Robust PID Controller Design for Both Delay-Free and Time-Delay Systems

Abstract

Robust PID controller design methods are proposed for linear single-input single-output systems. Non-parametric models represented by a finite number of frequency responses are used for them. Sufficient conditions for closed-loop stability are derived based on the Nyquist stability criterion and the sufficient conditions are reduced to convex constraints. Together with the convex constraints and closed-loop model matching problems the robust PID controller design problems are formulated as convex optimization problems. A important feature of the proposed design methods is that they can be applied to delay-free and time-delay systems in the same manner. Moreover, the proposed methods are extended to two-degree-of-freedom PID controller design methods.