Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes

The paper discusses the stability and robustness of the proportional-integral (PI), proportional-integral-derivative (PID), and proportional-integral-derivative-accelerative (PIDA) controller for the integral-plus-dead-time (IPDT) plants. To enable the implementation and measurement of noise attenuation, binomial low-pass filters are added to the traditional design of controllers with ideal transfer functions, and the impact of the low-pass filters on the robust stability of the circuit is studied in detail. The proposed controller tuning, which integrates the suboptimal controller and filter design, is based on explicit tuning formulas derived by using the multiple real dominant pole (MRDP) method. It is shown that by combining derivative actions with possibly higher-order low-pass filters, it is possible to either accelerate the transients or increase the closed loop robustness and that the problem of defining the robust stability area should be addressed at the stage of determining the process model. In addition, if wishing to maintain the closed loop robustness of unfiltered PI control, while increasing the degree of the derivative components, one needs to increase the filtering properties of the low-pass filter used accordingly. Simple analytical relations for setting filtered PI, PID, and PIDA controllers with equivalent robustness are derived.