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译文：婴儿车的滑模控制系统的研究北野武川岛机械工程系，神奈川工学院，1030下奥，厚木市，神奈川，243-0292，日本电子邮件：kawashimaeng.kanagawa-it.ac.jp摘要父亲为宝宝提供更好舒适性的婴儿车是必须的，然而更重要的是安全问题。开发舒适的童车，都需要基本婴儿选择和寻找快乐以及数据类型振动。为了获得这些数据,有必要开发一台振动婴儿车，有非线性特性,并开发一个振动台的控制系统遵循所需的特征作为输入随机波，来计算非线性特性。在这项研究中,我们是对一个单轴振动台婴儿车研究。该控制系统是一个比例控制器与外部反馈回路基于离散滑模控制器，即,一个输入波形整形滤波器。表示在适当的前轮婴儿车的动摇根据所需的波形。控制器的性能评估使用数值模拟。结果表明,通过使用比例控制器,对扰动的鲁棒性弱,而且可以增加鲁棒性提出的输入波形整形滤波器，尽管振动台位移只能遵循所需的波形。使用对照实验演示的效果。这个实验的结果显示的均方误差使用比例控制器时表位移随着输入波形整形滤波器相比误差约75%时只使用比例控制。关键词:振动控制、鲁棒控制、滑模控制、振动台、电磁致动器,婴儿车,波形整形1 介绍在日本,轻量级和中型婴儿车是常用的，家长必须持有婴儿和马车虽然升序或降序楼梯。例如，在一个车站。没有给婴儿车降低的空间和支持这样的重量。这些车厢几乎只在东南亚生产中国等亚洲国家,以减少劳动力成本。在下一代的婴儿车,相信婴儿车的舒适性以及安全性会成为最重要的因素。此外，增加的重量改善乘坐的婴儿车是不可取的。一个方法是为提高舒适性而减小设计框架的大小,但这样不能很好的的振动消除。完成这项任务，基本数据类型的振动首选的婴儿车是必需的。然而,婴儿车回流具有非线性特征的车,任何接触和婴儿之间的缓冲。因此,很难垂直动摇一个婴儿车根据所需的波形。在这项研究中,一个单轴振动台可以垂直震动婴儿车重量超过15公斤(包括婴儿)设计,和必要的控制系统开发和正确的前轮上的婴儿车表根据所需的波形。15赫兹频率范围设置为从5赫兹考虑婴儿车的第一固有频率,共振频率的内部器官婴儿似乎变得不适和瓶的下限频率。摇表、控制的各种技术被提出和研究开发过程中所谓的巨大的振动台,即。,并建立了利用经验教训从汉淡路岛地震灾害,就是能动摇和破坏一个全尺寸模型。应用滑模控制的振动台,研究将滑模控制理论应用于液压驱动振动台报道减少摩擦力(1)的波形失真。2 振动台婴儿车图1显示了婴儿车摇晃的照片使用铝组件系统制作。大小长1200毫米,宽700毫米,416毫米高。框架构造主要由使用50505毫米角度。5毫米厚的铝板上排列的顶部框架上除了摇床放置的位置创建一个表面模拟婴儿车的平地。振动台安装的婴儿车是长665毫米,宽500毫米,也是由一盘5毫米厚,某些角度。振动台是由一个电磁振动器(514年,位的有限公司,最大限度的激发力294 N)。然而,最大的振动台的振幅减少,如果直接支持振动台安装。宝宝的婴儿车包括虚拟重18公斤,和摇床包括婴儿车总是调整控制在25公斤。因此,表是由四个弹簧。弹簧张力型弹簧,弹簧常数k = 2.47 kN / m(25.0 N的初始张力,参考负载为101 N)。选择弹簧常数,这样弹簧延伸约15毫米的振动台的重量越来越多的婴儿车,因为振动的振幅的电枢是5毫米。从框架通过弹簧固定接合,以弥补婴儿车的重量分布的不平衡。同时,振动台的高度调整的电枢,摇床的严重性并不影响电枢。3 控制系统的婴儿车振动系统图2显示了震动的控制系统正确的前轮的婴儿车根据所需的波形。附近的位移振动台正确的前轮是衡量激光位移传感器(LB-02日本基恩士有限公司)。信号发送到数字信号处理器(DSP),(天地盒,利用mtt有限公司:1350 MFLOPS)通过嵌入式广告转换器。使用实测位移计算控制输入,并输出到一个放大器瓶(373年,位的有限公司:373 va)通过一个embdded数模转换器,使振动台振动。因此,构成反馈回路。此外,电枢的位移振动测量的激光位移传感器来获取系统的频率响应。4 婴儿车摇系统的分析模型 婴儿车摇系统的分析模型,推导出控制律。婴儿车假定为一个粒子,和回卷运输框架和婴儿之间的任何联系,期待着的垫子被忽略控制律的鲁棒性,这样的效果。图3显示了婴儿车摇系统的分析模型。瓶,摇表近似为一个简单的阻尼弹簧质点系统。,x(t)的位移振动台在适当的前轮的婴儿车,x(t)是吗位移的电枢瓶),F(t是电磁力影响电枢,m是婴儿车的质量,M11公路+ M12摇床的质量,K1和C1是内部的刚度和阻尼系数的弯曲变形振动台,分别M0电枢的质量,k开始0和C0弹簧常数和电枢的承重构件的阻尼系数,分别,k是弹簧的弹簧常数支持振动台。分析模型的运动方程推导如下:考虑到放大器的瓶,安排方程,得到了下列方程:考虑到放大器的瓶,安排方程,得到了下列方程:02 = (K0 + K1 ) (M0 + M11 ) , 12 = (K1 + 4k) (M12 + m) , 012 = K1 /(M12 + m) , 200 = (C0 + C1 ) (M0 + M11 ) , 2101 = C1 (M12 + m) and = (M12 + m) (M0 + M11 ) .分析模型的参数识别使用下面的实验。限带白噪声波形的频率范围从5赫兹到205赫兹频率范围对应的振动器是由间隔的正弦波的叠加每0.5赫兹。瓶的波形是放大器的输入,使婴儿车安装在振动台是动摇了20年代。婴儿车包含一个假,是一个沙袋形状像一个婴儿,和重8.5公斤。附近的位移振动台对前轮的婴儿车和电枢的瓶,从输入的频率响应放大器的位移电枢和衔铁位移的位移振动台得到的快速傅里叶转换(FFT)。然后,频率响应函数的参数计算使用(2)式。结果, 我们获得0 = 939 rad / s,1 = 377 rad / s,12 = 366 rad / s,0 = 0.34,弗吉尼亚州1 = 0.040= 6.21 / 2 = 66.6 m / s。测量和计算频率响应函数的输入放大器的位移电枢图4所示。电枢的频率响应位移的位移振动台图5所示。从输入放大器的频率响应的位移振动台是图6所示。从图6,数据支持的有效性分析模型,虽然小峰在58个赫兹是不明的。同时,我们看到,实验结果在低干扰频率范围由于电枢的摩擦。5 控制律图7显示仿真结果,特别是时间响应的位移振动台附近的前轮婴儿车,和输入信号作为参考。引用是一种限带白噪声的频率范围从2.5赫兹到15赫兹,和最大位移是3毫米。表位移偏离参考,因为频率响应函数不是恒定的频率范围。因此,我们观察到一个控制系统是必需的。图7婴儿车摇系统的仿真结果没有反馈控制器6 控制实验使用设备进行控制实验无花果。1和2所示确认该输入波形整形滤波器的有效性。首先,比例控制器的性能进行了测试。均方误差和最大误差如表1所示。实验结果为250=,均方误差最小,图12所示。表位移同意引用在大多数情况下,尽管在高频率范围再次输入生成的,类似于图9所示的仿真结果。表1实验结果的均方误差和最大误差在使用比例控制器只(KP = 5)图12只使用比例控制器时实验结果(250=)接下来,使用输入波形整形滤波器的影响与比例控制联合检查。均方误差和最大误差如表2所示。实验结果为01= 0。和= 1,均方误差和最大误差最小,图13所示。相比,由于只使用比例控制器,如图12所示,均方误差约为75%,最大误差也约75%,虽然略高频率生成组件。同样的数据显示表位移可以按照参考,即使参考成为持续短暂,如箭头所示在无花果。12和13。从这些结果,我们确认该输入波形整形滤波器的有效性。