Global switching control with input constraints for finite dimensional microwave heating model

This work focuses on the global switching temperature control for microwave heating system with the input and output constraints. The traditional partial differential equation (PDE) model contains a spatial differential operator whose eigenspectrum can be divided into an infinite dimensional complement and finite dimensional one. This feature indicates that the existence of finite dimensional ordinary differential equation (ODE) model can approximately captures the dominant dynamics of the initial PDE model. The global switching controller with input constraints is proposed based on the ODE model to regulate the dynamic characteristics of traditional PDE model. Moreover, the exponential stability of closed-loop temperature system is also discussed and proved using the semigroup characteristics. The synthetic controller is implemented on a one-dimensional cavity model and the extensive numerical simulations demonstrate the controller performance and stability.