A Novel Boundary Control Solution for Unstable Heat Conduction Systems Based on Active Disturbance Rejection Control

In this study, a new boundary control scheme is proposed for a class of unstable heat conduction systems based on active disturbance rejection control and frequency domain analysis methods. The unstable heat conduction systems studied here corresponds to a thin rod with surface heat loss and internal heat generation. An active disturbance rejection boundary controller is designed to stabilize the unstable heat conduction systems. Using the frequency domain analysis method, the Nyquist stability criterion for distributed parameter systems, the relative stability indices (gain margin, phase margin, and exponential stability speed) can be obtained for performance evaluation, and a constructive parameter-tuning method for controller is proposed. Finally, it is proved that an active disturbance rejection boundary controller can stabilize the unstable heat conduction systems with one unstable pole, and the simulation results demonstrate that the temperature profile of the whole rod has good convergence properties under both Dirichlet and Neumann boundary control.