Time-varying system identification using modulating functions and spline models with application to bio-processes

Time dependent parameters are frequently encountered in many real processes which need to be monitored for process modeling, control and supervision p urposes. Modulating functions methods are especially suitable for this task because they use the original continuous-time differential equations and a void differentiation of noisy signals. Among the many versions of the metho d available, Pearson-Lee method offers a computationally efficient alternat ive. In this paper, Pearson-Lee method is generalized for non-stationary co ntinuous-time systems and the on-line version is developed. The time depend ent parameters are modeled as polynomial splines inside a moving data windo w and recursion formulae using shifting properties of sinusoids are formula ted. The simple matrix update relations considerably reduce the number of c omputations required when compared with repeatedly using FFT. The method is illustrated for estimating the kinetic rates and yield factors as time-var ying parameters in a fermentation process. The Monod law along with tempera ture dependency models were used to simulate the data. The simulation study shows that it is not necessary to assume a growth model in order to estima te the kinetic rate parameters. (C) 2000 Elsevier Science Ltd. All rights r eserved.