370158 Selection of Control Configurations for Economic Model Predictive Control Systems

Thursday, November 20, 2014: 4:43 PM
404 - 405 (Hilton Atlanta)
Matthew Ellis, Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA and Panagiotis D. Christofides, Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA

Control structure design (i.e., the selection of manipulated, controlled, and measured variables or outputs) has been the subject of extensive research within the process control community for many years resulting in many methods for input-output and control configuration selection  (e.g. [1]-[2]). Most of the control structure selection methodologies have been developed using linear steady-state or dynamic process models with the assumption that the system is to be operated at steady-state (i.e., the main control objective is to force the system to the desired operating steady-state and maintain operation at this state in the presence of disturbances). Within the context of dynamic operation of nonlinear systems, fewer results and methodologies on control structure selection exist that explicitly consider the process dynamics and nonlinearities. A simple and potentially effective method for evaluating control configurations of multivariable nonlinear systems is to employ a relative degree analysis which may be useful since the relative degree is essentially a measure of the direct effect or physical closeness between an input and an output [3]. Recently, economic model predictive control (EMPC), which is a nonlinear predictive control scheme that optimizes an objective function describing the process economics a control scheme, has been proposed to integrate economic optimization and process control (e.g., [4]-[6]). EMPC may operate the system in a possibly dynamic fashion (i.e., forced dynamic operation) to optimize the process economics. For EMPC, not all of the possible manipulated inputs must have a direct effect on the economic cost of the EMPC since it is not derived from traditional control objectives. As a consequence, control configuration selection for  EMPC (i.e., which inputs to manipulate for a given EMPC cost) is an open and relevant problem. Since EMPC may dictate a dynamic operating policy, the system may be operated in a larger region of operation (i.e., the effect of nonlinearities in the process may become significant) compared to traditional/conventional control schemes which force the system to operate in a small neighborhood of the steady-state. Thus, traditional methods that evaluate control structures on the basis of steady-state operation using linear or linearized models may not provide sufficient results within the context of EMPC.

Owing to the aforementioned considerations, a methodology for control configuration selection for EMPC is proposed. Treating the economic cost function as the output, a relative degree analysis is completed to determine which inputs have the most direct dynamic effect on the economic cost. The choice of inputs that are controlled by EMPC are the inputs that have a low relative degree with respect to the cost function (typically, one or two). The remaining possible inputs are partitioned to the set of inputs controlled by EMPC and the set of remaining inputs that are not controlled by EMPC on the basis of a sensitivity analysis and a relative degree analysis of any known disturbances. Furthermore, the set of inputs selected for EMPC is ensured to be a stabilizing one. The remaining inputs not controlled by EMPC may be held constant if the control configuration selected has a sufficient degree of robustness or they may be manipulated through other control systems (i.e., outside of EMPC). An evaluation and analysis of the control configuration selection methodology is provided using a chemical process example.

[1] Heath JA, Kookos IK, Perkins JD. Process control structure selection based on economics. AIChE Journal. 2000;46:1998-2016.
[2] Skogestad S. Self-optimizing control: the missing link between steady-state optimization and control. Computers \& Chemical Engineering. 2000;24:569-575.
[3] Daoutidis P, Kravaris C. Structural evaluation of control configurations for multivariable nonlinear processes. Chemical Engineering Science. 1992;47:1091-1107.
[4] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[5] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[6] Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.

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