ABSTRACT
This chapter contains seven sections plus an appendix. Section 2.2 presents the Laguerre functions, describes how they may be used to develop a transfer function model of a process (called the Laguerre model), and defines the Laguerre coefficients in both the time domain and frequency domain. Sect ion 2.3 refines a classic optimization approach for selecting the time scaling factor in the Laguerre model. Section 2.4 introduces the step response modelling algorithm, in which the model coefficients and the optimal time scaling factor are estimated directly from the step response data itself. Sect ion 2.5 analyzes the statistical properties of the estimated coefficients, leading to the conclusion that their variances are related to the power spectrum of the disturbance. Section 2.6 further analyzes the errors associated with the estimated coefficients in the time domain and proposes a simple data pretreatment procedure that can be applied to the step response data to improve the model accuracy. In Section 2.7, the modelling algorithm
is applied to step response data obtained from a pilot-scale polymerization reactor.
