Experiment design with applications in identification for control

Abstract: The main part of this thesis focuses on optimal experiment design for system identification within the prediction error framework.A rather flexible framework for translating optimal experiment design into tractable convex programs is presented. The design variables are the spectral properties of the external excitations. The framework allows for any linear and finite-dimensional parametrization of the design spectrum or a partial expansion thereof. This includes both continuous and discrete spectra. Constraints on these spectra can be included in the design formulation, either in terms of power bounds or as frequency wise constraints. As quality constraints, general linear functions of the asymptotic covariance matrix of the estimated parameters can be included. Here, different types of frequency-by-frequency constraints on the frequency function estimate are expected to be an important contribution to the area of identification and control.For a certain class of linearly parameterized frequency functions it is possible to derive variance expressions that are exact for finite sample sizes. Based on these variance expressions it is shown that the optimization over the square of the Discrete Fourier Transform (DFT) coefficients of the input leads to convex optimization problems.The optimal input design are compared to the use of standard identification input signals for two benchmark problems. The results show significant benefits of appropriate input designs.Knowledge of the location of non-minimum phase zeros is very useful when designing controllers. Both analytical and numerical results on input design for accurate identification of non-minimum phase zeros are presented.A method is presented for the computation of an upper bound on the maximum over the frequencies of a worst case quality measure, e.g. the worst case performance achieved by a controller in an ellipsoidal uncertainty region. This problem has until now been solved by using a frequency gridding and, here, this is avoided by using the Kalman-Yakubovich-Popov-lemma.The last chapter studies experiment design from the perspective of controller tuning based on experimental data. Iterative Feedback Tuning (IFT) is an algorithm that utilizes sensitivity information from closed-loop experiments for controller tuning. This method is experimentally costly when multivariable systems are considered. Several methods are proposed to reduce the experimental time by approximating the gradient of the cost function. One of these methods uses the same technique of shifting the order of operators as is used in IFT for scalar systems. This method is further analyzed and sufficient conditions for local convergence are derived.