In this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter-varying approach to design a state-feedback controller for a control moment gyroscope (CMG) to track a user-defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter-varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and -gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully- and under-actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods.

中文翻译：

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使用虚拟控制收缩度量的陀螺仪非线性参数变化状态反馈设计

在本文中，我们提出了一种基于虚拟控制收缩度量 (VCCM) 的非线性参数变化方法，用于设计控制力矩陀螺仪 (CMG) 的状态反馈控制器，以跟踪用户定义的轨迹集。这种基于 VCCM 的非线性 (NL) 稳定性和性能综合方法类似于线性参数变化 (LPV) 控制方法，允许精确保证NL 系统的指数稳定性和增益性能相对于来自预定的所有轨迹设置，这与传统的 LPV 方法不同。在 CMG 的全驱动和欠驱动操作模式下进行的模拟和实验研究表明，与标准 LPV 控制方法相比，这种方法是有效的。