表2实验结果的均方误差和最大误差在使用一个输入波形整形滤波器与比例控制(KP = 5)图13实验结果在使用一个输入波形整形滤波器以及比例控制(01= 0。,= 7 结论为了收集基本数据类型的振动首选婴儿乘坐马车,婴儿车震动系统发展。这个系统可以垂直震动婴儿车根据所需的波形具有非线性特征。控制系统是由一个比例控制器的一个输入波形整形滤波器基于离散滑模控制理论。从数值模拟,阐明了控制系统对扰动的鲁棒性是使用输入波形整形滤波器改善。从一个实验,它是也表明,振动台位移的均方误差在使用输入波形整形滤波器与比例控制是75%的错误只在使用比例控制。这演示了该控制系统的有效性。引用(1)日本久保田公司,T。、Kozuma F。Kubokawa,n和杉,F。研究在减少波形失真,液压振动器(2),KAYABA技术审查,19号(1999),pp.3-9。原文：Investigation of a Sliding Mode Control Systemfor a Shaking Table for Baby CarriagesTakeshi KAWASHIMADepartment of Mechanical Engineering, Kanagawa Institute of Technology,1030 Shimo-ogino, Atsugi-shi, Kanagawa, 243-0292, JapanE-mail: kawashimaeng.kanagawa-it.ac.jpAbstractIn the next generation of baby carriages, better comfort for both the baby as well as the parent is required, in addition to safety concerns.To develop a comfortable baby carriage, fundamental data are required about the types of vibrations babies prefer and find pleasant. In order to obtain such data, it is necessary to develop a shaking table for baby carriages having nonlinear characteristics, and develop a control system in which the shaking table follows a desired input characterized as a random wave.In this study, a single axis shaking table for a baby carriage is studied.The table under the right front wheel of the baby carriage is shaken according to a desired waveform. The proposed control system is a proportional controller with an outer feedback loop based on a discrete-time sliding mode controller, i.e., an input waveform shaping filter.The performance of the controller is evaluated using a numerical simulation. The results show that although the shaking table displacement could follow the desired waveform by using only the proportional controller, the robustness of the response to disturbance was weak, and also that the robustness could be improved with the addition of the proposed input waveform shaping filter.The effectiveness is demonstrated using a control experiment. The results of this experiment show that the mean square error of the table displacement when using proportional controller along with the input waveform shaping filter was about 75% compared with the error when using only the proportional control.Key words: Vibration Control, Robust Control, Sliding Mode Control, Shaking Table, Electromagnetic Actuator, Baby Carriage, Waveform Shaping 1 IntroductionIn Japan, lightweight and easy-to-fold baby carriages are commonly used in light of the fact that a parent has to hold both the baby and its carriage while ascending or descending a flight of stairs, for example,at a station. There is no room for reducing the weight of such baby carriages further.These carriages are manufactured almost exclusively in SoutheastAsian countries such as China to reduce labor costs. In the next generation of baby carriages, it is believed that riding comfort for the baby as well as the comfort of the parent handling the carriage will be important factors, in addition to safety concerns.Furthermore, increasing the weight of the baby carriage for improving the ride is not desirable.One method for improving the riding comfort and reducing weight is to design the frame such that the unpleasant vibrations are eliminated.To