PID controller tuning via quasi pole assignment method

In this paper, a new tuning method for PID control is proposed. We set the controlled system to be a controllable and observable SISO system. First, we consider an optimal servo problem by two methods. For each method, the optimal state feedback control law is obtained by applying the optimal regulator theory, and optimal poles of the closed-loop system are calculated. Next, we consider the problem that poles of the closed-loop system by PID control are best approximated to the optimal poles as close as possible. This technique is called the quasi-pole assignment. The problem becomes a nonlinear programming problem with some equality constraints, and is solved by an exterior point penalty method. Finally, the simulation results is reported, demonstrating the effectiveness of the proposed methods.