Uncertain state observer for command filtered adaptive backstepping with application to hydraulic systems

The industry utilises hydraulic actuators due to their high power density and robustness. Especially the control of mobile hydraulic systems is challenging, among others, because of unknown and time-variant system parameters and the limited use of sensors. Firstly, parameters such as viscous damping, inertia and external load might change during operation and need to be estimated. Secondly, mobile hydraulic machines are commonly equipped with pressure sensors only but lack position or velocity sensors because of high cost and poor robustness. From a control perspective, systems with uncertain parameters are typically addressed by adaptive control methods to estimate uncertainties and stabilise the system. As the primary objective is to track the velocity, an observer for the uncertain system is necessary, which is not common in adaptive control. This paper presents an adaptive and command filtered backstepping algorithm, including an observer for the uncertain system for a class of hydraulic systems with fast valve dynamics. The algorithm adapts physically meaningful parameters and observes the velocity of the uncertain system. In addition, the adaptation laws are reformulated by partial integration to remove the requirement to measure the velocity ultimately. Stability is proven based on Lyapunov theory, and performance is demonstrated on a nonlinear simulation model of an exemplary hydraulic system.