一个可调的零点振动输入整形控制策略桥式起重机系统

抽象

This article presents a modified zero vibration (ZV) input shaping technique to address the sensitivity and flexibility limitations of the classic ZV shapers commonly implemented in overhead crane applications. Starting with the classical ZV formulation, new parameters are introduced to optimize the control system performance according to a versatile objective function. The new shaper enhances the design flexibility and operational domain of the shaper, while it inherits the robustness properties and computational efficiency of the ZV scheme. Unlike the original ZV shaper, the proposed shaper allows for the point-to-point maneuver time to be fixed. The sensitivity analysis of the controller confirms that the new shaper effectively reduces the ZV sensitivity to the cable length variations.

1.简介

桥式起重机广泛应用于制造工厂，核设施和运输场，其中重的有效载荷需要转移[1]。虽然快速起重机操作帮助提高了整体工作效率，提高机动速度可导致不安全的有效载荷振荡和残余的影响力。因此，许多研究都探讨了这些结构不同的鲁棒控制解决方案。除了耐用性和减少摆动功能，开销控制方案必须能够在不同的起重机的配置和载荷条件[拒绝外部干扰和功能2，3]。此外，起重机控制器的性能应该是直观的人类用户来部署它[4]。

研究人员已经广泛研究各种闭环控制解决方案的用于有效载荷振荡抑制在起重机系统中的应用[五-7]。Gholabi等。[8] proposed a sensorless control approach based on real-time crane demand. Fuzzy logic and data-driven predictive models were also implemented for sway reduction [9]。陈等人。[10]开发了一种基于成形能量状李亚普诺夫函数被证实是渐近稳定的和改进的在参数不确定性的存在控制器的鲁棒性的自适应跟踪器。在最近的研究中，张某等人。[11]求值的误差跟踪控制器平台，以尽量减少在经受参数不确定性和外部扰动的起重机的残余摇摆。杨等人。[12] designed an adaptive controller to effectively control the state variables of a ship-mounted crane under harsh operating conditions. Command smoothing control was also proven to be effective for a crane machine with a distributed-mass payload subjected to external force (e.g., wind) [13]。虽然大多数antisway控制解决方案已为点至点演习开发，研究人员还设计和测试从事在紧急情况下安全地带来的开销系统完全停止状态控制器[14]。除了传统的反馈策略，基于优化的控制方案，特别是模型预测控制（MPC），最近已应用于桥式起重机的平台。MPC用于状态，最大限度地减少在后退预测范围所构建的目标函数的最优集合提供解决方案。此功能的制剂的确定需要由所述控制器来满足系统约束的类型和严重性。Schindele和Aschemann [15] developed a nonlinear MPC to minimize the tracking error at crane rest conditions. Smoczek and Szpytko [16] proposed a soft-constrained MPC to minimize the oscillation of a scaled crane setup. In a recent study, the researchers implemented an MPC-based subcontroller to optimize the velocity of the crane cart throughout the prediction horizon with the desired objective of minimizing the payload oscillation [17]。

由歌手等人提出。在1990年[18]，输入成形已被证明是降低动力学应用振动的功能强大的控制工具。而反馈控制器的有效性在很大程度上依赖于状态测量的可用性，输入整形器不需要连续感测/反馈。因此，它们更易于使用和更便宜的实施在工业环境中桥式起重机平台[19，20]。到目前为止，不同类别的塑造者已经开发并用于起重机应用[21-24]。零振动（ZV）方法获得的这些输入整形技术在第一代中。尽管他们的鲁棒性[25]，ZV整形器通常具有缓慢的响应时间相关联。因此，更复杂的输入整形策略，包括零振动和最小积分（ZVI）和最小振动和积分（MVI），后来发展到提供自适应性在机动时间设定，起重机的电缆长度，以及输入的命令[26]。分布式零振动（DZV）整形器也通过引入一个延迟分布用于实时起重机控制用例[形成27]。Mohammed et al. [28]研究的遗传算法的应用来优化加速度曲线为具有严格的运动和安全限制的起重机用的非线性输入整形器。通过优化加速度输入，优化的整形器提供了一种更快的系统响应，同时满足系统约束。拉马等。[29]训练神经网络中操作的实时单位幅度零振动（UMZV）基于人工神经网络的整形器。虽然实验分析证实了该方法的适用性与可变参数起重机应用，它的实现高度依赖于足够的数据集网络训练的可用性。近年来，基于输出指令整形（OS）的技术进行了调查摇摆振荡引起的提升和外部干扰，诸如风力[三十]。

In this paper, inspired by the standard ZV formulation, a new shaper is proposed with a flexible objective function that allows the controller to optimize and fix the maneuver time. The existing ZV-based shapers provide limited control over the maneuver time, input acceleration, input jerk, and cable length sensitivity. However, the new shaper can optimize the maneuver time while satisfying the system jerk and sensitivity requirements. This method allows for the input function to be adjusted according to the predefined objective for different operating cases. Simulations are conducted to evaluate the performance of the implemented methodology in mitigating the payload sway and addressing the parameter uncertainties. Moreover, various operating conditions including different cable lengths are investigated. Finally, the effectiveness of the proposed controller is studied in terms of dimensionless metrics, which represent the sensitivity and control jerk.

