Robust controller synthesis for high order unstable processes with time delay using mirror mapping technique

In this note, a general scheme is proposed for the high order unstable delay process with one or more positive poles, using the mirror mapping technique. The Nyquist criteria is employed to establish a systematic methodology to tune the parameter. The stabilizing parameter region could guarantee the prespecified robustness specification. In the scheme, a control law is designed based on the all-pole Padé approximated model. The unstable process was first mapped into a minimum-phase system, and the actual control is obtained by the closed-loop gain shaping algorithm (CGSA). The advantages are that one has a concise design procedure and can achieve good performance such as disturbance rejection and robustness. Finally, three highly cited examples are used to illustrate the effectiveness of the proposed method.