Department of Mechanical Engineering, Universidade de Vigo, 36310 Pontevedra, Spain.
Department of Mechanical Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA.
Sensors (Basel). 2018 Jun 4;18(6):1817. doi: 10.3390/s18061817.
Input shaping is an Optimal Control feedforward strategy whose ability to define how and when a flexible dynamical system defined by Ordinary Differential Equations (ODEs) and computer controlled would move into its operative space, without command induced unwanted dynamics, has been exhaustively demonstrated. This work examines the issue of Embedded Internet of Things (IoT) Input Shaping with regard to real time control of multibody oscillatory systems whose dynamics are better described by differential algebraic equations (DAEs). An overhead crane hanging a double link multibody payload has been appointed as a benchmark case; it is a multibody, multimode system. This might be worst scenario to implement Input Shaping. The reasons can be found in the wide array of constraints that arise. Firstly, the reliability of the multibody model was tested on a Functional Mock-Up Interface (FMI) with the two link payload suspended from the trolley by comparing the experimental video tapping signals in time domain faced with the signals extracted from the multibody model. The FFTs of the simulated and the experimental signal contain the same frequency harmonics only with somewhat different power due to the real world light damping in the joints. The application of this approach may be extended to other cases i.e., the usefulness of mobile hydraulic cranes is limited because the payload is supported by an overhead cable under tension that allows oscillation to occur during crane motion. If the payload size is not negligible small when compared with the cable length may introduce an additional oscillatory mode that creates a multibody double pendulum. To give the insight into the double pendulum dynamics by Lagrangian methods two slender rods as payloads are analyzed dealing with the overhead crane and a composite revolute-revolute joint is proposed to model the cable of the hydraulic crane, both assumptions facilitates an affordable analysis. This allows developing a general study of this type of multibody payloads dynamics including its normal modes, modes ratios plus ranges of frequencies expected. Input Shapers were calculated for those multimodes of vibration by convolving Specified Insensitivity (SI) shapers for each mode plus a novel Direct SI-SI shaper well suited to reduce the computational requirements, i.e., the number of the shaper taps, to carry out the convolution sum in real time by the IoT device based on a single microcontroller working as the command generator. Several comparisons are presented for the shaped and unshaped responses using both the multibody model, the experimental FMI set-up and finally a real world hydraulic crane under slewing motion commanded by an analog Joystick connected by two RF modules 802.15.4 to the IoT device that carry out the convolution sum in real time. Input Shaping improves the performances for all the cases.
输入整形是一种最优控制前馈策略，它能够定义由常微分方程（ODE）和计算机控制定义的柔性动力系统如何以及何时进入其工作空间，而不会引起命令诱导的不需要的动态，这已经得到了详尽的证明。这项工作研究了实时控制多体振荡系统的嵌入式物联网（IoT）输入整形问题，其动力学由微分代数方程（DAE）更好地描述。一个悬挂双连杆多体有效负载的桥式起重机被指定为基准案例；这是一个多体、多模态系统。这可能是实施输入整形的最坏情况。原因可以在出现的广泛约束中找到。首先，通过将带有双连杆有效负载的小车悬挂在功能模拟接口（FMI）上，对多体模型的可靠性进行了测试，通过比较时域中的实验视频点击信号和从多体模型中提取的信号，来验证多体模型的可靠性。由于关节中的实际阻尼较小，因此模拟和实验信号的 FFT 仅包含相同的频率谐波，但功率略有不同。这种方法的应用可以扩展到其他情况，例如，移动液压起重机的用途有限，因为有效负载由张紧的架空电缆支撑，这允许在起重机运动过程中发生振荡。如果与电缆长度相比，有效负载的尺寸不小，则可能会引入额外的振荡模式，从而创建多体双摆。为了通过拉格朗日方法深入了解双摆动力学，分析了两个作为有效负载的细长杆，处理桥式起重机，并提出了一种复合旋转-旋转关节来模拟液压起重机的电缆，这两种假设都有助于进行负担得起的分析。这允许对这种类型的多体有效负载动力学进行一般研究，包括其固有模态、模态比以及预期的频率范围。通过对每个模态进行特定灵敏度（SI）整形器的卷积以及适合于降低计算要求的新型直接 SI-SI 整形器，为这些多模态振动计算了输入整形器，即通过基于单个微控制器作为命令生成器的物联网设备实时执行卷积和的整形器 taps 数量。使用多体模型、实验 FMI 设置以及最后在模拟操纵杆命令下进行回转运动的实际液压起重机，对成形和未成形响应进行了几种比较，该操纵杆通过两个射频模块 802.15.4 连接到执行实时卷积和的物联网设备。输入整形可以提高所有情况下的性能。
