Identification of Continuous Dynamical Systems with "Spline-Type Modulating Functions Method"

Abstract In the paper a technique is presented for identification of continuous dynamical processes by means of a digital computer. The method is basically an equation error, linear-in-the-parameter ("" l -i-p") one, by which the parameters ofa differential equation can be estimated. The essential part of the method is a special "" l -i-p" model of the process, which is based on weighted integration of the measured input-output signals of the process and which is very well suited for digital implementation. The estimation of the parameters of the "" l -i-p" model is done by "least squares" or "instrumental variable" techniques (either OFF- or ON-LINE). After a description of the building of the above model, the properties of this model are investigated (especially with respect to the noise influence) and the possibilities of its implementation are shown. In the practical part of the paper, the properties of the proposed method are demonstrated by use of a simple testprocess. The accuracy of the parameter estimation is thereby compared with the maximum achievable accuracy (Craimer-Rao lower bound).