Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers

Abstract

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.