Non-Iterative Data-Driven Model Reference Control

In model reference control, the objective is to design a controller such that the closed-loop system resembles a reference model. In the standard model-based solution, a plant model replaces the unknown plant in the design phase. The norm of the error between the controlled plant model and the reference model is minimized. The order of the resulting controller depends on the order of the plant model. Furthermore, since the plant model is not exact, the achieved closed-loop performance is limited by the quality of the model. In recent years, several data-driven techniques have been proposed as an alternative to this model-based approach. In these approaches, the order of the controller can be fixed. Since no model is used, the problem of undermodeling is avoided. However, closed-loop stability cannot, in general, be guaranteed. Furthermore, these techniques are sensitive to measurement noise. This thesis treats non-iterative data-driven controller tuning. This controller tuning approach leads to an identification problem where the input is affected by noise, and not the output as in standard identification problems. A straightforward data-driven tuning scheme is proposed, and the correlation approach is used to deal with measurement noise. For linearly parameterized controllers, this leads to a convex optimization problem. The accuracy of the correlation approach is compared to that of several solutions proposed in the literature. It is shown that, if the order of the controller is fixed, both the correlation approach and a specific errors-in-variables approach can be used. The model reference controller-tuning problem is extended with a constraint that ensures closed-loop stability. This constraint is derived from stability conditions based on the small-gain theorem. For linearly parameterized controllers, the resulting optimization problem is convex. The proposed constraint for stability is conservative. As an alternative, a non-conservative a posteriori stability test is developed based on similar stability conditions. The proposed methods are applied to several numerical and experimental examples.

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