Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems

Estimation of physical parameters is an important subclass of system identification. The specific objective is to obtain accurate estimates of the model parameters, while the objective of other aspects of system identification might be to determine a model where other properties, such as responses for certain input in the time or frequency domain, are emphasised. Consequently, some special techniques are required, in particular for input signal design and model validation. The model structure containing physical parameters is constructed from basic physical laws (mathematical modelling). It is possible and essential to utilise this physical insight in the input design and validation procedures. This project has two objectives: 1. To develop and apply theories and techniques that are compatible with physical insight and robust to violation of assumptions and approximations, for system identification in general and estimation of physical parameters in particular. 2. To apply the new methods for modelling of specific objects, such as loudspeakers, ac- and dc-motors wind turbines and beat exchangers. A reliable quality measure of an obtained parameter estimate is a prerequisite for any reasonable use of the result. It is also necessary for experiment design, in particular for determination of optimal input signals. The prevalent quality compared to this approach is · More independent of assumptions and approximations, e.g. about the noise, · Due to a geometric interpretation (the "sensitivity ellipsoid"), it is very compatible with physical insight, and iii) it is applicable for physical parameters as well, whether these parameters are estimated directly, or indirectly from the discrete-time parameters. Under the usual assumptions about the noise, a simple relationship between the sensitivity and the relative parameter variance and confidence ellipsoid is demonstrated. The relation is based on a new theorem on maxima of an ellipsoid. The procedure for input signal design and physical parameter estimation is tested on a number of examples, linear as well as nonlinear and simulated as well as real processes, and it appears to perform very well.