TABLE OF CONTENTS The output error method has been very successfully used for estimation of parameters of linear/nonlinear dynamical systems. However, the method poses difficulties when applied to inherently unstable systems [10]. Even if the basic unstable plant is operating with a stabilising feedback loop, application of the output error method to estimate directly parameters of the state space models of the system from its input-output data is difficult because of the numerical divergence resulting from integration of state equations. Hence, special care has to be taken to avoid this problem. Two approaches are feasible: i) an artificial stabilisation in the mathematical model (called feedback-in-model) used in output error method; and ii) the filter error method (described in Chapter 5).
This method is based on the fact that the system model used in the parameter estimation (software) can be stabilised by a local feedback in the model [10]. We note that the feedback achieved in this approach is not related to the control system feedback to stabilise the plant (see Fig. 9.1). This observation is also true for the filter error method. The feedback in the feedback-in-model method prevents the numerical divergence and achieves the stabilisation. The method achieves stabilisation of the parameter estimation process, somewhat in a similar fashion as the filter error method. It is applicable to many practical situations if proper care is taken to choose the feedback gain (in the mathematical model of the open-loop unstable plant).
Let...
