基于线性分式变换的多体动力学参数依赖平衡模型
Linear Fractional Transformation modeling of multibody dynamics around parameter-dependent equilibrium
摘要：
提出了一种新的线性分式变换（LFT）建模方法，用于不确定线性变参数（LPV）多体系统的参数相关平衡。传统的多体方法，包括建立整个结构的非线性模型，并在数值修剪后将其线性化到平衡点附近，不允许用LFT形式隔离参数变化。虽然其他技术（如多项式拟合或符号线性化）可以提供LFT模型，但它们可能很耗时或错过最差情况配置。所提出的方法依赖于修剪和线性化的方程在子结构的水平，组装前的多体结构，这允许只执行操作，保持LFT形式在整个线性化过程。由于保留了参数的物理来源，因此结构的线性化LFT-LPV模型在单个参数模型中精确地覆盖了所有设备，而不会引入保守性或拟合误差。应用LFT-LPV建模的机器人手臂，在其标称配置，与所提出的方法得到的模型匹配的软件Simscape多体提供的模型，但它是增强与LFT形式的参数变化，一个强大的LPV综合使用Matlab鲁棒控制工具箱进行控制设计的能力。
英文摘要：
This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The proposed approach relies on the trimming and linearization of the equations at the substructure level, before assembly of the multibody structure, which allows to only perform operations that preserve the LFT form throughout the linearization process. Since the physical origin of the parameters is retained, the linearized LFT-LPV model of the structure exactly covers all plants, in a single parametric model, without introducing conservatism or fitting errors. An application to the LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration, the model obtained with the proposed approach matches the model provided by the software Simscape Multibody, but it is enhanced with parametric variations with the LFT form; a robust LPV synthesis is performed using Matlab robust control toolbox to illustrate the capacity of the proposed approach for control design.
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