Vibration control of Stewart platform based on an improved nonlinear proportional-derivative control method

This paper proposes an improved switching nonlinear proportional-derivative (S-NPD) control algorithm for a six-degree-of-freedom Stewart platform which has strong nonlinearity and uncertainty characteristics, designed to achieve vibration isolation and suppression over a wide bandwidth range while solving the problem of the difficulty in parameter tuning. The controller is designed based on the idea of variable-structure control, which achieves independent real-time adjustments of the control gains of the six legs and takes the sign of the proportional and differential errors as the switching function to realize the feed-forward correction of the proportional gain. This control input can track the expected value more precisely, thus strengthening the system's ability to cope with high dynamics. To validate the results of the proposed approach, numerical simulations are compared with those obtained from PD and NPD controls. The findings confirmed that the designed S-NPD controller shows commendable stability and robustness, and the vibration attenuation of the upper platform under low- and medium-frequency conditions is substantially improved. In addition, it obtains smoother vibration waveforms and lower control force under random disturbance conditions. Consequently, it is proved that the S-NPD control can obtain better regulation accuracy. Compared with the PD and NPD controls, the S-NPD control achieves up to 64% and 31.4% relative performance improvement in vibration attenuation rate, respectively.