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首页> 外文会议>2002 ASME International Mechanical Engineering Congress and Exposition , Nov 17-22, 2002, New Orleans, Louisiana >Feedback Linearization of the Lorenz System: Stabilization and Tracking Control
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Feedback Linearization of the Lorenz System: Stabilization and Tracking Control

机译：Lorenz系统的反馈线性化：稳定和跟踪控制

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摘要

This paper presents a control study of the Lorenz system by using feedback linearization. The effects of the state transformation on the dynamics of the Lorenz system are studied first. Then, composite controllers are developed for both stabilization and tracking of the system. The controls are designed to overcome the barrier in controllability imposed by the state transformation. The transition through the manifold defined by such a singularity is achieved by inducing the chaotic response within a boundary layer that contains the singularity. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole state space and the need for high control efforts is substantially mitigated. Tracking problems that involve single and cooperative objectives are studied by using the differential flatness property of the system. A good understanding of the system dynamics proves to be invaluable in the design of better controls. In all numerical examples, the proposed approach led to excellent control performances.
机译：本文通过反馈线性化对Lorenz系统进行了控制研究。首先研究了状态变换对Lorenz系统动力学的影响。然后，开发了用于稳定和跟踪系统的复合控制器。这些控件旨在克服状态转换所带来的可控性障碍。通过在包含奇异点的边界层内引起混沌响应，可以实现通过这种奇异点定义的流形过渡。在该区域之外，应用常规的反馈非线性控制。以这种方式，将控制权扩大到整个状态空间，并且大大减轻了对高控制力的需求。通过使用系统的差分平坦度特性，研究了涉及单个目标和合作目标的跟踪问题。事实证明，对系统动力学的深入了解对于设计更好的控件至关重要。在所有数值示例中，所提出的方法均具有出色的控制性能。

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