Optimized Characteristic Ratio Assignment for Low-Order Controller Design

Abstract

It is known that polynomial method is particularly suitable for designing low-order controllers. So far most of the controller design using the polynomial method was based on a pre-defined standard form of the characteristic ratio assignment (CRA). Meanwhile, with limited parameters of the low-order controllers, an exact CRA following a standard form becomes impossible when the order of the control plant is sufficiently high. This paper proposes a systematic design scheme for an optimized CRA. First the influences of the characteristic ratios are quantified as weight coefficients. Then the objective function of the optimization problem is constructed to minimize the difference between the actual CRA and its nominal form. In addition to damping (i.e., the CRA), the requirements on the stability, speed of response, and robustness are also considered as constraints in an optimization problem. The so-called robust optimization problem is then formulated and solved via an inner-outer optimization formulation. Finally, the controller design for a three-mass benchmark system is applied a case study. The simulation results validate the propose scheme especially the robustness against parameter variation, unmodeled dynamics, and disturbance torque.