Adaptive backstepping motion control of hydraulic actuators with velocity and acceleration constraints

In this paper, an adaptive backstepping controller is designed for positioning servo system driven by a hydraulic actuator. The constraints on both output velocity and acceleration are taken into consideration due to performance and/or physical limitations. The mechanism of these constraints satisfaction uses a barrier Lyapunov function, which grows to infinity when its arguments approach some pre-set limits, to prevent constraint violation. By ensuring the stabilization of the barrier Lyapunov function in the dynamic motion closed loop, and propagating a hard-bound imposed on associated error signals through the steps of the backstepping procedure, we guarantee that the system output velocity and acceleration constraints are not transgressed. Furthermore, a stable discontinuous projection based adaptive controller is constructed to tackle systems unknown parameters. Asymptotic tracking is achieved without violation of the constraints under mild initial conditions. Extensive simulation results are provided to illustrate the performance of the proposed control scheme, compared with a standard adaptive backstepping controller based on a Quadratic Lyapunov function.