New Method on Design of Robust Controller for Unstable Process

In the formulation of H∞ weighted mixed sensitivity problem, any unstable poles of the plant inside the specified control bandwidth will be shifted approximately to its jω-axis mirror image once the feedback loop is closed with an H∞ controller. The symmetric values of zero-poles in the open right-half plane of the unstable process about the imaginary axis are defined as their mirror-images. An unstable process is transformed into a minimum-phase system through mirror-injection in the paper, then solving the robust controller using closed-loop gain shaping algorithm. When the plant is a pure unstable process whose all poles lie in the open right half plane it is loop-shaped through adding left half plane poles and zeros so that the system is converted into a regular unstable system, then the loop-shaped unstable process is transformed into a minimum-phase system through mirror-injection, the robust controller is acquired using closed-loop gain shaping algorithm. Because its largest singular value curves are similar before or after the unstable process is mirror-injected, and the closed-loop gain shaping algorithm constructs directly the robust controller using parameters having engineering sense according to the shape of the singular value curves of the robust performance index, the designed controller has equally robustness to the unstable process. The method has the advantages of simple design procedure and obvious physical meaning.