Dynamic Inverse Control of Uncertain Pure Feedback Systems Based on Extended State Observer

Abstract

A novel, precise disturbance rejection dynamic inversion control algorithm has been proposed. In the high-order dynamic surface control system, an innovative approach utilizes a monotonically increasing inverse hyperbolic sine function to construct an extended state observer, which estimates the uncertain functions at each step. The monotonicity of the inverse hyperbolic sine function simplifies the system stability analysis. Additionally, being a smooth function, it avoids the disturbances caused by piecewise functions at their breakpoints in conventional observer construction, thereby enhancing system stability. The accurate prediction capability of the new observer improves the system’s disturbance rejection performance. To address the inherent differential explosion phenomenon in traditional dynamic inversion control schemes, this paper ingeniously employs a tracking signal observer as a substitute for traditional filters, thus avoiding the differential explosion that may occur with first-order filters. Finally, comparative simulations were conducted to validate the effectiveness of the proposed method. The results show that both the observer and the controller possess high-gain characteristics, and the closed-loop system exhibits a fast convergence rate.