Cross-coupling integral adaptive robust posture control of a pneumatic parallel platform

A pneumatic parallel platform driven by an air cylinder and three circumambient pneumatic muscles was considered. Firstly, a mathematical model of the pneumatic servo system was developed for the MIMO nonlinear model-based controller designed. The pneumatic muscles were controlled by three proportional position valves, and the air cylinder was controlled by a proportional pressure valve. As the forward kinematics of this structure had no analytical solution, the control strategy should be designed in joint space. A cross-coupling integral adaptive robust controller（CCIARC） which combined cross-coupling control strategy and traditional adaptive robust control（ARC） theory was developed by back-stepping method to accomplish trajectory tracking control of the parallel platform. The cross-coupling part of the controller stabilized the length error in joint space as well as the synchronization error, and the adaptive robust control part attenuated the adverse effects of modelling error and disturbance. The force character of the pneumatic muscles was difficult to model precisely, so the on-line recursive least square estimation（RLSE） method was employed to modify the model compensation. The projector mapping method was used to condition the RLSE algorithm to bound the parameters estimated. An integral feedback part was added to the traditional robust function to reduce the negative influence of the slow time-varying characteristic of pneumatic muscles and enhance the ability of trajectory tracking. The stability of the controller designed was proved through Laypunov＇s theory. Various contrast controllers were designed to testify the newly designed components of the CCIARC. Extensive experiments were conducted to illustrate the performance of the controller.