(712c) A Computationally Efficient Approach to Economic Model Predictive Control Via Carleman Approximation

Authors: 
Fang, Y., The Pennsylvania State University
Armaou, A., The Pennsylvania State University
A Computationally Efficient Approach to Economic Model Predictive Control via Carleman Approximation

Yizhou Fang and Antonios Armaou, the Pennsylvania State University, University Park, PA

Proposed Session: Systems and Process Control (10B) 10B00 Economics and Process Control

Abstract:

In recent years, Economic Model Predictive Control (EMPC) has gained popularity in chemical and petrochemical industries. The primary difference of EMPC from traditional MPC is that EMPC is directly formulated to maximize the economic profits. However, one of the remaining major challenges is the heavy burden in computation. The economically optimal cost functions representing the economic performances, unlike traditional tracking MPC, are usually non-quadratic or even non-convex. That may require significant amount of computation and puts a heavy load on the optimizer to identify the economically optimal control inputs. If the optimizer fails to converge to the solution fast enough, the delay in sending the control signals, or sending non-optimal control signals to the system may degrade its closed loop performance, or even cause potential stability issues.

The approach we propose to address this problem is built upon two foundations: the theory of Carleman approximation and the theory of bilinear control systems. Following a Two-Tier approximation, we use high order polynomial states to capture the nonlinearity of the original dynamic process. With an extended bilinear expression and assuming piecewise constant manipulated inputs, we then analytically predict future state trajectories and economic performance. We also analytically calculate the sensitivity of the economic cost function to the manipulated inputs. The sensitivity information significantly increases optimizer performance and reduces the number of iterations. Hence, the computational effort in solving the EMPC problem is sufficiently reduced.

As an application example, we consider a CSTR where ethylene is oxidized by air in a catalytic environment to produce ethylene oxide. The economic performance of the reactor is characterized by the time-averaged yield of the product. We simulate the system under nominal conditions, under system noise and under model mismatches. Compared with the “standard” EMPC method via numerical simulation, we demonstrate that the proposed method is applicable and leads to significant computational effort savings.

Key words: Economic Model Predictive Control, Carleman Approximation, Computational Efficiency

Reference:

1. Fang Y, Armaou A. Nonlinear Model Predictive Control using a bilinear Carleman linearization-based formulation for chemical processes. 2015 Am Control Conf. 2015;1:5629-5634. doi:10.1109/ACC.2015.7172221.

2. Fang Y, Armaou A. Carleman approximation based quasi-analytic model predictive control for nonlinear systems. AIChE J. 2016;62(11):3915-3929. doi:10.1002/aic.15298.

3. Fang Y, Armaou A. A Formulation of Advanced-step Bilinear Carleman Approximation-based Nonlinear Model Predictive Control. Proc 55th IEEE Conf Decis Control. 2016:4027-4032.

4. Fang Y, Armaou A. A Computationally Efficient Approach of Economic Model Predictive Control via Carleman Approximation. Proc 56th IEEE Conf Decis Control. 2017:submitted.