FOPI controller in the presence of actuator rate saturation. A careful simulation study is presented to validate all the conclusions.