Receding horizon H_∞ guaranteed cost tracking control for microwave heating medium with temperature-dependent...

Area of Science:

• Control Systems Engineering
• Microwave Heating Technology
• Applied Mathematics

Background:

• Microwave heating models present complex control challenges including asymmetrical input saturation, nonhomogeneous boundary conditions, and temperature-dependent material properties.
• Existing control strategies may not adequately address the combined effects of these factors, potentially limiting performance and stability.
• Accurate temperature spectrum tracking is crucial for efficient and safe microwave heating applications.

Purpose of the Study:

• To develop a robust temperature spectrum tracking control strategy for microwave heating systems.
• To address the challenges posed by asymmetrical input saturation, nonhomogeneous Neumann boundary conditions, and temperature-dependent permittivity.
• To ensure guaranteed cost performance and minimize the H∞ norm of the closed-loop system.

Main Methods:

• Derivation of a finite-dimensional ordinary differential equation (ODE) error model from the microwave heating dynamics.
• Proposal of a sufficient condition for the existence of receding horizon H∞ guaranteed cost control.
• On-line updating and solving of linear matrix inequalities (LMIs) optimization problems to obtain the constrained tracking controller.

Main Results:

• A novel control strategy is proposed and theoretically validated through the derivation of existence conditions for H∞ guaranteed cost control.
• The controller effectively minimizes the H∞ norm while satisfying quadratic cost performance criteria.
• Simulations on a one-dimensional cavity heating model demonstrate the successful implementation and performance of the proposed control strategy.

Conclusions:

• The developed receding horizon H∞ guaranteed cost control strategy effectively manages complex dynamics in microwave heating.
• The approach provides a robust solution for temperature spectrum tracking under challenging operational conditions.
• The methodology offers a promising framework for advanced process control in microwave-assisted applications.