空间控制技术与应用 ›› 2013, Vol. 39 ›› Issue (1): 15-22.doi: 10.3969/j.issn.1674-1579.2013.01.003
王明昊, 刘刚, 杨述华
Abstract：According to the strong coupling and nonlinear characteristics of the hypersonic vehicle model, we propose a gainscheduled statefeedbackbased robust control design method, which is based on polytopic LPV systems. Firstly, Jacobian linearization is used on several selected equilibrium points in the trajectory of the scheduling parameters to get the LPV models. Then the system matrix is discretized and stored into a tensor, and the reducedrank tensor is reconstructed to obtain a finite number of LTI polytopic vertex systems by HOSVD approach. To reduce the conversation of controller design, slack variable matrix is introduced and different Lyapunov function matrix is used on each vertex. The designed polytopicLPVsystembased control in the form of LMI can place all the system closedloop poles in the required region and satisfy the H∞ performance. The numerical simulation results illustrate the validity of the proposed method.
摘要： 摘要： 针对高超声速飞行器模型高度非线性、强耦合的特点，提出一种多胞形线性变参数(LPV,linear parameter varying)系统变增益状态反馈控制器的设计方法.首先在感兴趣的变参数轨迹上选取若干平衡点进行雅克比线性化并拟合得到高超飞行器的LPV模型，将其离散化后存储于一张量中，利用高阶奇异值分解(HOSVD ,higher order singular value decomposition)进行多胞形转换，得到有限个LTI顶点系统.同时为了降低控制器设计的保守性，通过引入松弛变量矩阵，在各顶点使用不同的Lyapunov函数矩阵，推导出能同时将闭环极点配置到指定区域并满足H∞性能的多胞LPV系统状态反馈控制器设计的线性矩阵不等式（LMI，linear matrix inequality）算法.最后的仿真结果验证了算法的有效性.
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