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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62751d119221806f9d1e8d0d/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">一级直线倒立摆的最优控制</div><div class="t m0 x2 h4 y3 ff2 fs1 fc0 sc1 ls0 ws0">1 <span class="ff1 sc0">引言</span></div><div class="t m0 x3 h5 y4 ff3 fs2 fc0 sc1 ls0 ws0">1.1 <span class="ff1 sc0">倒立摆介绍以及应用</span></div><div class="t m0 x4 h6 y5 ff1 fs3 fc0 sc1 ls0 ws0">倒立摆控制系统是一个复杂的、不稳定的、非线性系统，是进</div><div class="t m0 x5 h6 y6 ff1 fs3 fc0 sc1 ls0 ws0">行控制理论教学及开展各种控制实验的理想实验平台。对倒立摆系</div><div class="t m0 x5 h6 y7 ff1 fs3 fc0 sc1 ls0 ws0">统的研究能有效的反映控制中的许多典型问题：如非线性问题、鲁</div><div class="t m0 x5 h6 y8 ff1 fs3 fc0 sc1 ls0 ws0">棒性问题、镇定问题、随动问题以及跟踪问题等。通过对倒立摆的</div><div class="t m0 x5 h6 y9 ff1 fs3 fc0 sc1 ls0 ws0">控制，用来检验新的控制方法是否有较强的处理非线性和不稳定性</div><div class="t m0 x5 h6 ya ff1 fs3 fc0 sc1 ls0 ws0">问题的能力。</div><div class="t m0 x4 h6 yb ff1 fs3 fc0 sc1 ls0 ws0">通过对它的研究不仅可以解决控制中的理论和技术实现问题，</div><div class="t m0 x5 h6 yc ff1 fs3 fc0 sc1 ls0 ws0">还能将控制理论涉及的主要基础学科：力学，数学和计算机科学进</div><div class="t m0 x5 h6 yd ff1 fs3 fc0 sc1 ls0 ws0">行有机的综合应用。其控制方法和思路无论对理论或实际的过程控</div><div class="t m0 x5 h6 ye ff1 fs3 fc0 sc1 ls0 ws0">制都有很好的启迪，是检验各种控制理论和方法的有效的“试金石”。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62751d119221806f9d1e8d0d/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x5 h6 yf ff1 fs3 fc0 sc1 ls0 ws0">倒立摆的研究不仅有其深刻的理论意义，还有重要的工程背景。在</div><div class="t m0 x5 h6 y10 ff1 fs3 fc0 sc1 ls0 ws0">多种控制理论与方法的研究与应用中，特别是在工程实践中，也存</div><div class="t m0 x5 h6 y11 ff1 fs3 fc0 sc1 ls0 ws0">在一种可行性的实验问题，使其理论与方法得到有效检验，倒立摆</div><div class="t m0 x5 h6 y12 ff1 fs3 fc0 sc1 ls0 ws0">就能为此提供一个从理论通往实践的桥梁，目前，对倒立摆的研究</div><div class="t m0 x5 h6 y13 ff1 fs3 fc0 sc1 ls0 ws0">已经引起国内外学者的广泛关注，是控制领域研究的热门课题之一。</div><div class="t m0 x4 h6 y14 ff1 fs3 fc0 sc1 ls0 ws0">倒立摆不仅仅是一种优秀的教学实验仪器，同时也是进行控制</div><div class="t m0 x5 h6 y15 ff1 fs3 fc0 sc1 ls0 ws0">理论研究的理想实验平台。由于倒立摆系统本身具有的高阶次、不</div><div class="t m0 x5 h6 y16 ff1 fs3 fc0 sc1 ls0 ws0">稳定、多变量、非线性和强耦合特性，许多现代控制理论的研究人</div><div class="t m0 x5 h6 y17 ff1 fs3 fc0 sc1 ls0 ws0">员一直将它视为典型的研究对象，不断从中发掘出新的控制策略和</div><div class="t m0 x5 h6 y18 ff1 fs3 fc0 sc1 ls0 ws0">控制方法，相关的科研成果在航天科技和机器人学方面获得了广阔</div><div class="t m0 x5 h6 y19 ff1 fs3 fc0 sc1 ls0 ws0">的应用。