Control of nonlinear systems using polynomial ARMA models

Abstract

Most of the advanced nonlinear control algorithms require a model of the system to be controlled. Unfortunately, most of the processes in the chemical industry are nonlinear, and fundamental models describing them are lacking. Thus there is a need for the identification and control of nonlinear systems through available inputoutput data. In this article, we brief& introduce the input-output model used (polynomial ARMA models), and analyze its stability and invertibility. This paves the way to the development of a nonlinear-model-predictive controller. Implementation issues such as modeling of disturbance, state and parameter estimation are discussed. The theory presented is illustrated through examples.

Discrete‐time nonlinear controller synthesis by input/output linearization

“…Similar results were presented very recently (Hernandez and Arkun, 1991) for polynomial ARMA models.…”

“…December 1992 extension of the linear MPC techniques (Biegler and Rawlings, 1991;Hensonand Seborg, 1991b;Hernandez and Arkun, 1991;Hidalgo and Brosilow, 1990;Pathwardhan et al, 1990;Sistu and Bequette, 1991). Geometric process control methods have evolved after about a decade of research on the mathematical characteristics of continuous-time nonlinear systems, using techniques from differential geometry.…”

Discrete‐time nonlinear feedback control of multivariable processes

“…The main advantage of the continuous-time formulation is that physical parameters are explicit in the process model and therefore in the control law. The main advantages of discrete-time formulation are that: the process model and control law are directly suitable for computer implementation; the presence of deadtime does not complicate the control problem; and system identification is, in a sense, more straightforward, for example, one can fit the data to a polynomial ARMA model (Hernandez and Arkun, 1993). Because of these appealing features, the discrete-time formulation has been the recent trend in the literature.…”

Model Predictive Control of Nonlinear Processes

“…This type of polynomial model structures have been used by various researchers for process control (Morningred et al, 1992 ;Hernandez and Arkun, 1993). The main advantage of this model is that it represents the process nonlinearities in a structure with linear model parameters, which can be estimated by using efficient parameter estimation methods such as recursive least squares.…”