Assessment and Future Directions of Nonlinear Model Predictive ...

368 R.D. BartusiakDuring the past decade, ExxonMobil Chemical has concentrated its efforts inNLMPC on implementing applications. During this period, the general state ofthe art has progressed from a sense that NLMPC was computationally infeasible[6], through demonstrations of practicality by the research community [7], to thepoint where several process control vendors now offer nonlinear control products[8] [9].In this paper, Section 2 outlines the control algorithm as licensed. Section3 discusses modeling and parameter estimation. Section 4 provides closed loopresults from several industrial processes. Section 5 discusses the current state ofindustrial practice and highlights needs for improvement of the technology.2 Control AlgorithmThe moving horizon controller that was developed solves the following nonlinearoptimization problem online. In the objective function (Eqn. 1), J 1 is a coston deviations of the controlled variables from their reference trajectories, J 2 isan economic cost associated with input, output, or state variables, J 3 is a coston incremental moves of the manipulated variables, and µ i are weights. Theobjective function is detailed below in Eqns. 10, 11, and 12.subject tominu(µ 1 J 1 + µ 2 J 2 + µ 3 J 3 ) (1)0= f(ẋ, x, u, v, p)0= g(x, u, v, p)0=y − h(x, u, v, p)(2)x(0) = x 0 and y(0) = y 0 (3)ẏ =(SP h − (y + b))/τ c + P h − S h (4)ẏ =(SP l − (y + b))/τ c + S l − P l (5)P h ,S h ,P l ,S l ≥ 0 (6)b = y meas − y (7)u LB ≤ u ≤ u UB (8)|u k − u k−1 |≤∆u B (9)