Tuning PID controllers for time-delay processes with maximizing the degree of stability

In this paper, we propose a method of tuning PID controller parameters for first-order plus dead-time processes with the objective of maximizing the degree of stability. Since the presence of dead-time in a feedback loop gives rise to an infinite-dimensional closed-loop system, which has an infinite number of poles and thus the conventional Routh-Hurwitz algebraic criterion of stability cannot be applied to characterize the necessary conditions of the maximum degree of stability. To overcome this difficulty, we make use the theory of D-partition technique. Based on analytically characterizing the D-partition boundaries of the controller parameter space, necessary conditions of the maximum degree of stability are derived. With these derived conditions, the problem of maximizing the degree of stability is converted to a set of parametric optimization problems, whose solutions can be obtained by an existing method. For showing the applicability of the method, a tuning example with graphical illustrations is given.