Complexity Issues, Validation and Input Design for Control in System Identification

Abstract: System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control.To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems.Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory.The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.