Continuous-Time Multiple-Input, Multiple-Output Wiener Modeling Method

Abstract

This paper introduces a methodology for obtaining accurate continuous-time multiple-input, multiple-output models of nonlinear dynamic systems with Wiener characteristics. The models are obtained from complete reliance on experimental data, and this work demonstrates the effectiveness of optimal statistical design of experiments (SDOE) to fully obtain Wiener models. This method is evaluated on a highly nonlinear continuous stirred tank reactor, and its performance is compared to conventional discrete-time Wiener modeling (DTM) using a pseudo-random sequence design (PRSD) and the same SDOE as the proposed method. The proposed method greatly outperforms the DTM developed from PRSD and moderately outperforms the DTM based on SDOE. This paper introduces a methodology for obtaining accurate continuous-time multiple-input, multiple-output models of nonlinear dynamic systems with Wiener characteristics. The models are obtained from complete reliance on experimental data, and this work demonstrates the effectiveness of optimal statistical design of experiments (SDOE) to fully obtain Wiener models. This method is evaluated on a highly nonlinear continuous stirred tank reactor, and its performance is compared to conventional discrete-time Wiener modeling (DTM) using a pseudorandom sequence design (PRSD) and the same SDOE as the proposed method. The proposed method greatly outperforms the DTM developed from PRSD and moderately outperforms the DTM based on SDOE.

A Study of Experimental Design Optimality for Wiener Systems

“…To calculate the derivative matrix for each design, the analytical derivatives are needed in Equation (2). In this work the true output response, nðtÞ, is modeled using a block-oriented Wiener system and applying the method in Bhandari and Rollins (2003). In the next section, details of this model will be discussed.…”

“…Rollins et al (1998Rollins et al ( , 2003b proposed a closed-form exact solution to the Hammerstein system that they call H-BEST (Hammerstein block-oriented exact solution technique). Bhandari and Rollins (2003) extended this approach to multiple-input, multiple-output (MIMO) Wiener systems and called it the Wiener block-oriented exact solution technique or W-BEST. Because it is given in closed form, the W-BEST …”

“…The solution given above is an exact solution under certain restrictions. Details of these conditions and a mathematical proof are presented in Bhandari and Rollins (2003). However, when the linear dynamic function is first order, the only restriction is that the input changes be step changes, which is the case for this work.…”

Optimal Experimental Design for Human Thermoregulatory System Identification

“…In BOM static nonlinear (N) blocks (i.e., functions) and linear (L) dynamic blocks (i.e., dynamic transfer functions) are connected in series and parallel 'sandwich' networks (Pearson and Ogunnaike, 1997). The NL network is formally called a 'Hammerstein system' (see Rollins et al, 2003) and the LN network is formally called a 'Wiener system' (see Bhandari and Rollins, 2003). Block-oriented systems are capable of representing physical processes with nonlinear static and nonlinear dynamic behaviour.…”

Continuous‐time Hammerstein nonlinear modeling applied to distillation

“…Thus, this methodology is able to obtain very accurate ultimate response models over a well designed input space. Rollins et al (2003a) show the superiority of SDOE over PRSD through the use of a quantitative measure of information content based on the D-optimality criterion (Bates and Watts, 1988) and Bhandari and Rollins (2003) demonstrates the superiority of SDOE over PRSD in a study involving a continuous stirred-tank reactor.The main objective of this article is to demonstrate greater accuracy of H-BEST in modeling this high purity distillation column as compared to DTM, which is unable to vary in its structure in the ultimate response over the input space. To this end, this note has the following outline.…”