Assessment and Future Directions of Nonlinear Model Predictive ...

Chance Constrained Nonlinear Model PredictiveControlLei Xie 1,3 ,PuLi 2 ,andGünter Wozny 31 State Key Laboratory of Industrial Control Technology, Institute of AdvancedProcess Control, Zhejiang University, Hangzhou 310027, ChinaLeiX@iipc.zju.edu.cn2 Institute of Automation and Systems Engineering, Ilmenau University ofTechnology, P.O. Box 100565, Ilmenau 98684 GermanyPu.Li@tu-ilmenau.de3 Department of Process Dynamics and Operation, Berlin University of Technology,Sekr. KWT 9, Berlin 10623, GermanyGuenter.Wozny@tu-berlin.deSummary. A novel robust controller, chance constrained nonlinear MPC, is presented.Time-dependent uncertain variables are considered and described with piecewisestochastic variables over the prediction horizon. Restrictions are satisfied with auser-defined probability level. To compute the probability and its derivatives of satisfyingprocess restrictions, the inverse mapping approach is extended to dynamic chanceconstrained optimization cases. A step of probability maximization is used to addressthe feasibility problem. A mixing process with both an uncertain inflow rate and anuncertain feed concentration is investigated to demonstrate the effectiveness of theproposed control strategy.1 IntroductionModel predictive control (MPC) refers to a family of control algorithms whichutilize an explicit model to calculate the manipulated variables that optimize thefuture plant behaviour. The inherent advantages of MPC, including its capabilityof dealing with multivariate variable problems as well as its capability of handlingconstraints, make it widely used in the process industry.Due to the nature of process uncertainty, a robust MPC is desired to obtainsatisfactory control performances. Including uncertainty in control system designwill enhance the robustness of MPC. Generally speaking, there are threebasic approaches to address uncertainty. The constant approach which assumesthe model mismatch is unchanged during the prediction horizon [1] leads to anaggressive control strategy. In contrary, the Min-Max approach in which theboundaries of the uncertain variables are taken into account [2] is too conservative.The third one is the stochastic approach, or chance constrained MPC[3], [4], in which uncertain variables in the prediction horizon are described asstochastic variables with known probability distribution functions (PDF). Restrictionsare to be satisfied with a user-defined probability level. Due to thefact that using this method a desired compromise between the optimal functionR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 295–304, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007