Performance Evaluation of an Adaptive Sigmoid Friction Compensation for Pneumatic Trajectory

Trajectory tracking is a challenging task in pneumatics due to the classification of the actuator as a nonlinear system. In addition to the said factor, nonlinear disturbances occur within the system, such as valve-dead zone, air compressibility, air density, internal valve and actuator friction. Actuators' internal friction is one of the most critical disturbances. For a near-zero velocity motion of an actuator, many scholars have designed and improved dynamic friction models for modeling and friction compensation. However, compensation using the dynamic model is complex and computationally exhaustive in real-time. Owing to this factor, a modified adaptive friction estimator and compensator are presented in this research. The adaptive sigmoid friction (FASF) function is designed to compensate both the pre-sliding and sliding regimes of the friction force. The function is coupled with a nonlinear hyperbolic PID (NPID+FASF) controller. The performance of the compensator was evaluated based on maximum tracking error (MTE), root mean square error (RMSE) and fast Fourier transform (FFT) error. The proposed NPID+FASF is observed to reduce all errors strategically. The improvement of MTE to the basic PID is up to 45.75%, RMSE of 27.88% and FFTE of 38.91%. To further improve the trajectory tracking performance, a ‘tracking differentiator’ has been proven to increase the performance of trajectory tracking and precise positioning.