Critical actuator rate limit effect on control performance in first-order plus time-delay systems

In industrial control systems, actuator rate limit is an ubiquitous phenomenon and results in the deterioration of control performance and even system instability. However most of the compensation strategies of the rate limit effect are still inadequate and impractical. Thus it is necessary to provide a guidance for engineers to determine whether to consider rate limit effect in controller design. In this context, this study proposes a criterion of the critical rate limit value that results in a 50% overshoot in the step response of the first-order plus time delay (FOPTD) processes where rate limit is not considered in controller design. To simply the analysis, normalization of the control plant is firstly introduced. Then the M-constrained integral gain optimization (AMIGO) method and Skogestad internal model control (SIMC) method are employed to tune the PID and PI controller. The relation between the critical rate limit value and normalized system delay is firstly obtained based on the various simulations. Then this relation function is converted to describe the real critical rate limit value for the original FOPTD processes. The illustrative example has demonstrated the effectiveness of the proposed critical rule.