Robust Stability and Control of Fractional Polynomials Including Integer and Fractional Natural Exponential Functions
本文研究了含整数和分数阶自然指数函数的不确定分数阶多项式的稳定性，提出了鲁棒有界输入有界输出稳定性分析方法，并设计了最优分数阶相位超前控制器用于刚柔耦合空间结构的残余振动抑制。
This article focuses on the stability of uncertain fractional order (FO) polynomials involving integer and FO natural exponential functions. These functions arise from the flexibility property and time delays in the control loop of the system of rigid–flexible coupling space structures. The coefficients of the polynomial are assumed to be complex numbers which are linear functions of uncertain real parameters. An analytical method is presented to check the robust bounded-input bounded-output stability of the control system. Furthermore, a method is developed to determine up to how much the amplitude of the uncertain parameters can grow such that the controller preserves the stability of the system. In the end, an improved optimal FO phase-lead controller is designed for the residual vibration suppression of the FO model of a rigid–flexible coupling space structure. Then, the merit of the presented theoretical results is demonstrated by applying them to the designed control loop.