PDE modelling and switch strategy controller design for a flexible detection system with output constraint and actuator failure

A novel approach for modelling a mine detection robot system is presented in this paper using partial differential equations and Hamilton's principle. The system comprises a rigid arm, a detecting sensor module, and a flexible string. The paper addresses the challenges of boundary deflection constraint and actuator fault. To overcome these challenges, a unique controller is developed using Barrier Lyapunov function and switching strategy. This controller enables the robot system to achieve the desired position and eliminate the vibration of flexible string. The superiority of the designed control law is demonstrated through simulation results. Furthermore, the asymptotic stability of the closed-loop flexible system is established by the use of extending LaSalle's Invariance principle to an infinite dimensional system. This principle ensures that the system will eventually reach a stable state over time.