A Lyapunov controller for stable haptic manipulation of hydraulic actuators

Abstract

SUMMARY A scheme for bilateral control of hydraulic actuators is developed and experimentally evaluated in this paper. The control laws are derived based on Lyapunov's feedback control design technique. Owing to the discontinuity originating from a sign function in the control laws, the control system is non‐smooth. First, the existence, continuation, and uniqueness of Filippov's solution to the system are proven. Next, the extensions of Lyapunov's stability theory to non‐smooth systems and LaSalle's invariant set theorems are employed to prove the asymptotic stability of the control system. Effectiveness of the proposed controller is verified by simulation and experimental studies. It is shown that beside stability, the system has good transparency in terms of position and force exchanges between the master and slave actuators. Copyright © 2011 John Wiley & Sons, Ltd.