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class="1">第五章数控加工中心龙门电磁悬浮系统无源</span></a></p> <div class="Section1"> <p class="11" style="margin-top:0cm;margin-right:0cm;margin-bottom:16.85pt; margin-left:1.0pt;line-height:22.0pt;mso-line-height-rule:exactly;mso-pagination: lines-together;page-break-after:avoid;background:transparent"><a name="bookmark37"><span class="1">控制</span></a></p> <p class="21" align="left" style="margin-top: 0cm; text-indent: 26pt; line-height: 23.3pt; background: transparent;"><span class="2">随着科技的不断发展，控制领域也获得了长足的发展。从传统的线性控制</span><span class="2TimesNewRoman26"><span style="font-size: 11.5pt; font-family: 宋体;">、</span></span><span class="2TimesNewRoman26"><span lang="EN-US" style="font-size: 11.5pt;">PID </span></span><span class="2">控制发展到智能控制。由于电磁力与电流之间具有二次方的关系，因此电磁悬浮系统 是非线性系统。为了实现对电磁悬浮系统的精确控制，以保证加工部件的精度，需要 对电磁悬浮系统设计良好的控制器以达到龙门数控加工中心的性能指标。文献</span><span class="2"><span style="font-family: SimSun;">[46] </span></span><span class="2">利用最优算法对悬浮系统控制器参数进行优化。文献</span><span class="2"><span style="font-family: SimSun;">[47]</span></span><span class="2">利用模糊算法对</span><span class="2TimesNewRoman26"><span lang="EN-US" style="font-size: 11.5pt;">PID</span></span><span class="2">控制器 参数进行了整定。他们都在一定程度上满足了悬浮系统的性能指标。本文为电磁悬浮 系统设计了无源控制器，为悬浮系统的控制算法库扩充了一种新的、有效地控制算法。</span></p> <p class="22" style="margin-top:0cm;margin-right:0cm;margin-bottom:10.1pt; margin-left:0cm;line-height:13.0pt;mso-line-height-rule:exactly;mso-pagination: lines-together;page-break-after:avoid;background:transparent"><a name="bookmark38"><span class="20"><span style="font-family: SimSun;">5.1</span></span></a><span class="20">磁链控制数学模型</span></p> <p class="21" align="left" style="margin: 0cm 0cm 21.45pt; text-indent: 26pt; line-height: 23.3pt; background: transparent;"><span class="2">由第二章已经推导出电磁悬浮系统数学模型，由于电流间接控制电磁力会使磁路 饱和产生非线性因素，因此采用磁链控制能直接控制电磁力，可以消除磁路饱和所产生的非线性因素。</span><a name="bookmark52"><span class="20"><span lang="EN-US" style="mso-ansi-font-size:11.0pt; mso-bidi-font-size:11.0pt;mso-hansi-font-family:MingLiU;mso-bidi-font-family: 宋体;letter-spacing:0pt;mso-ansi-language:EN-US"><o:p></o:p></span></span></a></p> <p class="22" style="margin-top:0cm;margin-right:0cm;margin-bottom:22.3pt; margin-left:0cm;line-height:13.0pt;mso-line-height-rule:exactly;mso-pagination: lines-together;page-break-after:avoid;background:transparent"><span class="20"><span style="font-family: SimSun;">5. 4</span></span><span class="20">仿真结果及分析</span></p> <p class="640" align="left" style="margin: 0cm 0cm 13.35pt 26pt; text-indent: 0cm; line-height: 11.5pt; background: transparent;"><span class="64">系统的仿真参数见第三章。平衡点磁链</span><span class="64"><span style="font-family: SimSun;">/.= </span></span><span class="64">3.178。反馈控制器表示式中</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">a</span></span><span class="64"><span style="font-family: SimSun;">, </span></span><span class="64">1^两</span><span class="64">个参数分别为20, 5000。</span></p> <p class="640" align="left" style="margin: 0cm 0cm 13.35pt 26pt; text-indent: 0cm; line-height: 11.5pt; background: transparent;"><!