A Model based Global Stable Control for Pneumatic Pistons with Long Transmission Air Hoses

For magnetic resonance imaging (MRI) guided surgical robots, pneumatic piston-based ones are the most widely studied due to their excellent MR-compatibility, simpler structure, and sterility. However, necessary control components such as pressure sensors and proportional valves can only be placed far away from the MRI scanner via long transmission air hoses due to magnetic safety concerns. Pressure attenuation and mass flow rate delay are inevitably introduced, complicating the control of pneumatic piston-based MRI-compatible surgical robots. Aiming at surmounting this obstacle, this paper proposes a state space estimator to estimate chamber pressures inside a piston cylinder and corresponding mass flow rates within a long transmission air hose. Dynamic models for a pneumatic piston system are developed first, followed by establishment of the state space estimator. An energy based Lyapunov candidate function considering the kinematic energy within the long air hoses and potential energy within piston cylinders is designed and mathematically proved to be globally stable. An estimator-based sliding mode controller is then designed. According to simulation results, the control scheme we proposed has achieved satisfactorily good position tracking accuracy with little amplitude attenuation and little phase delay even under as high as 2Hz frequency and with a 10-meter long air transmission hose.