Assessment and Future Directions of Nonlinear Model Predictive ...

466 Z.K. Nagy et al.straightforward. First-principles models are transparent to engineers, give themost insight about the process, and are globally valid, and therefore well suitedfor optimization that can require extrapolation beyond the range of data usedto fit the model. Due to recent developments in computational power and optimizationalgorithms, NMPC techniques are becoming increasingly accepted inthe chemical industries, NMPC being one of the approaches, which inherentlycan cope with process constraints, nonlinearities, and different objectives derivedfrom economical or environmental considerations. In this paper an efficient realtimeNMPC is applied to an industrial pilot batch polymerization reactor. Theapproach exploits the advantages of an efficient optimization algorithm basedon multiple shooting technique [FAww], [Die01] to achieve real-time feasibilityof the on-line optimization problem, even in the case of the large control andprediction horizons. The NMPC is used for tight setpoint tracking of the optimaltemperature profile. Based on the available measurements the complexmodel is not observable hence cannot be used directly in the NMPC strategy.To overcome the problem of unobservable states, a grey-box modelling approachis used, where some unobservable parts of the model are described through nonlinearempirical relations, developed from the detailed first-principles model.The resulting control-relevant model is fine tuned using experimental data andmaximum likelihood estimation. A parameter adaptive extended Kalman filter(PAEKF) is used for state estimation and on-line parameter adaptation to accountfor model/plant mismatch.2 Nonlinear Model Predictive Control2.1 Algorithm FormulationNonlinear model predictive control is an optimization-based multivariable constrainedcontrol technique that uses a nonlinear dynamic model for the predictionof the process outputs. At each sampling time the model is updated on the basisof new measurements and state variable estimates. Then the open-loop optimalmanipulated variable moves are calculated over a finite prediction horizon withrespect to some cost function, and the manipulated variables for the subsequentprediction horizon are implemented. Then the prediction horizon is shifted orshrunk by usually one sampling time into the future and the previous steps arerepeated. The optimal control problem to be solved on-line in every samplingtime in the NMPC algorithm can be formulated as:∫ t Fmin {H(x(t),u(t); θ) =M(x(t F ); θ)+u(t) ∈Ut kL(x(t),u(t); θ)dt} (1)s.t. ẋ(t) =f(x(t), u(t); θ), x(t k )=ˆx(t k ), x(t 0 )=ˆx 0 (2)h(x(t), u(t); θ) ≤ 0, t ∈ [t k ,t F ] (3)