--[if gte vml 1]><o:wrapblock><v:shapetype id="_x0000_t202" coordsize="21600,21600" o:spt="202" path="m,l,21600r21600,l21600,xe"> <v:stroke joinstyle="miter" /> <v:path gradientshapeok="t" o:connecttype="rect" /> </v:shapetype><v:shape id="_x0000_s1026" type="#_x0000_t202" style='position:absolute; left:0;text-align:left;margin-left:52.55pt;margin-top:42pt;width:328.55pt; height:18.75pt;z-index:-1;mso-wrap-distance-left:52.3pt; mso-wrap-distance-right:60pt;mso-position-horizontal-relative:margin' wrapcoords="0 0 21600 0 21600 18752 17053 19048 17053 21600 5062 21600 5062 19048 0 18752 0 0" filled="f" stroked="f"> <v:textbox style='mso-fit-shape-to-text:t' inset="0,0,0,0"> <![if !mso]> <table cellpadding=0 cellspacing=0 width="100%"> <tr> <td><![endif]> <div> <p class=MsoNormal align=center style='text-align:center'><span lang=EN-US style='font-size:1.0pt;mso-bidi-font-family:"Times New Roman"; color:windowtext;mso-ansi-language:EN-US'><o:p> </o:p></span></p> <p class=60 align=center style='margin:0cm;margin-bottom:.0001pt; text-align:center;line-height:15.1pt;mso-line-height-rule:exactly; background:transparent'><span lang=EN-US><o:p> </o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> <w:wrap type="topAndBottom" anchorx="margin" /> </v:shape><![endif]--><!--[if !vml]--> <!--[endif]--><!--[if gte vml 1]></o:wrapblock><![endif]--><br clear="ALL" /> <span class="64">系统仿真框图如图5.1。</span></p> <p class="640" align="left" style="margin-left: 26pt; text-indent: 0cm; line-height: 11.5pt; background: transparent;"><span class="64">仿真</span><span class="64"><span style="font-family: SimSun;">1:</span></span><span class="64">无扰动仿真效果对比实验</span></p> </div> <div class="Section2"> <p class="640" style="margin-bottom:8.3pt;text-indent:26.0pt;line-height:11.5pt; mso-line-height-rule:exactly;background:transparent"><span class="64">当系统中不加扰动时对</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控制、模糊</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控制和无源控制的仿真曲线进行比</span><span class="64">较。</span></p> <p class="640" style="text-indent:26.0pt;line-height:23.3pt;mso-line-height-rule: exactly;background:transparent"><span class="64">从仿真图</span><span class="64"><span style="font-family: SimSun;">5.2</span></span><span class="64">中可知无源控制使得响应曲线在不到</span><span class="64"><span style="font-family: SimSun;">0.1</span></span><span class="64">秒就到达了设定的悬浮位</span><span class="64"> </span><span class="64">置并且没有超调量。相比于</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控制、模糊</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控制使电磁悬浮系统具有了更快的</span><span class="64"> </span><span class="64">响应速度。</span></p> <p class="640" style="text-indent:26.0pt;line-height:23.3pt;mso-line-height-rule: exactly;background:transparent"><span class="64">仿真2:有扰动仿真效果对比实验</span></p> <p class="640" style="text-indent:26.0pt;line-height:23.3pt;mso-line-height-rule: exactly;background:transparent"><span class="64">在系统响应第3秒时对悬浮系统施加</span><span class="64"><span style="font-family: SimSun;">500</span></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">N</span></span><span class="64">的阶跃扰动，同时观察三种控制器的 仿真曲线，仿真曲线如图5.3。</span></p> </div> <div class="Section3"> <p class="640" align="left" style="text-indent: 25pt; line-height: 23.3pt; background: transparent;"><span class="64">由图</span><span class="64"><span style="font-family: SimSun;">5.3</span></span><span class="64">可知当系统受到</span><span class="64"><span style="font-family: SimSun;">500</span></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">N</span></span><span class="64">阶跃干扰时无源控制系统响应曲线相比于</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控</span><span class="64"> </span><span class="64">制和模糊</span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">PID</span></span><span class="64">控制的系统的波动超调幅度小且在</span><span class="64"><span style="font-family: SimSun;">0.1</span></span><span class="64">秒左右就恢复到了设定的位置</span><span class="64">， </span><span class="64">因此相比于这两种控制算法无源控制加强了系统的鲁棒性。