On Structured System Identification and Nonparametric Frequency Response Estimation

University dissertation from Stockholm : KTH Royal Institute of Technology

Abstract: To keep up with the ever increasing demand on performance and efficiency of control systems, accurate models are needed. System identification is concerned with the estimation and validation of mathematical models of dynamical systems from experimental data. The main problem considered in this thesis is how to take advantage of structural information in system identification. Including this additional information can significantly improve the quality of the identified model.First, the problem of input design for networked systems is considered. Results from closed-loop input design are generalized to the networked case. The main difference between the networked setting and the classical open- or closed-loop setting is the possibility of using measurable, or known, disturbances to improve the excitation. Such  disturbances cannot be affected during the experiment and are common in industrial applications.A framework to include the additional information about the measurable disturbances in the input design is presented. The framework is evaluated in two simulation examples and several interesting observations are made.Second, the result from an input design is often the correlation properties of the input signal.The question is then how to generate the input signal that can be applied to the system with the given properties.  This thesis presents a novel signal generation method that is able to handle input and output constraints. In industrial applications, it is often vital to satisfy constraints on both the input and the output signals during the system identification experiment. The method is formulated as a reference tracking Model Predictive Controller (MPC), with the desired correlation properties of the signal as reference, while satisfying the input and output constraints on the considered system.  The core of the algorithm is the formulation of the signal generation as an MPC which allows the use existing tools to make the algorithm robust and adaptive. The proposed method is evaluated in several simulation studies and successfully applied to a physical lab process.Third, nonparametric estimates of the frequency response function of a system are used in almost all engineering fields. The final contribution of this thesis is to present a novel nonparametric method, called the Transient and Impulse Response Modeling Method (TRIMM). The method is inspired by the local polynomial method, but uses more information about the known structure of the leakage error in the estimation of the frequency response. The bias and variance errors of TRIMM are analyzed and the results are used to connect system properties and the choice of user parameters with the performance of the method. The analysis can also be used to compare the performance of different methods and to give guidelines to the user on how to choose method.