accomplish this task, fundamental data about the types of vibrations preferred by the babies riding in the carriage are required.However, a baby carriage has nonlinear characteristics by backrushes of the carriage frame, any contact between the baby and the cushion, and so forth. Therefore, it is difficult tovertically shake a baby carriage according to a desired waveform. In this study, a one-axis shaking table that can vertically shake a baby carriage weighing over 15 kg (this includes the baby) is designed, and the necessary control system is developed to shake the right front wheel of the baby carriage on the table according to a desired waveform. The frequency range is set to 15 Hz from 5 Hz considering a first natural frequency of a baby carriage, resonant frequencies of internal organs in which an infant seems to becomeFor the control of shaking tables, various techniques have been proposed and studied during the development process of the so-called giant shaking table, i.e., E-defense, which was constructed to utilize lessons learned from the HanShin Awaji Earthquake disaster,and which is able to shake and destroy a full scale model. For the application of a sliding mode control to a shaking table, research applying sliding mode control theory to a hydraulically driven shaking table has been reported to reduce the waveform distortion by frictional forces(1). discomfort and the lower-limit frequency of the shaker. For the control of shaking tables, various techniques have been proposed and studied during the development process of the so-called giant shaking table, i.e., E-defense, which was constructed to utilize lessons learned from the HanShin Awaji Earthquake disaster, and which is able to shake and destroy a full scale model. For the application of a sliding mode control to a shaking table, research applying sliding mode control theory to a hydraulically driven shaking table has been reported to reduce the waveform distortion by frictional forces(1).2 Shaking Table for Baby Carriage Figure 1 shows the photograph of the baby carriage shaking system fabricated by using aluminum components. The size is 1200 mm long, 700 mm wide, and 416 mm high. The frame is constructed mainly by using 50 50 5 mm angles. 5 mm thick aluminum plates are arranged on the top of the frame except where the shaking table is placed to create a surface simulation in which the baby carriage is running along flat ground.The shaking table mounting the baby carriage is 665 mm long and 500 mm wide, and it is also constructed by a plate 5 mm thick and some angles. The shaking table is driven by an electromagnetic shaker (514A, Emic Co., with a maximum exciting force of 294 N). However, the maximum amplitude of the shaking table decreases, if the shaker directly supports the shaking table mounting. The baby carriage including a dummy of the baby weighs 18 kg, and the shaking table including the baby carriage is always adjusted at 25 kg for the control. Therefore, the table is supported by four springs. The springs are tension type springs, and the spring constant is k = 2.47 kN/m (the initial tension is 25.0 N, and the reference load is 101 N). The spring constant is