(622m) Model Predictive Control with Gradient of a Function of the Optimizing Targets

The industrial processes usually operate under a hierarchical structure, where the Real Time Optimization (RTO) and the Model Predictive Control (MPC) are executed in separated layers, resulting in a two or three-layer architecture of plant-operation strategy [1]. The RTO stage determines the operating values of the outputs and inputs that produce the maximum economic profit or the lowest operating costs. In the context of the hierarchical structure, the objective of the MPC controller is to follow the economic targets in presence of disturbances and manipulating directly the process inputs or the set-points of local PID controllers in a cascade configuration. In a recent work [2], the gradient of the economic function is incorporated in the objective function of the MPC controller in order to solve the RTO and MPC problem in one single layer. The approach was successfully simulated in a FCC unit. The strategy consisted in minimizing the gradient of the economic function in a quadratic term so as to maximize the economic profit, and therefore the method requires the convexity of the economic function.

In this work we propose to use the gradient of a convex function that links the RTO targets to the MPC controller, resulting in a two-layer approach. The convex function is a nu+1 dimensional paraboloid of the process inputs, with the minimum corresponding to the input targets resulting from the RTO routine. This controller has infinite prediction horizon and terminal state constraint [3] and operates according to the zone control strategy [4]. The inclusion of slack variables in the MPC optimization problem makes it implementable in practice. In addition, we provide a stability analysis of the closed-loop system for the nominal case.

The proposed MPC was initially tested in a linear system and then, the real time optimization of a continuous polymerization process under the proposed structure was developed. The simulation results of the MPC in a polymerization process showed that the production rate can be maximized in presence of disturbances, preserving the polymer quality and respecting the allowed limits for the controlled outputs.

References

[1] C.M. Ying and B. Joseph. Performance and Stability Analysis of LP-MPC and QP-MPC Cascade Control Systems. AIChE J. 45 (1999) 1521-1534.

[2] G. De Souza, D. Odloak and A. Zanin. Real Time Optimization (RTO) with Model Predictive Control (MPC). Comp. Chem. Eng. 34 (2010) 1999-2006.

[3] D. Odloak, Extended Robust Model Predictive Control. AIChE J. 50 (2004) 1824-1836.

[4] A. González and D. Odloak. A stable model predictive control with zone control. J. Proc. Cont. 19 (2009) 110-122.