Dynamic modeling and robust nonlinear control of a six-DOF active micro-vibration isolation manipulator with parameter uncertainties

Dynamic model and vibration control of the Stewart platform are sophisticate and significant for vibration isolation especially the case with the base excitation. However, in the literature, no complete and accurate solution is presented. In this paper, a novel nonlinear dynamic model of six-spherical-prismatic-spherical (SPS) Stewart platform with the base excitation has been derived via Kane's method. Peculiarly, the dynamic model can be utilized for control algorithm designation to attenuate the base excitation. The order of the nonlinear coefficients has been evaluated to simplify the model. The uncertainties of stiffness, damping and mass center location have been studied based on the practical situation. An improved robust nonlinear controller, which is composed of the linear control part, nonlinear part and excitation compliment part, has been proposed to satisfy the two requirements at low frequency. The uniformly ultimate boundary of the state vector has been verified by theoretical proof accompanied with numerical simulation. It is concluded that the controller is of fine adjustability and can isolate a wide range of external disturbance.