PID controller design for robust performance

A new design method of PID controller for a robust performance feedback control system is presented. Conditions for robust stability and robust performance are shown to be expressed by linear equalities when either proportional gain kp or derivative and integral gains ki, kd are fixed. Based on this, optimal solution of kp, ki, kd (generally local optimum) is obtained by repeating calculations by fixing kp or ki, kd in turn, and by optimizing them by linear programming. In comparison with the previous results, the approach proposed in this article provides better prospect, and the calculation is simpler. Further, the approach is applicable to PID controller design containing a double derivative term. Numerical examples are given to show the effectiveness.