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 purposes. Modulating functions methods are especially suitable for this task because they use the original continuous- time differential equations and avoid differentiation of noisy signals. Among the many versions of the method available, Pearson–Lee method offers a computationally efficient alternative. In this paper, Pearson–Lee method is generalized for non-stationary continuous- time systems and the on-line version is developed. The time dependent parameters are modeled as polynomial splines inside a moving data window and recursion formulae using shifting properties of sinusoids are formulated. The simple matrix update relations considerably reduce the number of computations required when compared with repeatedly using FFT. The method is illustrated for estimating the kinetic rates and yield factors as time - varying parameters in a fermentation process. The Monod law along with temperature 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 estimate the kinetic rate parameters.