Using Structural Information in System Identification
Abstract: Recent advances in small and cheap communication and sensing have opened up for large scale systems with intricate interconnections and interactions. These applications pose new challenges for analysis and control design. To keep up with the increasing demand on performance and efficiency, accurate models of these systems are needed. Often some prior knowledge of the system, such as system structure, is available.Prior knowledge should whenever possible be used in system identification to improve the model estimate.This thesis addresses the problem of using prior information about the overall structure of the system in system identification. Two special structures are considered, the cascade and the parallel serial structure. The motivation for looking at these structures are two folded; they are common in industrial applications and they can be used to build up almost all interesting feedforward interconnected systems. The effect of sensor placement, input signals and common dynamics of the subsystems on the quality of the estimated models for these two structures is considered.In many control applications it is vital that the model has a physical interpretation. Hence, it is important that the system identification method retains the physical interpretation of the identified model. However, it has proven hard to incorporate prior knowledge of structure in subspace methods. This thesis presents two methods for identifying systems with known structures using subspace methods. The first method utilizes that the state-space matrices of a system on cascade form have a certain structure. The idea is to find a transform that takes the identified system back to this form. The second method uses the known structure of the extended observability matrix. The state-space matrices for the subsystems can then be found by solving linear least squares problems. However, the method is only applicable if the second subsystem has order one. But this is a common case in practice. The two methods are applied to a two tank lab process with promising results.Nonparametric estimates of the frequency response function of systems are used in most engineering fields. The second contribution of this thesis is a new method for estimating the frequency response. The method uses the known structure of the transient or leakage error. The feasibility of the method is tested in simulations. For the two cases considered, one with a large amount of random systems, the second with a resonant system, the method shows good performance compared to current state of the art methods.
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