Stabilization of an arbitrary order transfer function with time delay using a PID controller

This paper is concerned with developing a procedure for stabilizing a linear time-invariant plant of any order with time delay utilizing a proportional-integral-derivative (PID) controller. The method presented here is based on calculating the stability bounds in terms of the three planes (K_p,K_i), (K_p,K_d) and (K_i,K_d), where K _p, K_i, and K_d are proportional, integral and derivative gains, respectively. The advantage of this procedure is the fact that it does not require the knowledge of the plant transfer function parameters, but only its frequency response. In addition, if the plant function is known, the procedure may also be used to analytically obtain the stabilizing controllers. We also present the tuning rules for user specified gain and phase margins