Recursive prediction error identification and scaling of non-linear state space models using a restricted black box parameterization

A recursive prediction error algorithm for identification of systems described by non-linear ordinary differential equation (ODE) models is presented. The model is an ODE model, parameterized with coefficients of a multi-variable polynomial that describes one component of the right-hand side function of the ODE. This avoids over-parameterization problems. The selected model can also handle systems with more complicated right-hand side structure, by identification of a local input–output equivalent system in the coordinate system of the selected state variables. A novel technique based on scaling of the sampling period is proposed. The technique can improve the conditioning of the identification problem, thereby enhancing the chances of convergence to the correct minimum of the criterion. The algorithm is applied to live data from a system consisting of two cascaded tanks, with promising results. A MATLAB software package, which implements the proposed algorithm and a set of support scripts, can be freely downloaded from http://www.it.uu.se/research/reports/.