Spatiotemporal-response-correlation-based model predictive control of heat conduction temperature field

Abstract

In many engineering fields, controlling the transient temperature field of the heat conduction process is significant practically. For the temperature field control problem, a spatiotemporal-response-correlation-based model predictive control (STRC-MPC) method is developed. In this method, a spatiotemporal mapping eigenvector of control inputs to temperature field is determined by transient heat conduction equations. According to the correlation degree between the temporal mapping eigenvectors of different spatial points, a finite number of representative spatial points (RPs) are extracted, of which can cover the full mapping characteristic of the temperature field. Meanwhile, the predictive model of the temperature field is reduced offline to temperature predictive models of the RPs. Then, the predictive models of the RPs are applied to design a model predictive controller of the temperature field. In addition, a correlation formulation between the temperature responses of the RPs and that of the measurement points (MPs) is derived by making the control inputs as intermediate variable, and a correlation model between the predictive errors of the two kinds of points is established. Combining the correlation model and the predictive errors of the MPs, the predictive errors at the RPs are estimated and the feedback correction of the predictive model of the RPs is achieved. The STRC-MPC method is employed to control the preheating temperature field of a die casting mold by numerical simulations. The model predictive controller and the feedback correction scheme involved in the proposed control method are verified respectively.