Simultaneous parametric uncertainty modeling and robust control synthesis by LFT scaling

Abstract

Given a set of experimental data points in the plant parameter space, the objective of this paper is to give a systematic method for designing a controller to achieve a prescribed level of robust performance for the closed-loop system. A standard procedure would be to model the data first and then to design a controller. Our focus here, instead, is to complete these two tasks simultaneously, eliminating the conservatism caused by the fact that the data is modeled independently of the closed-loop objective. To this end, integral quadratic constraints (IQCs) are used as a tool for uncertainty modeling. We propose the LFT scaling to integrate the IQC modeling with the control synthesis. It is shown that the LFT scaling provides a condition dual to the standard IQC for linear time-invariant systems, and this duality result is essential for solving the simultaneous modeling and synthesis problem. A solution is given in terms of matrix inequalities and its computational aspects are discussed. The proposed method is applied to the control design for an AC linear servo motor, and experimental results demonstrate that our method achieves the performance superior to that achieved by existing methods.