Constrained Optimal PID Controller Design: Convex-Concave Optimization Approach

In this paper, an algorithm is proposed to improve the design of constrained PID controller based on convex-concave optimization. This design method is based on the optimization of a performance cost function, taking into account the stability and efficiency constraints with frequency domain analysis in which the concepts of sensitivity and complementary sensitivity has been used. It is shown, using a counter example that the previous methods are not effective for some systems, the optimization problem becomes unbounded and interrupts. To solve this problem, attentions are paid to conditions that the optimization problem fails to have any response, and then previous limitations are eliminated by representing a new designing method. The performance of the proposed method is shown by applying it to the counter example. In the end, the controller is designed for an unstable system.