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针对同时具有干扰和时变输入时滞的挠性航天器的H∞控制问题,首先采用状态空间法描述一类具有干扰和输入时滞的挠性航天器模型;然后基于李亚普诺夫稳定理论和线性矩阵不等式(linear matrix inequality,LMI)法,通过构造一个新型的增广李亚普诺夫泛函,建立基于LMI形式的时滞相关的H∞状态反馈控制器设计方法,此法设计的反馈控制器增益依赖松弛矩阵而非正定的李亚普诺夫矩阵;最后,通过数值仿真验证该控制方法的有效性并分析其时滞量、H∞性能指标及时滞积分不等式分解系数对闭环系统性能的影响.与传统的设计相比,由于引入了松弛矩阵并在泛函求解过程中引入了时滞积分不等式分解系数,因此该设计方法既能提升设计的灵活性又能降低设计的保守性.
Aiming at the H∞ control problem of a flexible spacecraft with both disturbance and time-varying input delay, a state space method is first used to describe a class of flexible spacecraft model with disturbance and input delay. Then, based on Lyapunov stability theory and The linear matrix inequality (LMI) method is adopted to establish a new delay-dependent H∞ state feedback controller design method based on the LMI form by constructing a new augmented Lyapunov functional. The feedback controller The gain depends on the relaxation matrix instead of positive definite Lyapunov matrix. Finally, the effectiveness of this control method is verified by numerical simulation and the influence of time delay, H∞ performance index and delay integral inequality factor on the closed-loop system performance are analyzed. Compared with the traditional design, the relaxation matrix is introduced and the integral coefficient inequalities decomposition coefficient is introduced in the process of functional solution. Therefore, the design method can not only improve the design flexibility but also reduce the design conservativeness.