A Continuous-Time Nonlinear Dynamic Predictive Modeling Method for Hammerstein Processes

Abstract

This paper extends the method introduced by Rollins et al. (ISA Trans. 1998, 36, 293) to multiple-input, multiple-output systems that give an exact closed-form solution to continuous-time Hammerstein processes written in terms of differential equations and nonlinear inputs. This ability is demonstrated on a theoretical nonlinear Hammerstein process of complex dynamics where perfect identification of the closed-form model is assumed. This paper then demonstrates the simplicity of the proposed identification procedure to obtain an accurate estimate of the exact model using a theoretical Hammerstein model. A powerful attribute of this methodology is the ability to make full use of the statistical design of experiments for optimal data collection and accurate parameter estimation. Application of the proposed method is demonstrated on a household clothes dryer with four input and five output variables. Only 27 trials (input changes) of a central composite design were needed for accurate model development of all five outputs over the input space, and the accurate predictive performance is demonstrated. This paper extends the method introduced by Rollins et al. (ISA Trans. 1998, 36, 293) to multipleinput, multiple-output systems that give an exact closed-form solution to continuous-time Hammerstein processes written in terms of differential equations and nonlinear inputs. This ability is demonstrated on a theoretical nonlinear Hammerstein process of complex dynamics where perfect identification of the closed-form model is assumed. This paper then demonstrates the simplicity of the proposed identification procedure to obtain an accurate estimate of the exact model using a theoretical Hammerstein model. A powerful attribute of this methodology is the ability to make full use of the statistical design of experiments for optimal data collection and accurate parameter estimation. Application of the proposed method is demonstrated on a household clothes dryer with four input and five output variables. Only 27 trials (input changes) of a central composite design were needed for accurate model development of all five outputs over the input space, and the accurate predictive performance is demonstrated.

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.…”

“…The specific BOM method we use for this study is based on a compact closed-form continuous-time exact solution to the Hammerstein system derived by Rollins et al (2003) and validated for the surrogate subject by Rollins et al (2006). This approach is called the Hammerstein Blockoriented Exact Solution Technique or H-BEST and we use in this article what we called in Rollins et al (2006) the 'restricted' prediction algorithm.…”

An Unrestricted Algorithm for Accurate Prediction of Multiple-Input Multiple-Output (MIMO) Wiener Processes

“…However, for processes that are higher than first-order, this algorithm is only valid for step input changes spaced far enough in time for the output responses to approach steady-state conditions. A mathematical proof of this algorithm is given in the work by Rollins et al 13 For step changes that occur, such as those in eq 5, the restricted W-BEST algorithm for the intermediate variable for the (k + 1)th input change in the interval t k < t e t k+1 is given by eq 8:…”

Identification and Nonlinear PID Control of Hammerstein Model using Polynomial Structures

“…Many chemical processes have been modeled with it, for examples, pH neutralization processes [6], distillation columns [7] [8], polymerization reactor [9] [10] and dryer process [11].…”