Dynamic modeling and effective vibration reduction of dual-link flexible manipulators with two-stage cascade PID and active torque actuation

Flexible manipulators, praised for their adaptability, face challenges in controlling inherent vibrations. This study introduces an advanced control strategy that employs active torque actuation to effectively mitigate tip vibrations in a dual-link flexible manipulator, enhancing stability and performance. An accurate dynamic model, developed using extended Hamilton's principle and the assumed mode method, addresses the system's natural frequencies and mode shapes, transforming coupled nonlinear partial differential equations into simpler ordinary differential equations with defined boundary conditions. The robust control strategy employs a two-stage cascade Proportional-Integral-Derivative (PID) controller, managing rigid and flexible motions separately to ensure precise control and stability despite the manipulator's complexities. Analytical and experimental results show that this control strategy significantly improves transient response by reducing settling time and overshooting, with minor changes to peak time. MATLAB simulations and experiments confirm the effective damping of flexible deflections, aligning closely with dynamic model predictions. These results underscore the effectiveness of the control strategy and dynamic model in achieving superior vibration suppression and improved transient response, thereby optimizing system performance.