(61c) Stability and Performance of Economic Model Predictive Control with Discrete Actuators

Authors: 
Risbeck, M., University of Wisconsin--Madison
Rawlings, J. B., University of Wisconsin-Madison
With ever-increasing computing power and availability of data, there exists a significant potential to use mathematical optimization to improve process operation. Model predictive control (MPC) is an advanced process control technique whereby inputs are chosen by solving (in real time) an optimization problem with an embedded process model. Tracking-oriented MPC (in which the objective function is artificially designed to drive the system to a predetermined operating point) has achieved success due to its ability to incorporate satisfaction of constraints with process dynamics. The downside of this approach is that the setpoint must be chosen outside of the control layer, and therefore its selection may not be informed by the best available disturbance forecasts. To ease this restriction, economic MPC has recently been developed to allow the objective function to represent a more concrete goal (e.g., minimizing energy use or maximizing profit) However, accompanying control theory for this class of problem has traditionally applied only to systems with continuous-valued actuators, which means discrete-valued decisions (e.g., on/off, either/or, etc.) must still be made in a different layer, often via heuristic methods. This separation requires MPC to react to the discrete choices rather than proactively make them, and thus it would be desirable to consider all of the decisions in a single optimization. Recent results have extended the theory for tracking MPC to cover systems in which actuators are both discrete and continuous. In this presentation, we take this idea a step further and extend results for stability and closed-loop performance of economic MPC to allow discrete-valued inputs.

By incorporating discrete actuators, economic MPC can be applied to a much wider variety of systems, for example switched systems whose dynamics can change based on the current operating mode, as well as scheduling environments in which discrete assignments must be made between units and specific tasks. Due to the geometry of the input set, steady-state operation is often not sufficient to achieve low economic cost while still satisfying all of the necessary constraints, and thus we show how a periodic reference trajectory can be used to bound closed-loop performance. In addition, we demonstrate how cost structures like demand charges, which penalize the peak value of a state rather than a time-varying sum, can be incorporated into the economic MPC framework. Finally, by means of of simulation, we will examine the gap between realized closed-loop cost and the optimal infinite-horizon cost. The end goal is to provide a means to utilize the ongoing advances in math programming methods to implement real-time dynamic optimization within a rigorous mathematical framework. By incorporating feedback at each timestep, these controllers can quickly respond to unexpected disturbances to ensure that the process continues to operate as close to optimally as possible. With the addition of discrete actuators, economic MPC can be used to make higher-level decisions that have previously been outside the realm of feedback control, leading to improved economic performance.

Works Cited

  1. Rawlings, J.B., Risbeck, M.J., 2017. Model predictive control with discrete actuators: Theory and application. Automatica 78, 258-265.

  2. Angeli, D., Amrit, R., Rawlings, J.B., 2012. On average performance and stability of economic model predictive control. IEEE Trans. Auto. Cont. 57, 1615-1626.

  3. Allan, D.A., Risbeck, M.J., Rawlings, J.B., 2016. Stability and robustness of model predictive control with discrete actuators. Proceedings of the American Control Conference, 32-37.