Error-triggered spatial model predictive control for oven temperature

Abstract

An error-triggered spatial model predictive control (MPC) strategy is present for the parabolic partial differential equation (PDE) system, utilizing input/output data. The initial model is first constructed, in which the spatial basis functions (SBFs) are obtained through Karhunen-Loève expansion, and the temporal models are trained by the neural network. Due to the time-varying nature of the PDE system and the poor control performance during model updates, an error-triggered mechanism is developed to update the SBFs. Besides, a temporal sliding window is designed to update the temporal models, which can strike a balance between capturing the latest dynamics and maintaining temporal model accuracy. Based on the aforementioned model, a spatial MPC incorporating spatial distribution information is proposed. Theoretical analysis affirms the stability of the proposed controller. To demonstrate the superiority of this method, experiments during the thermal process in an oven are carried out. Compared with the methods with fixed update step size, the proposed method has the smoother actuator response and better control performance.