chosen such that the springs extend about 15 mm by the weight of the shaking table mounting the baby carriage, because the amplitude of the shakers armature is 5 mm. The springs are fixed from the frame through aturnbuckle to compensate for the imbalance of weight distribution of the baby carriage.Also, the height of the shaking table is adjusted to that of the armature so that the gravity of the shaking table does not affect the armature.3 Control System for the Baby Carriage Shaking SystemFigure 2 shows the control system that shakes the right front wheel of the baby carriage according to the desired waveform. The displacement of the shaking table near the right front wheel is measured by a laser displacement sensor (LB-02, Keyence Co.). The signal is sent to a digital signal processor (DSP), (s-BOX, mtt Co.: 1350 MFLOPS) through an embedded AD convertor. The control input is calculated using the measured displacement, and it is output to an amplifier for the shaker (373-A, Emic Co.: 330VA) through an embdded DA converter, so that the shaking table vibrates. Therefore, a feedback loop is constituted. In addition, the displacement of the armature of the shaker is measured by a laser displacement sensor to obtain the frequency response of the system.4 Analytical Model of the Baby Carriage Shaking SystemAn analytical model of the baby carriage shaking system is formulated to derive the control law. The baby carriage is assumed to be a particle, and backrushes of the carriage frame and any contact between the baby and the cushion are ignored by expecting the robustness of the control law to account for such effects. Figure 3 shows the analytical model of the baby carriage shaking system. The shaker and the shaking table are approximated as a simple damped mass-spring system. Where, x(t) is the displacement of the shaking table under the right front wheel of the baby carriage, X(t) is the displacement of the armature of the shaker, )F(t is the electromagnetic force affecting the armature, m is the mass of the baby carriage, M11 + M12 is the mass of the shaking table, K1 and C1 are the stiffness and the internal damping coefficient for the bending deformation of the shaking table, respectively, M0 is the mass of the armature, K0 and C0 are the spring constant and the damping coefficient of the supporting member of the armature, respectively, and, k is the spring constant of the spring supporting the shaking .The equations of motion for the analytical model are derived as follows:Considering the amplifier of the shaker and arranging the equations, the following equations are obtained.Where, u is the input voltage to the amplifier as the control input, a is the coefficient including the amplification factor of the amplifier, 02 = (K0 + K1 ) (M0 + M11 ) , 12 = (K1 + 4k) (M12 + m) , 012 = K1 /(M12 + m) , 200 = (C0 + C1 ) (M0 + M11 ) , 2101 = C1 (M12 + m) and = (M12 + m) (M0 + M11 ) .The parameters of the analytical model are identified using the following experiment. A band-limited white noise waveform of the frequency range from 5 Hz to 205 Hz corresponding to the frequency range of the shaker is generated by the superposition of the sine wave at interval of