Full-state feedback LQR with integral gain for control of induction heating of steel billet

Induction heating is widely used in industrial furnaces due to its rapid response and energy efficiency. Computer-aided modelling and simulation are necessary for the design and optimisation of these furnaces. This article focuses on modelling and simulating induction heating of a one-dimensional spatial partial differential model for a rectangular carbon steel billet. The simulation considered temperature dynamics, including the skin effect and heat loss via radiation. The partial differential model was converted into a state-space model for designing a full-state feedback Linear Quadratic Regulator (LQR) with integral action. This controller was effectively applied to regulate the billet’s core temperature from 1000 °C to 1200 °C, under different input, R and state, Q, weighing matrices for the LQR, as well as in the presence of disturbances.