Stabilization and algorithm of integrator plus dead-time process using PID controller

In this paper, we develop an algorithm to determine the entire set of stabilising PID parameters for the integrator plus dead-time process. Our method is a combination of the traditional D-partition technique and graphical technique. We first apply the D-partition technique to address the stability regions in the plane of proportional and integral gains, which depend on the steady-state gain and the time delay. Next for fixed proportional gain, again using the D-partition technique we obtain a series of critical straight lines in the plane of integral and derivative gains and then choosing the derivative gain as a parameter, we investigate how the derivative gain affects the distribution of the roots of the corresponding characteristic equation of the closed-loop control system, which provide the stability regions in the plane of integral and derivative gains. On the base of the results obtained in the previous two steps, an efficient algorithm for determining the entire set of stabilising PID parameters is also proposed. Finally, numerical simulations are given to support our theoretical results.