</span></p> <p class="640" align="left" style="text-indent: 25pt; line-height: 23.3pt; background: transparent;"><span class="64">仿真3:悬浮系统周期扰动仿真实验</span></p> <p class="640" style="margin-bottom:66.55pt;text-indent:25.0pt;line-height:23.3pt; mso-line-height-rule:exactly;background:transparent"><span class="64">移动悬浮横梁的水平导向单元采用的是永磁同步直线电机驱动。由于直线电机运 行时存在着纹波扰动、端部效应等周期扰动严重影响到了电磁悬浮系统的悬浮精度和 部件的加工精度。为了能够很好的抑制直线电机的这一缺点，因此所设计的控制器需 要使悬浮系统对周期扰动具有一定的抵抗性。当系统受到系统受到</span><span class="64"><span style="font-family: SimSun;">500</span></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">N</span></span><span class="641pt">，</span><span class="641pt">周期为2 </span><span class="64">秒，占空比为1的脉冲周期扰动时的仿真误差曲线如图5.4。</span></p> <p class="640" style="margin-bottom:66.55pt;text-indent:25.0pt;line-height:23.3pt; mso-line-height-rule:exactly;background:transparent"><span class="64">由图</span><span class="64"><span style="font-family: SimSun;">5.4</span></span><span class="64">可知当悬浮系统受到周期扰时悬浮气隙偏差为</span><span class="64"><span style="font-family: SimSun;">6</span></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">xl</span></span><span class="64"><span style="font-family: SimSun;">(</span></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">T</span></span><span class="64"><sup><span style="font-family: SimSun;">5</span></sup></span><span class="64TimesNewRoman1"><span lang="EN-US" style="font-size: 11pt;">m</span></span><span class="64">左右</span><span class="64">，</span><span class="64">且在</span><span class="64"><span style="font-family: SimSun;">0.1</span></span><span class="64">秒左右就恢复到设定点</span><span class="64">，</span><span class="64">由此表明无源控制器使得悬浮系统对周期扰动也具有一定的</span><span class="64"> </span><span class="64">鲁棒性。因此可以适应直线电机所带来的周期干扰。</span></p> <p class="22" style="margin-top:0cm;margin-right:0cm;margin-bottom:10.35pt; margin-left:0cm;text-align:justify;text-justify:inter-ideograph;text-indent: 0cm;line-height:13.0pt;mso-line-height-rule:exactly;mso-pagination:lines-together; page-break-after:avoid;mso-list:l0 level1 lfo1;tab-stops:18.3pt;background: transparent"><a name="bookmark53"><!--[if !supportLists]--><span style="font-family: SimSun;">4.<span style="font-stretch: normal; font-size: 7pt; line-height: normal; font-family: 'Times New Roman';"> </span></span><!--[endif]--><span class="20">5本章小结</span></a></p> <p class="640" align="left" style="text-indent: 25pt; line-height: 23.3pt; background: transparent;"><span class="64">基于无源控制理论本章介绍了单磁悬浮系统无源控制器的设计。首先建立了电磁 悬浮系统的能量函数，然后建立出电磁悬浮系统哈密尔顿方程，通过选取适当的互联</span><span class="64">阵和耗散阵来重新建立电磁悬浮系统的哈密尔顿方程。通过三个哈密尔顿函数约束条 件来求解偏微分方程，从而推出单电磁悬浮系统无源控制器的表达式。无源控制器设 计简单、易于实现。仿真结果表明无源控制器加快了单电磁悬浮系统较强的响应速度, 提高了其鲁棒性，最终提高了悬浮精度。</span></p> </div> <p><span style="font-size:11.5pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";mso-ansi-language:#0400;mso-fareast-language: #0400;mso-bidi-language:AR-SA"><br clear="all" style="page-break-before:always; mso-break-type:section-break" /> </span></p> <p><span style="font-size:9.0pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language: 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