Lyapunov-based friction compensation for accurate positioning of a hydraulic actuator

A Lyapunov-based discontinuous friction compensation technique is developed for the position regulation of a hydraulic actuator. The control scheme is capable of asymptotic position regulation with no steady-state error despite friction effects. Although, no knowledge of actuator friction, servovalve dynamics, or hydraulic parameters is required for control action, stability and effectiveness of the control scheme considering hydraulic nonlinearities, servovalve dynamics, and realistic friction model is verified both analytically and experimentally. Due to the discontinuity of the control law and the friction model, the control system is nonsmooth. Therefore, existence, continuation and uniqueness of the Filippov´s solution are, first, proven using Filippov´s solution theories. The extension of LaSalle´s invariance principle to nonsmooth systems is then employed to prove the asymptotic convergence of the system trajectories to the equilibria. Experimental results verify the effectiveness of the proposed controller in counteracting frictional effects and asymptotic convergence of the system to the desired position with no steady state error.