(172d) A Multiple Model Predictive Control Approach Based on Dynamic Discrepancy Reduced Order Modeling

Model predictive control (MPC) has been widely used in industrial process applications due to its ability to forecast the dynamic behavior of multiple-input, multiple-output systems and to incorporate constraints associated with the physical system into the controller formulation. To reduce the MPC online computational burden, the dynamic system model developed for MPC purposes can be represented using a reduced-order model. The plant-model mismatch of a reduced-order model is only negligible in a subset of the dynamic operating region. A possible solution to this problem is to cover the operating region with a set of linearized models in a multiple-model adaptive control algorithm^[1]. However, a systematic approach to build a reduced-order model set for MPC applications is lacking, especially when the system is operating under uncertainty. Reduced-order models can increase the output variances when the dynamic system is affected by stochastic disturbances, which can lead to suboptimal controller performance.

To address the aforementioned challenges of reduced-order models in advanced control, a novel grey box model identification algorithm for process control is developed by integrating dynamic operability mapping and statistical calibration. In the developed framework, the plant is represented by a high-fidelity model and the reduced-order models are initially chosen to be linear time-invariant state-space models. Dynamic operability mapping^[2] is performed to analyze the mismatch between the plant model and the reduced-order models and new linearizations at high mismatch neighborhoods are performed to enhance the model bank for MPC. For each linearized model, discrepancy terms in the form of Gaussian processes with Bayesian smoothing spline are added to the disturbance matrix, and the linear model is calibrated to the plant model using a Bayesian approach^[3].

For the application in focus, a setpoint tracking MPC is implemented for a Fischer-Tropsch synthesis process that takes place in a slurry bubble column reactor. The Fischer Tropsch process is a collection of reactions that rearrange the carbon and hydrogen molecules in the syngas to produce higher-value hydrocarbons in the liquid products. Because the products of this process include a wide range of hydrocarbons from C₁ to C₅₀₊ and the product distribution is influenced by the reactor pressure and temperature, controlling the process conditions simultaneously and accurately is crucial to yield the product with desired specifications. The high-fidelity dynamic model is developed based on a hydrodynamic model from literature^[4] and extended to paraffin and olefin products in the slurry phase. A bank of reduced-order models for this process is built for MPC purposes employing dynamic discrepancy. The proposed multi-model controller with the novel framework is implemented and compared to a traditional MPC and a nonlinear MPC to evaluate its tracking performance.

References:

[1] Rao, R. R., Aufderheide, B., & Bequette, B. W. (2003). Experimental studies on multiple-model predictive control for automated regulation of hemodynamic variables. IEEE Transactions on Biomedical Engineering, 50(3), 277-288.

[2] Gazzaneo, V., Carrasco, J. C., Vinson, D. R., & Lima, F. V. (2020). Process operability algorithms: past, present, and future developments. Industrial & Engineering Chemistry Research, 59(6), 2457-2470.

[3] Bhat, K. S., Mebane, D. S., Mahapatra, P., & Storlie, C. B. (2017). Upscaling uncertainty with dynamic discrepancy for a multi-scale carbon capture system. Journal of the American Statistical Association, 112(520), 1453-1467.

[4] Maretto, C., & Krishna, R. (1999). Modelling of a bubble column slurry reactor for Fischer–Tropsch synthesis. Catalysis today, 52(2-3), 279-289.