Design and application of wiener-type inputoutput data-based predictive control to a continuous polymerization reactor

Abstract

Wiener-type input/output data-based predictive control scheme is proposed and applied to a continuous methyl methacrylate (MMA) solution polymerization reactor. The proposed controller is designed on the basis of the Wiener model, which consists of a linear time invariant (LTI) dynamic part and a static nonlinear part. In this study, we identify both linear and nonlinear parts in a manner different from the conventional Wiener model identification methods. For the LTI part identification, we use the linear input/output data-based prediction model which is based on the subspace identification method. We can reduce one more step in calculating the control input in comparison to the earlier studies on the Wiener model, because there is no need to install a stochastic observer by using the linear input/output data-based prediction model. For the static nonlinear part, the inverse of the static nonlinear function is directly identified using the Tchebychev polynomial as a basis function whose order is specified as 5. Instead of identifying, the static nonlinear function itself, its inverse function is used to obtain the linear counterparts of the set-point and the process output. In addition, the LTI part and the inverse of the static nonlinear function are repeatedly identified in turn until the linear output from the LTI part and the linear counterpart from the identified inverse of the static nonlinear function coincide in order to separate the LTI part from the nonlinear part more significantly. The control performance of the proposed control scheme is corroborated by applying the designed controller to the quality control of the polymer product in a continuous MMA solution polymerization reactor. From the on-line digital control experiment, it is observed that the Wiener-type input/output data-based predictive controller performs satisfactorily for the polymer property control in the multi-input multi-output (MIMO) system with input and output constraints.