This article treats the design and implementation of a multi-input multi-output fractional-order controller for a nonlinear system composed of a tendon-driven continuum mechanism. As the continuum can be deformed along all Cartesian directions, it is suitable for the application as a flexible neck of a humanoid robot. In this work, a model-based control approach is proposed to control the position of the head, that is, the rigid body attached to the top of the continuum mechanism. Herein, the system is modeled as a rigid body on top of a nonlinear Cartesian spring, with an experimentally obtained deflection characteristic which provides a simple and real-time capable model. By nonlinear feedback, the output dynamics are linearized and decoupled, which enables the design of single-input single-output fractional-order controllers for the regulation of each output independently. The design of a fractional-order P D α controller is discussed to incorporate robustness and a fast transient response. The proposed control approach is tested in several experiments on the real system.

中文翻译：

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欠驱动连续介质的多输入多输出分数阶控制

本文讨论了由腱驱动的连续介质机构组成的非线性系统的多输入多输出分数阶控制器的设计和实现。由于连续体可以沿所有笛卡尔方向变形，因此适合作为仿人机器人的柔性颈部应用。在这项工作中，提出了一种基于模型的控制方法来控制头部的位置，即附着在连续体机构顶部的刚体。在这里，系统被建模为非线性笛卡尔弹簧顶部的刚体，具有实验获得的挠度特性，提供了一个简单且实时的模型。通过非线性反馈，输出动态被线性化和解耦，这使得能够设计用于独立调节每个输出的单输入单输出分数阶控制器。讨论了分数阶 PD α 控制器的设计，以结合鲁棒性和快速瞬态响应。所提出的控制方法在实际系统的几个实验中得到了测试。