Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor

For an electrical six-degree-of-freedom Stewart platform, it is difficult to compute the equivalent inertia of each motor in real time, as the inertia is time-varying. In this study, an analysis using Kane's equation is undertaken of the driven torque of the movements of motor systems (including motor friction, movements of motor systems along with the actuators, rotation around axis of rotors and snails), as well as driven torque of the platform and actuators. The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor (PMSM) dynamics. By equalizing the driven torque and electromagnetic torque, a model was established. This method, taking into consideration the influence of counter electromotive force (EMF) and motor friction, could be applied to the real-time dynamic control of the platform, through which the calculation of the time-varying equivalent inertia is avoided. Finally, simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined. With this approach, the multi-body dynamics of the electrical Stewart platform is better understood.