Accurate Sub-Millimeter Servo-Pneumatic Tracking using Model Reference Adaptive Control (MRAC)

Abstract

A model reference adaptive controller (MRAC) for compensating friction and payload uncertainties in a servo-pneumatic actuation system is presented in this paper. A friction model combining viscous and Coulomb friction is formulated within the framework of an adaptive controller. Due to the asymmetric nature of Coulomb friction in pneumatic piston actuators, a bi-directional Coulomb friction model is adopted. An update law is presented to estimate three friction parameters: linear viscous friction, Coulomb friction for positive velocity, and Coulomb friction for negative velocity. The force needed to both overcome the estimated friction forces and to supply the desired pressure-based actuation force to obtain a dynamic model reference position response is then used as the command to a sliding mode force controller. Both the force control loop and the adaptation law are Lyapunov stable by design. To ensure stable interaction between the sliding mode force controller and the adaptive controller, the bandwidth of the parameter update law is designed to be appreciably slower than the force tracking bandwidth. Experimental results are presented showing position tracking with and without an unknown payload disturbance. The steady-state positioning accuracy is shown to be less than 0.05 mm for a 60 mm step input with a rise time of around 200 ms. The tracking accuracy is shown to be within 0.7 mm for a 0.5 Hz sinusoidal position trajectory with an amplitude of 60 mm, and within 1.2 mm for a 1 Hz sinusoidal position trajectory with an amplitude of 60 mm. Both step and sinusoidal inputs are shown to reject a payload disturbance with minimal or no degradation in position or tracking accuracy. The control law generates smooth valve commands with a low amount of valve chatter.