On input design in system identification for control

University dissertation from Stockholm : Signaler, sensorer och system

Abstract: There are many aspects to consider when designing system identification experiments in control applications. Input design is one important issue. This thesis considers input design both for identification of linear time-invariant models and for stability validation.Models obtained from system identification experiments are uncertain due to noise present in measurements. The input spectrum can be used to shape the model quality. A key tool in input design is to introduce a linear parametrization of the spectrum. With this parametrization a number of optimal input design problems can be formulated as convex optimization programs. An Achilles' heel in input design is that the solution depends on the system itself, and this problem can be handled by iterative procedures where the input design is based on a model of the system. Benefits of optimal input design are quantified for typical industrial applications. The result shows that the experiment time can be substantially shortened and that the input power can be reduced.Another contribution of the thesis is a procedure where input design is connected to robust control. For a certain system structure with uncertain parameters, it is shown that the existence of a feedback controller that guarantees a given performance specification can be formulated as a convex optimization program. Furthermore, a method for input design for multivariable systems is proposed. The constraint on the model quality is transformed to a linear matrix inequality using a separation of graphs theorem. The result indicates that in order to obtain a model suitable for control design, it is important to increase the power of the input in the low-gain direction of the system relative to the power in the high-gain direction.A critical issue when validating closed-loop stability is to obtain an accurate estimate of the maximum gain of the system. This problem boils down to finding the input signal that maximizes the gain. Procedures for gain estimation of nonlinear systems are proposed and compared. One approach uses a model of the system to design the optimal input. In other approaches, no model is required, and the system itself determines the optimal input sequence in repeated experiments.