every 0.5 Hz. The waveform is input to the amplifier of the shaker, so that the baby carriage mounted on the shaking table is shaken for 20 s. The baby carriage contains a dummy that is a sandbag shaped like a baby, and weighs 8.5 kg. The displacements of the shaking table near the right front wheel of the baby carriage and the armature of the shaker are measured, and the frequency response from the input of theamplifier to the displacement of the armature and from the armature displacement to the displacement of the shaking table are obtained by a fast Fourier transfer (FFT). Then, the parameters are calculated from the frequency response functions using Eq. (2). As a result, we obtain 0 = 939 rad/s , 1 = 377 rad/s , 12 = 366 rad/s , 0 = 0.34 , 1 = 0.040 , = 6.21 , /Va = 66.6 m/s 2 . The measured and calculated frequency response functions from the input of the amplifier to the displacement of the armature are shown in Fig. 4. The frequency responses from the armature displacement to the displacement of the shaking table are shown in Fig. 5. The frequency responses from the input of the amplifier to the displacement of the shaking table are shown in Fig. 6.From Fig. 6, the data supports the validity of the analytical model, although a small peak in 58 Hz is unidentified. Also, we see that the experimental results are disturbed in the low frequency range due to the friction of the armature. 5. Control LawFigure 7 shows simulation results, in particular, the time response of the displacement of the shaking table near the right front wheel of the baby carriage, and the input signal as a reference. The reference is aband-limited white noise of the frequency range from 2.5 Hz to 15 Hz, and the maximum displacement is 3 mm. The table displacement deviated from the reference, because the frequency response function is not constant over the frequency range. Therefore, we observe that a control system is required.Fig. 7 Simulation result of the baby carriage shaking system without feedback controller6 Control Experiment A control experiment was performed using the equipment shown in Figs. 1 and 2 toconfirm the effectiveness of the proposed input waveform shaping filter. First, the performance of the proportional controller was examined. The mean square error and the maximum error are shown in Table 1. The experimental result for 250 = , in which the mean square error is minimum, is shown in Fig. 12. The table displacement agrees with the reference for the most part, although the input in the high frequency range is again generated, similar to the simulation result shown in Fig. 9.Table 1 Mean square error and maximum error of experimental result when using a proportional controller only ( KP = 5 )Fig. 12 Experimental result when using a proportional controller only ( 250 = )Next, the effects of using the input waveform shaping filter jointly with proportional control were examined. The mean square error and the maximum error are shown in Table 2. The experimental result for 01 = 0. and = 1 , in which the mean square error and the maximum error are minimum, is shown in Fig. 13. In comparison with the result from using only the proportional controller, as shown pre