IDENTIFICATION AND MODEL PREDICTIVE CONTROL OF NONLINEAR AND MULTIVARIABLE PROCESSES

Abstract

It is a well known fact that nonlinear model predictive control (NMPC) exhibits greater potential for improving process operation in comparison to linear model predictive control (MPC). It, however presents a number of theoretical and practical problems which are considerably more challenging than those associated with linear MPC. These major challenges include determination of nonlinear model which can be used in the MPC framework and solution of the non-convex optimization problem that results from the use of nonlinear models in NMPC algorithm (Henson 1998). Through the present work, solution to some of the above problems have been investigated by undertaking research problems related to data driven model identification and model predictive control of highly nonlinear and interactive multivariable processes. An experimental setup, consisting of two such nonlinear and interactive multivariable processes namely the mixing tank process and. the quadruple tank process, has been simulated, designed and installed. The mixing tank process aims at control of three output variables such as level, temperature and conductivity in the mixing tank by manipulating three input variables namely: fresh water flow rate, concentrated salt solution flow rate and heater power. The quadruple tank process consists of two controlled variables (levels in the two bottom tanks) and two manipulated variables (inlet water flow rates). These two experimental processes have been designed to share several common instruments and equipment to reduce the total cost of the set-up. Nonlinear block-oriented Hammerstein and Wiener models (consisting of linear dynamic and nonlinear static functions in series) of the mixing tank process are identified using a two stage procedure, involving closed-form exact solution technique developed by Bhandari and Rollins (2003). In this technique, the statistical design of experiments is used to obtain optimal input-output simulated data for the purpose of parameter estimation. Multivariable interactions and process nonlinearities are handled effectively with this modeling technique, which is confirmed by the high R2 values (greater than 99 %). Further, linear transfer function models of this process are also identified from the same simulated data. Thus obtained linear transfer function model as well as nonlinear Hammerstein and Wiener models have been validated using the experimental data from the mixing tank process. Validation results show that Hammerstein and Wiener models exhibit better prediction accuracy as compared to the linear transfer function model. Further, linear transfer function models of quadruple tank process are identified for three operating configurations namely - minimum phase, verge-of-instability and non-minimum phase. Validation of these linear transfer function models with the experimental data obtained from the quadruple tank process show that the prediction accuracy of the linear models decrease when the process changes from minimum phase to non-minimum phase, which is indicated by an increase in the sum of squared prediction (SSPE) values for the two process outputs. Novel NMPC frameworks based on Hammerstein and Wiener models are proposed for controlling the multivariable mixing tank process. The proposed new Hammerstein model based NMPC (HNMPC) is an extension of MPC controller developed by Fruzetti et al. (1997) for SISO and lower order nonlinear processes. Similarly, the proposed Wiener model based nonlinear generalized predictive controller (WNGPC) is an extension of the work by Norquay et al. (1998) for SISO processes. The challenges involved in extending the SISO controllers to higher order, nonlinear and multivariable interactive processes such as dealing with intermediate variables and solution of simultaneous nonlinear equations are successfully addressed. Simulation results obtained for newly designed HNMPC and WNGPC for the mixing tank process show significant performance improvement over their linear counter parts in both unconstrained and constrained cases. For quadruple tank process, two types of control configurations i.e. multi-loop PI control and MPC control are tested for all the three operating configurations. As the quadruple tank process exhibits linear dynamics, nonlinear model predictive controllers based on Hammerstein and Wiener models are not tested. It is observed that the proposed MPC for quadruple tank process is superior to multi-loop PI controllers for the minimum phase and the verge-of-instability operating configurations. For the non-minimum phase configuration, this process posed control challenge in terms of uncontrollability. In order to achieve closed loop stability of the non-minimum phase configuration, a new tuning rule for MPC is proposed and tested. The proposed tuning rule exhibits better results, though the stable closed loop response is slower than the response in the minimum phase.