This paper proposes a neural networks-based approach of finding flat output of linearized underactuated mechanical systems (UMS). Given that differential flatness and controllability are equivalent for linear systems, the problem is equivalent to finding the Brunovsky canonical form of linearized UMSs. We use a two degree-of-freedom (2DOF) system to illustrate the theoretical development. The proposed method identifies the local flat output of nonlinear mechanical systems from the measurements only, without a detailed mathematical model. The identification allows us to combine the well-known active disturbance rejection control (ADRC) and differential flatness control. A time-domain direct identification (TDDI) algorithm and its variant based on the algebraic method are proposed for flat output identification (FOID). The neural networks for implementing the TDDI algorithm called FOID-NN are created to evaluate flat output candidates and to use the flat output to reconstruct the system states in terms of a linear mapping. The neural networks are trained with the loss functions defined by reconstruction errors. Two special layers, namely tracking differentiator (TD) and algebraic layer, are inserted in the FOID-NN to handle noisy signal differentiations. Simulations of a cart–pole system and a stable 2DOF nonlinear UMS are carried out to show the range of applications of the FOID-NN. The experimental data of an underactuated rotary crane are used to validate the identified flat output.

中文翻译：

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使用神经网络识别线性平坦输出——二自由度欠驱动机械系统的示例


本文提出了一种基于神经网络的方法来寻找线性欠驱动机械系统（UMS）的平坦输出。鉴于微分平坦度和可控性对于线性系统是等效的，该问题相当于寻找线性化 UMS 的 Brunovsky 规范形式。我们使用二自由度（2DOF）系统来说明理论发展。该方法仅根据测量结果识别非线性机械系统的局部平坦输出，无需详细的数学模型。该识别使我们能够将众所周知的自抗扰控制（ADRC）和微分平坦度控制结合起来。提出了一种用于平坦输出识别（FOID）的时域直接识别（TDDI）算法及其基于代数方法的变体。创建用于实现 TDDI 算法（称为 FOID-NN）的神经网络来评估平坦输出候选并使用平坦输出根据线性映射重建系统状态。神经网络使用重建误差定义的损失函数进行训练。 FOID-NN 中插入了两个特殊层，即跟踪微分器 (TD) 和代数层，以处理噪声信号微分。对车杆系统和稳定的 2DOF 非线性 UMS 进行了仿真，以展示 FOID-NN 的应用范围。欠驱动旋转起重机的实验数据用于验证确定的平坦输出。