Assessment and Future Directions of Nonlinear Model Predictive ...

NLMPC: A Platform for Optimal Control 371Avoiding operating point-specific tuning – alternatively stated, achieving invarianceof the closed loop output dynamics – was an important design basis forour nonlinear controller development project. The move suppression based tuningspecification of LQR and traditional MPC results in output dynamics thatare a function of the operating point for the nonlinear case. This is illustratedin Figure 1 from a simulation study detailed in [17]. Invariance of the outputdynamics was a primary reason why the quasilinearized MPC formulation wasnot pursued during the development project.Fig. 1. Operating point dependent output dynamics with quasilinearized MPC formulation.(left) Invariant output dynamics with the NLMPC formulation using Eqn. (1)objective function. (right)3 Models and Parameter EstimationThe majority of the models used to date in ExxonMobil Chemical’s NLMPCapplications consists primarily of first-principles elements with some empiricalelements. For example, a polymerization model that uses fundamentals to predictthe statistical moments of molecular weight distribution may use regressions forpolymer end use properties as a function of the moments, the comonomer composition,etc. A minority of the NLMPC models consists primarily of empiricalelements.The process model will have various parameters that must be specified, such asequipment volumes, physical property constants, kinetic constants, coefficientsin empirical models, and tuning parameters in embedded models of regulatorycontrols. Most of the fitting work is directed at kinetic constants and coefficientsin empirical models. The tuning parameters in the embedded models ofregulatory controls can be calculated directly, or estimated from step tests.The primary means of estimating parameters, p, is weighted least squaresminimization with steady state data collected from process history.minp(N∑OBSj=1∑N Yi=1wi Y (y i,j − yi,jMEASyi,jSCALE ) 2 ) (14)