AN INTERPOLATING MODEL-PREDICTIVE CONTROL STRATEGY WITH APPLICATION TO A WASTE TREATMENT-PLANT

In this paper a new model predictive control (MPC) strategy, applicabl e to a set of nonlinear systems, is proposed and the use of it is demo nstrated on a model of a waste treatment reactor. The MPC strategy is an extension of earlier work in optimization-based control [2]. The mo tivation for the study is to search for approaches to nonlinear MPC wi thout having to solve the full nonlinear problem. We restrict our prob lem by defining a nonlinear model set as a convex combination of a set of bounding linear models. The weighting factors between the models c an be a function of the states and/or inputs. At a given time-instant we compute an optimal future control sequence for each of the bounding linear models. A novel feature is that all models must obey the const raints for each of the control sequences. The reason for these additio nal constraints is that they provide us with feasibility guarantees. I t also is a means of robustifying the MPC. The final control sequence is found by interpolating the control sequences derived from the optim ization problems. There are different possible approaches for choosing the interpolation variables. Provided the optimization criterion and the constraint sets for the control variables and states are convex, t he proposed control algorithm involves only convex optimization proble ms. The interpolating MPC strategy is applied to a waste treatment rea ctor, where the process dynamics are nonlinear and time-varying depend ing on the disturbance. Linearization is carried out to obtain boundin g models for the process. The interpolating MPC is designed based on t he bounding models. Through the example we demonstrate significant imp rovements over a standard quadratic MPC strategy based on linear model s.