Iterative identification and two step control design for partially unknown unstable plants

In this paper we shall extend the applications of iterative identification and control design to partially unknown unstable plants. We show that by employong a two step approach, where an unstable plant is first stabilized by a parallel feedback stabilizer, it is possible to design systematically an overall closed-loop system that has good step responses with little overshoots by using the iterative identification and control design methodology. Furthermore, this approach easily preserves the simplicity of an IMC design through tuning the overall designed closed-loop bandwidth with a single design parameter. Specifically, similarly to situations where the plant is stable (apart from possibly including a simple integrator), we can design a system with a small initial overall designed closed-loop bandwidth (after the plant is stabilized by a known parallel feedback stabilizer) such that high frequency unmodelled dynamics of the plant are not overly excited. Through iterative applications of a control-relevant closed-loop system identification procedure and the standard IMC design method to the stabilized plant, the overall designed closed-loop bandwidth of the system can be widened progressively while maintaining good step responses with little overshoots. Two simulation examples are employed to illustrate the method. These examples show that, irrespective of the presence of adverse unstable real pole-zero structures, the expected results are achievable by the method described.