On two-step controller design for partially unknown unstable systems

This paper reports an improvement in the control design procedure of iterative identification and control design for partially unknown unstable (not necessarily minimum-phase) systems. It proposes a systematic two-step control design approach, which ultimately results in a two degrees-of-freedom structure. In this approach, the unstable plant is first stabilized by a parallel feedback stabilizer with minimum weighted energy. In the second step of the design, a mixed-sensitivity H_∞ controller is designed on the basis of the stabilized plant to improve the overall performance of the closed-loop system. Through the proposed method, the bandwidth of the overall closed-loop system can be systematically expanded (increased) in the second step of the design. The effectiveness of this algorithm is verified by a numerical example and a real-time experiment on a non-minimum phase unstable active magnetic bearing system. The proposed method offers a simple but effective design structure which provides desirable results that may not be achievable by a single-step controller design method.