Vibration control method of hydraulic-driven continuum manipulator based on PID algorithm

Abstract The high-frequency pressure pulsation of the hydraulic power source and the dynamic response of the actuator in the hydraulic driven continuous robotic arm generate strong coupling effects with the inherent structural vibration of the flexible connecting rod in a wide frequency band. Traditional rigid controllers are difficult to effectively suppress the sustained structural oscillation caused by this while achieving precise pose control. This article proposes a hydraulic driven continuous robotic arm vibration control method based on PID algorithm. Firstly, by combining Lagrange’s principle with the assumed modal method, a coupled dynamic model was constructed that simultaneously covers joint rigid body motion and low order modes of flexible linkages. For the first time, the hydraulic force kernel function was explicitly introduced in the modal equation, accurately describing the interaction mechanism between hydraulic actuators and flexible body vibration. Subsequently, an integral separation digital PID controller was designed based on this model. By setting a deviation threshold, the controller has the ability to adapt to operating conditions - using PD control in large deviation intervals to avoid hydraulic actuator saturation and prevent excitation of severe vibrations; Introducing integration in the small deviation range to eliminate steady-state errors and ensure final positioning accuracy. This move pre emptively integrates vibration suppression issues into the motion control framework, achieving a unified design of motion tracking and vibration suppression. The experimental results show that the curve corresponding to the method proposed in this paper overlaps highly with the actual joint angle curve, with an RMSE of only 0.05 rad; The vibration amplitude is reduced to 20%. And the control trajectory is very close to the expected trajectory, with the minimum deviation at each distance point, which can effectively control the robot arm to move along the expected trajectory.