Improved receding horizon H∞ temperature spectrum tracking control for Debye media in microwave heating process

Abstract This paper considers the problem of tracking control for the coupled thermal-electromagnetic model with temperature-dependent permittivity in microwave heating process, where the incident electrical field is subject to the asymmetrical saturation. Due to the nonhomogeneous Neumann boundary condition and inherent infinite-dimensional characteristics for microwave heating process, it is difficult for us to readily design and implement tracking controller. With the help of improved spectral Galerkin method, the traditional partial differential equation (PDE) model is transformed into the linear finite-dimensional ordinary differential equation (ODE) model which can be subsequently used for controller design. Then, the receding horizon H ∞ control strategy is improved to stabilize the derived uncertain ODE error model with asymmetrical input saturation and bounded external disturbance. The outcome of improved algorithm is formulated as a linear matrix inequalities (LMIs) optimization problem, which can be on-line updated by applying the finite-different time-domain (FDTD) method. Finally, the improved control strategy is successfully applied in one-dimensional cavity model for tracking temperature spectrum.