Energy-based analysis and disturbance rejection control of the distributed parameter rope under parafoil traction

Abstract

Residual modes of a distributed parameter rope induce control spillover and observation spillover, which reduce the closed-loop stability margin and may further cause vibration instability. To address this problem, this paper develops an energy-based analysis and observer-based disturbance rejection control framework for the axially moving rope under parafoil traction. First, a control-oriented reduced-order rope model is established from the distributed parameter model. By decomposing the rope dynamics into controlled modes and residual modes, the coupling effect of the residual modes on the controlled subsystem is explicitly formulated and incorporated into a generalized disturbance together with modeling errors and external disturbances. Second, a positive-definite quadratic energy function is constructed to characterize the energy exchange between the controlled modes and the residual modes, so that the influence of the residual modes on the stability margin and vibration response can be explained from an energy perspective. Then, for the first-to-second-order and first-to-fourth-order modal control problems, an exponential disturbance observer and a bandwidth-parameterized linear extended state observer are designed, respectively, to estimate and compensate for the generalized disturbance online. Finally, numerical simulations are conducted to verify the proposed method. The results show that residual modes have a significant influence on the vibration response of the distributed parameter rope, and that the proposed observer-based compensation strategy can effectively improve generalized disturbance estimation and rope vibration suppression performance.