Adaptive fast-finite-time extended state observer design for uncertain electro-hydraulic systems

This paper presents the design of an adaptive fast-finite-time extended state observer for electro-hydraulic actuator systems. First, state variables and subsequently the system model are divided into three independent parts, and fast-finite-time state observers with adaptive gains are designed independently for each part, guaranteeing the fast uniformly ultimate boundedness of the estimation errors. Then, based on the designed state observers and without any knowledge about the upper bounds of uncertainties or their derivatives, supplementary adaptive observers are presented to estimate the uncertainties. Besides, the adaptive gains of both observers are adjusted based on the evaluation of the absolute value of the observation errors in a straightforward manner, where rigorous analyses of the proposed strategy are provided through the Lyapunov approach. Finally, comparative simulations with respect to some leading strategies are presented to analyze the effectiveness of the proposed observers, where the convergence of the estimation errors to a small neighborhood of zero can be achieved almost regardless of the initial conditions. Indeed, in contrast to the earlier finite-time approaches which only have a relatively fast convergence rate around the equilibrium points, the proposed adaptive framework can also improve the convergence rate for zones far from the equilibrium points. It is concluded that the proposed scheme can compete with other leading strategies, making it a qualified alternative approach in the observer design with noteworthy potential.