Admittance Control Stability Analysis of a Lower Limb Rehabilitation Servo-Pneumatic System

In this study, a vertically placed double-acting pneumatic cylinder controlled by two On/Off solenoid valves is applied for the purpose of the lower limb rehabilitation. Because of the different physical conditions and degrees of disability of patients and changes of the system dynamic parameters, admittance control strategy is used to compliantly interact between users and actuator. To analyze the stability, a linear model of the servo-pneumatic system is developed and its continuous transfer function is derived. Due to the exponential functions in the continuous transfer function of the system, the necessary transformations are used to achieve the discrete closed-loop transfer function of the system. In this way, the determination of the stable performance boundaries of the admittance control parameters related to changes in other dynamic parameters of the system is possible by root locus analysis of the discrete closed-loop system. These dynamics parameters include equivalent mass, damping and stiffness of the actuator and leg impedance and the proportional and differential gains of the inner loop position controller. Good correspondence is observed between the analytical and experimental stability limits of the system. Analytical results for appropriate choice of the admittance control and other dynamic parameters of the servo-pneumatic system are applicable to get smoothly and stable performance during the rehabilitation process.