Licentiate thesis 2006-001

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

Linda Brus

January 2006


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 non-convex 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.

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