Estimação recursiva de características estáticas não lineares utilizando modelos polinomiais NARMAX

Abstract

Many real dynamical systems have well-defined nonlinear static characteristic curves. The system gain is, in general, determined by such curvesand varies both with the operating point and in time. The main objective of this work is to recursively estimate nonlinear static characteristic curves of a real system using polynomial NARMAX models. In this way it is hoped that temporal variations of such curves can be quantified. In order to test some of the ideas developed in this work, a simple thermalsystem was used. The nonlinear static characteristic curves of this system can be easily obtained from static testing thus suggesting its use to validate the results. Firstly, models with linear, quadratic and cubic terms were identified. In order to determine the model structures the following complimentary approaches were used: term cluster analysis, the Error Reduction Ratio (ERR) criterion and information criteria. The identied models were validated statistically and dynamically. Another aspect that was taken into account in choosing the best models was how well the nonlinear static characteristic was represented in each model. Ten models were described and compared using these criteria,Secondly, a few model structures, from the models obtained in the firststep, were chosen to perform the recursive identification. Hence the model parameters and respective nonlinear static characteristic curves were estimated using a recursive algorithm. A test was performed on the thermal system during which the nonlinear static characteristic curve was changed. The resulting data were used together with the estimation procedures defined previously and the results suggest that it was possible to recursively follow the changes in the nonlinear static characteristic curve It is believed that this type of information might be useful in control problems and supervision of nonlinear dynamical systems.