Recursive Black-box Identification of Nonlinear State-space ODE Models

Nonlinear system identification methods is a topic that has been gaining interest over the last years. One reason is the many application areas in controller design and system development. However, the problem of modeling nonlinear systems is complex and finding a general method that can be used for many different applications is difficult. This thesis treats recursive identification methods for identification of systems that can be described by nonlinear ordinary differential equations. The general model structure enables application to a wide range of processes. It is also suitable for usage in combination with many nonlinear controller design methods. The first two papers of the thesis illustrates how a recursive prediction error method (RPEM) can be used for identification of an anaerobic digestion process and a solar heating system. In the former case the model complexity is significantly reduced compared to a semi-physical model of the system, without loosing much in model performance. In the latter case it is shown that it is possible to reach convergence even for a small data set, and that the resulting model is of comparable quality as a previously published grey-box model of the same system. The third paper consists of a convergence analysis of the studied RPEM. The analysis exploits averaging analysis using an associated ordinary differential equation, and formulates conditions for convergence to a minimum of the criterion function. Convergence to a true parameter set is also illustrated by an example. The fourth, and last, paper of this thesis addresses the problem of finding suitable initial parameters e.g. for the RPEM. With a potentially nonconvex criterion function the choice of initial parameters becomes decisive for whether the algorithm converges to the global optimum, or a local one. The suggested initialization algorithm is a Kalman filter based method. Experiments using a simulated example show that the Kalman based method can, under beneficial circumstances, be used for initialization of the RPEM. The result is further supported by successful identification experiments of a laboratory scale cascaded tanks process, where the Kalman based method was used for initialization. List of Publications The thesis is based on the following papers (in order of appearance): (I) L. Brus, “Nonlinear Identification of an Anaerobic Digestion Process”, in Proceedings of IEEE International Conference on Control Applications, Toronto, Canada, Aug. 2005, pp. 137-142. (II) L. Brus. Nonlinear Identification of a Solar Heating System, in Proceedings of IEEE International Conference on Control Applications, Toronto, Canada, Aug. 2005, pp. 1491-1497. (III) L. Brus, ”Convergence Analysis of a Nonlinear Recursive Black-box Identification Algorithm”, Automatica, 2005, Submitted. (IV) L. Brus, T. Wigren, and B. Carlsson, “Black-box Identification of Nonlinear ODE models applied to Laboratory Plant Data”, Transactions on Control Systems Technology, 2005, Submitted. Parts of the material in Paper IV will be published in L. Brus and T. Wigren, ”Constrained ODE Modeling and Kalman Filtering for Recursive Identification of Nonlinear Systems”, in Proceedings of IFAC Symposium on System Identification 2006, Newcastle, Australia, March 2006. Since the papers were written to be understood separately, some of the information is overlapping.