(644b) Development of Offset-Free MPC Framework for Hydraulic Fracturing Process Using Sindy
AIChE Annual Meeting
Thursday, November 11, 2021 - 3:49pm to 4:08pm
Hydraulic fracturing is a highly complicated process where many vital characteristics are not considered when developing a mathematical model . In the proposed framework, we use SINDy to identify a model that captures the offset between plant measurements and first-principles model predictions of a fracturing process, namely fracture width, width at the wellbore, and fracture length. The resulting sparse model, which describes the offset, is considered as a disturbance term in the offset-free MPC formulation. Thus, the disturbance model in the framework represents the nonlinear dynamics of the offset which in this case represents the structural uncertainty. Structural uncertainty is a term in the offset-free MPC that describes the model bias which comes from the underlying knowledge of the process. This disturbance model is then augmented to the state-space model, and the states are driven to their set points using the modeled structural uncertainty. These state and disturbance estimates are used to initialize the MPC problem . Generally speaking, offset free control is guaranteed when there are no constraints or when the disturbance is either a constant or linear in nature [6,7]. Here, we apply the identified plant-model mismatch to the shrinking horizon optimal control problem to improve the prediction accuracy and closed-loop performance of the MPC . The disturbance estimates from the SINDy model strengthen the prediction accuracy in the shrinking horizon problem as the offset-free framework captures the system's nonlinear dynamics well.
The proposed SINDy-based offset-free MPC framework has high reference tracking performance, requires significantly lesser data to cope with rapid system changes by representing the offset's nonlinear nature. The framework is computationally more efficient and robust to noise than the nominal MPC models that use either neural networks for plant model mismatch or complex high-fidelity models. Furthermore, the closed-loop simulation results demonstrate that the proposed framework can efficiently model the intrinsic plant-model mismatch that should be handled for the performance of offset-free MPC. Thus, the proposed method is effective in enhancing the performance of offset-free MPC for real-time applications.
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