2024 AIChE Annual Meeting

(457a) Integrating Regulatory Rule-Based Control Logic in Supervisory Economic Model Predictive Control

Authors

Kalantar Neyestanaki, H. - Presenter, University of California, Davis
dela Rosa, L., California State University Long Beach
Ellis, M., University of California, Davis
Typical control system frameworks consist of two control layers: the (upper) supervisory control layer and the (lower) regulatory control layer, wherein the supervisory control layer computes setpoints used by the underlying regulatory control layer to steer the system to operate at these setpoints through manipulation of control actuators. Model predictive control (MPC) has been widely implemented in the supervisory control layer owing to its ability to account for system dynamics and constraints, multivariate interactions, and exogenous inputs while minimizing a cost function over a future time window (e.g., [1,2,3]). The regulatory control layer typically consists of several single-input single-output feedback control loops, such as proportional-integral-derivative (PID) controllers or rule-based controllers (RBCs).

Owing to time-scale separation arguments, the behavior of the regulatory control layer is often neglected in the supervisory MPC layer. For some applications, explicitly accounting for the regulatory control layer behavior in the MPC layer is required. One case is when there is a lack of time-scale separation between the two layers. When using economic MPC (EMPC), formulated with a cost function that represents the system economics, another case is the variable being manipulated by the regulatory control layer is directly correlated with the system economics. Numerous studies have explored the integration of regulatory PID controller behavior into EMPC [4, 5, 6]. However, in certain applications, the use of PID as a regulatory controller may not be applicable. For example, when the equipment to be manipulated can be turned on or off, the regulatory control layer can employ rule-based controllers (RBCs), defined by a set of logical rules to decide whether to turn on or off the equipment. In HVAC systems, for example, constant-speed fans and compressors are used, which can be turned on or off. The devices are also directly correlated to the operating cost. To explicitly account for the regulatory RBC behavior in supervisory EMPC, the RBC’s logical conditions must be converted into a suitable form that can be incorporated into the supervisory EMPC formulation, warranting the need to specifically address the modeling of RBCs within supervisory EMPC.

To this end, we develop a supervisory EMPC framework that accounts for the regulatory RBC control layer logic, which comprises RBCs, to ensure that the EMPC decisions are aware of the behavior of the regulatory control layer. Specifically, a specific class of systems characterized by on/off inputs regulated with RBCs is considered. This class of systems and regulatory RBCs are motivated by thermal systems where equipment can be turned on or off (e.g., HVAC systems) to maintain a temperature within a range around the setpoint. For this class of systems, the supervisory EMPC framework determines setpoints that are provided to the regulatory control layer to regulate the system. Incorporating the regulatory RBC layer into the supervisory EMPC framework necessitates the conversion of RBC logic into inequality constraints so that the RBC logic can be incorporated into the supervisory EMPC formulation. Under nominal conditions, the consistency between the resulting formulation and the system behavior under the RBC layer is validated. Subsequently, leveraging the availability of the RBC layer as an auxiliary control layer, a terminal constraint is developed to ensure that the closed-loop performance is no worse than that achieved under the RBC layer with a pre-specified setpoint schedule. A switching penalty on setpoint changes is incorporated to manage the trade-off between closed-loop performance and the frequency of setpoint changes. The supervisory EMPC framework is applied to a residential building HVAC system, and the results achieved under the supervisory EMPC framework are compared to those achieved under the RBC layer with a pre-specified setpoint schedule.

References

[1] X. Qian, K. Huang, S. Jia, H. Chen, Y. Yuan, L. Zhang, and S. Wang, “Composition/temperature cascade control for a Kaibel dividing-wall distillation column by combining PI controllers and model predictive control integrated with soft sensor,” Computers and Chemical Engineering, vol. 126, pp. 292–303, 2019.

[2] R. Singh, M. Ierapetritou, and R. Ramachandran, “System-wide hybrid MPC–PID control of a continuous pharmaceutical tablet manufacturing process via direct compaction,” European Journal of Pharmaceutics and Biopharmaceutics, vol. 85, no. 3, pp. 1164–1182, 2013.

[3] M. Ellis, H. Durand, and P. D. Christofides, “A tutorial review of economic model predictive control methods,” vol. 24, no. 8, pp. 1156–1178.

[4] H. Durand, M. Ellis, and P. D. Christofides, “Integrated design of control actuator layer and economic model predictive control for nonlinear processes,” Industrial and Engineering Chemistry Research, vol. 53, no. 51, pp. 20 000–20 012, 2014.

[5] P. Kumar, J. B. Rawlings, and P. Carrette, “Modeling proportional–integral controllers in tracking and economic model predictive control,” Journal of Process Control, vol. 122, pp. 1–12, 2023.

[6] A. Afram and F. Janabi-Sharifi, “Supervisory model predictive controller (MPC) for residential HVAC systems: Implementation and experimentation on archetype sustainable house in Toronto,” Energy and Buildings, vol. 154, pp. 268–282, 2017.