Iterative design of structured uncertainty models and robust controllers based on closed-loop data

A joint uncertainty modelling and robust control design method is presented for linear time-invariant (LTI) systems. The system is given as a linear fractional transformation (LFT) with structured uncertainty blocks. The goal is to optimise the robust performance of the closed loop by simultaneously creating an optimised uncertainty model consistent with measurement data and designing a robust controller using skew μ synthesis. The proposed modelling/validation and control design algorithm is placed in the iterative identification and control (IIC) framework (design-experiments-analysis loop). In the proposed IIC approach, weighting functions of structured perturbation models are designed, which may lead to less conservative controllers compared to unstructured perturbations and disturbances. No a priori information is required on the disturbances. An advantage of the proposed method in the μ-synthesis context is that the number of fixed design parameters used in robust control (typically frequency-dependent weighting functions) is reduced to those associated with the control performance specification. The weighting functions of the uncertainty model are parameterised in the frequency domain and tuned subject to model validation constraints. It is shown that using skew μ as a robust performance criterion for both uncertainty modelling and control design, the proposed scheme simultaneously improves the robustness and performance of the control system. The efficiency of the method is illustrated on a vehicle steering problem.