2.方法

A standard overhead crane model consists of a massless jib moving in a unidirectional motion along theX-axis with displacement function和恒定长度的非弹性连接的电缆。有效负载被表示为集中质量swings in theplane, as shown in Figure1。

The kinetic energyand potential energyof the system are given by 哪里是重力常数和一世s the swing angle. Using Lagrange’s equations to derive the equation of motion of the system gives

假定质量的一小摆动角度reduces equation (2A）to the linearized equation of motion of the system as 哪里一世s the natural frequency of the system, 。考虑到起重臂加速度（）一世s a piecewise function of four steps, each of持续时间，方程的一般溶液（3）通过应用杜哈明积分变哪里一世s the constant step input. Substituting the piecewise function在方程（4B）给出

执行的积分减少方程（五）to

鉴别式（6a）给出角速度用作

代加速阶段最后一次代入方程（6a）和（6b）给出

Equations (7a）和（7b）表示的质量的最终角位置和最终角速度。该系统的最终条件和约束由下式给出哪里是悬臂的期望速度在加速阶段的末。Equations (8a）和（8b）一世mpose two final conditions and one constraint to the system, which implies that three inputs are required to satisfy these requirements. However, an extra input is introduced here as the fourth constant to optimize the system performance according to a tailored objective function. This additional independent input provides the required adaptation to the system requirements according to the optimization criterion. By applying equations (8a）和（8b）to equations (7a）和（7b），的系统的条件和约束矩阵表示被发现为

重新整理公式（9）给出

方程（10）表示的前三个依赖性输入，这是起重臂的前三个分段加速度的步骤。这些步骤满足通过使用等式（给定的系统要求8a）和（8b）

3。Results and Discussion

3.1。敏感性分析

敏感指数的定义如下量化系统到电缆长度的振动幅度的灵敏度：哪里一世s the amplitude of vibration at the end of the maneuver case一世。的电缆长度的80％至120％的范围内被用于计算在每个点处的灵敏度指数。

数字2shows the overhead crane payload angle for a specific cable length. The system requirements are met by applying the step input generated by the proposed input shaper. The designated maneuver ends with zero payload angle and zero angular velocity, suggesting that the generated input steps eliminate the residual vibrations while the jib reaches the required final velocity.

数字3shows how the sensitivity index changes by changing the fourth input constant (C₄）在标准机动时间，这是1秒计算不同长度的电缆。结果表明，第四输入恒定的该灵敏度指数的影响随着电缆长度减小。对于电缆长度的给定范围，也有最佳C₄values for which the sensitivity index is minimized and the system is least sensitive to unexpected cable length variations.

数字4shows the values of all input constants measured at the optimalC₄and how they change as cable length changes. As the cable length increases, higher input constants are expected due to higher kinetic and potential energies of the system as the pendulum oscillates. It is also apparent that the input constants change in pairs:C₁withC₄andC₂withC₃。在，所有输入常数相等，这表明系统达到在整个机动恒定输入零振动的最终状态。对于给定的电缆长度值，选择所述相关联的优化输入常数（绘制在图4）guarantees that the system remains least sensitive to any unexpected cable length change within a variation range of 80% to 120%.

数字五示出了灵敏度指数不同的电缆长度和一系列的动作时间如何变化。对于一个特定的电缆长度，增加机动时间减少意外的电缆长度变化的系统的灵敏度。这种看法是适用于所有更长的电缆长度值。即使短电缆，其中SI在操纵开始由于在该系统的固有频率的减小而减小，SI随着机动继续。

A new metric is introduced to normalize the impact of the maneuver time on the sensitivity index. The normalized sensitivity index被定义为灵敏度指数的对于给定的电缆长度和机动的时间与标准时间机动但类似的电缆长度的灵敏度指数的比率。数字6示出了归一化的敏感指数与机动时间不同电缆长度的变化如何变化。值小于一个指示，相对于系统的在标准机动时间对于相同的电缆长度灵敏度系统是较不敏感。如图6，存在这样的情况，其中该系统是较不敏感的和操纵时间较短，这表明，该方法可以在同一时间，这降低了灵敏度降低的机动时间对于给定的电缆长度。

3.2。挺举分析

Significant differences between input values may be unfavorable due to the existence of a jerk. Therefore, jerk index一世s introduced to measure these differences as follows:

数字7示出（该系统的加加速度指数和第四输入常数之间的关系C₄）for different cable length settings. For a given cable length, there is an optimum value ofC₄，为此，该系统的加加速度指数被最小化。另外，如预期的，增加了电缆长度的增加，这导致更高的加加速度指数和最优的系统的总能量C₄值。

归挺举指数一世s defined as the ratio of the jerk index to the jerk index with zeroC₄对于相同的电缆长度如下：

NJI指示如何挺举指数是通过将受影响C₄该制剂。数字8shows the normalized jerk index and its relationship withC₄for different cable lengths. Values less than one indicate that the system is improved by addingC₄相比于具有三个输入常数的系统（即，）。增加电缆长度延伸,在which the normalized jerk index is less than one.

Jerk index variation被引入作为加加速度索引到输入常数的绝对值的平均值的比例为：

数字9示出了在计算出的最佳输入常数C₄to minimize the jerk index for different cable lengths. Higher values of jerk index variation indicate that the jerks are unfavorably high relative to the input constants.

数字10示出了加加速度指数的变化通过在一定范围的的机动倍改变电缆的长度如何变化。在大多数情况下，增加了加加速度指数的减小操纵时间的结果，同时它也减少了输入常数之间的偏差。挺举指数有较长的电缆短机动倍的最高值。具有这种配置的系统是具有挑战性的控制，因为它需要的输入中的大的变化。

4。结论

本文提出一种新颖的输入成形方法来解决在控制高架起重机具有苛刻的设计和操作要求的常规ZV成形技术的限制。所提出的方法导致最佳的机动时间以最小的挺举和参数不敏感。一个广泛的灵敏度分析以量化不同可行操作条件下的控制器的性能。挺举分析表明，通过整形的优化过程使其能够降低输入挺举同时最小化机动时间。结果证实，修改后的ZV整形提供了苛刻点至点的机动要求桥式起重机的强大而有效的和计算效率控制解决方案。

Data Availability

没有数据来支持这项研究。

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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冲击和振动

抽象