369922 Accounting for the Regulatory Control Layer in Economic Model Predictive Control of Nonlinear Chemical Processes

Thursday, November 20, 2014: 9:42 AM
404 - 405 (Hilton Atlanta)
Helen Durand1, Matthew Ellis1 and Panagiotis D. Christofides2, (1)Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA, (2)Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA

Industrial chemical process control architectures typically use two control layers, an upper advanced control layer and a lower regulatory control layer, to maintain stability and robustness of a process. In the advanced or constrained control layer, model predictive control (MPC) is often used to account for coupling of process dynamics, process constraints, and optimal process operation considerations. In the regulatory control layer, many proportional-integral-derivative (PID) control loops are used to implement the control actions computed by the advanced control layer. Recently, many researchers have considered using economic MPC (EMPC) in the advanced control layer since it combines feedback control with process economic optimization by employing an objective function that reflects the process economics in its formulation (e.g., [1]-[4]). Within the context of the theoretical developments of various EMPC systems, a common assumption made is that the control actuators operate with a zeroth-order hold (i.e., perfect actuation). However, control actuators have their own dynamics that cause the control actuators to deviate from this ideal behavior. Actual actuation of realistic control actuators is typically modeled as a first-order system with dead time. The parameters of the first-order system (i.e., gain, dead time, and time constant) may be fit to the response data of a given actuator. After this is completed, bounds on the stabilizing gains and time constants of the PID control loops can be established as well as robust stability guarantees can be made while explicitly accounting for the dynamics of each layer of the control architecture. Additionally, appropriate constraints limiting the change of the inputs between sampling periods may be imposed in the EMPC problem to ensure the EMPC solution may be implementable in the regulatory layer.

The main contribution of this work is to investigate the stability properties of control structures with EMPC accounting for the regulatory control layer and to propose a regulatory control layer monitoring methodology by taking advantage of the EMPC solution. To accomplish the goal of deriving conditions where robust stability guarantees can be made accounting for the regulatory control layer, a rigorous theoretical treatment of the overall control framework is completed. Constraints limiting the change of the inputs between sampling periods are imposed in the EMPC layer to ensure that the computed input profile may be tracked by the regulatory control layer (thus, ensuring the existence of a sufficient time-scale separation between the control layers). The closed-loop system (i.e., the system in closed-loop with both layers of the control architecture) may be written as a standard singular perturbation model (e.g., [5]-[6]). Using singular perturbation arguments, conditions for guaranteed closed-loop stability are derived while accounting for the supervisory and regulatory control layers, the actual dynamics of the control actuators, and process economic optimization. Furthermore, utilizing the computed input profile from the EMPC and an appropriate fault-detection and isolation filter (FDI) (e.g., [7]-[8]), a monitoring methodology is proposed for the regulatory control layer to monitor the performance of the PI control loops and to automatically re-tune the gain and time constant of the PI control loops that are performing poorly. The overall approach is demonstrated using several chemical process examples.

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[3] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
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[7] Leosirikul A, Chilin D, Liu J, Davis JF, and Christofides PD. Monitoring and retuning of low-level PID control loops. Chemical Engineering Science. 2012;69:287-295.
[8] Mhaskar P, Liu J, Christofides PD. Fault-Tolerant Process Control: Methods and Applications. London, England: Springer-Verlag, 2013.


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