Research On Stewart Platform's Decentralized Control Problems Based On LPV Method

With high accuracy, stiffness and load-carrying ability, Stewart platform can realize 3 freedom transmission and 3 freedom rotation and be applicable to hardware-in-the-loop flight simulation tests. When used to simulate the movement of flight vehicle, Stewart platform is required to provide satisfactory performance of position precision and dynamical response. It has an important theory and engineering significance to discuss the platform's dynamics and control problems.Firstly, the platform's forward rigid body dynamics is obtained. Then the inverse dynamic formula is achieved, and the hypothesis which doesn't accord with platform's actual motion in existing methods is removed in order to reduce the computing results'error.Secondly, the research on coupling property of Stewart platform dynamic model in joint space is carried out and then subsystem's dynamic model is obtained. Platform's parameter restricting conditions, which indicate the inertia matrix is block diagonally dominant, are deduced with study on neutral position's inertia matrix analytic formula. Furthermore, an algorithm is proposed to test the block diagonally dominant property in a given workspace. The platform is divided into 3 double inputs and double outputs subsystems in order to solve the strong coupling problem. Then, subsystem dynamic model's uncertainty is analyzed and weight function with less conservativeness is selected using output matching conditions.Thirdly, for the large parameter varying region in Stewart platform's subsystem's LPV dynamic model, piece-wise smooth Lyapunov function is introduced. The whole parameter varying region is divided into several small parts and parameter affine dependent and quadratic Lyapunov function is selected. Furthermore, to reduce control design computing burden, the relationship between Lyapunov function's matrix variables is analyzed with the piece-wise smooth property. The control design's PLMI condition is achieved on the basis of some lemmas about Dini derivate used in piece-wise system control. Then, in virtue of function magnification and monotony, 16 sufficient conditions with less conservativeness are presented to solve the infinite dimension PLMI.To the requirement of getting subsystem's best performance, the performance optimum design based on weight function selection is researched. Furthermore, performance optimum design algorithm's LMI index is given. An iterative algorithm is proposed and its convergence is analyzed based on Bode integral.Finally, for an electrical Stewart platform used in flight simulation, the subsystem's decentralized controller design is conducted and then realized. The proposed method's validation is then verified by experiment results.