二十世纪九十年代以来，更加复杂多种形式的倒立摆系统</div><div class="t m0 x5 h6 y1a ff1 fs3 fc0 sc1 ls0 ws0">成为控制理论研究领域的热点，每年在专业杂志上都有大量的优秀</div><div class="t m0 x5 h6 y1b ff1 fs3 fc0 sc1 ls0 ws0">论文出现。因此，倒立摆系统在控制理论研究中是一种较为理想的</div><div class="t m0 x5 h6 y1c ff1 fs3 fc0 sc1 ls0 ws0">实验装置。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62751d119221806f9d1e8d0d/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4 h6 yf ff1 fs3 fc0 sc1 ls0 ws0">倒立摆主要应用在以下几个方面<span class="ff4">:</span></div><div class="t m0 x4 h6 y1d ff5 fs3 fc0 sc1 ls0 ws0">(1)<span class="ff1">机器人的站立与行走类似于双倒立摆系统，尽管第一台机器</span></div><div class="t m0 x5 h6 y1e ff1 fs3 fc0 sc1 ls0 ws0">人在美国问世至今已有三十年的历史，机器人的关键技术<span class="ff4">--</span>机器人</div><div class="t m0 x5 h6 y1f ff1 fs3 fc0 sc1 ls0 ws0">的行走控制至今仍未能很好解决。</div><div class="t m0 x4 h7 y20 ff5 fs3 fc0 sc1 ls0 ws0">(2)<span class="ff1">在火箭等飞行器的飞行过程中，为了保持其正确的<span class="ff6">姿态</span>，要</span></div><div class="t m0 x5 h6 y21 ff1 fs3 fc0 sc1 ls0 ws0">不断进行实时控制。</div><div class="t m0 x4 h7 y22 ff5 fs3 fc0 sc1 ls0 ws0">(3)<span class="ff1">通<span class="ff6">信卫星</span>在<span class="ff6">预先</span>计算好的<span class="ff6">轨道</span>和确定的<span class="ff6">位</span>置上<span class="ff6">运</span>行的同时，</span></div><div class="t m0 x5 h7 y23 ff1 fs3 fc0 sc1 ls0 ws0">要保持其稳定的<span class="ff6">姿态</span>，使<span class="ff6">卫星</span>天线一直<span class="ff6">指向地球</span>，使它的<span class="ff6">太阳</span>能<span class="ff6">电</span></div><div class="t m0 x5 h7 y24 ff6 fs3 fc0 sc1 ls0 ws0">池板<span class="ff1">一直</span>指向太阳<span class="ff1">。</span></div><div class="t m0 x4 h7 y25 ff5 fs3 fc0 sc1 ls0 ws0">(4)<span class="ff6">侦察卫星<span class="ff1">中</span>摄像<span class="ff1">机的</span>轻微抖<span class="ff1">动</span>会<span class="ff1">对</span>摄像<span class="ff1">的</span>图像质<span class="ff1">量</span>产生<span class="ff1">很大</span></span></div><div class="t m0 x5 h7 y26 ff1 fs3 fc0 sc1 ls0 ws0">的<span class="ff6">影响</span>，为了提高<span class="ff6">摄像</span>的<span class="ff6">质</span>量，<span class="ff6">必须</span>能<span class="ff6">自</span>动<span class="ff6">地</span>保持<span class="ff6">伺服云</span>台的稳定，</div><div class="t m0 x5 h7 y27 ff6 fs3 fc0 sc1 ls0 ws0">消除震<span class="ff1">动。</span></div><div class="t m0 x4 h7 y28 ff5 fs3 fc0 sc1 ls0 ws0">(5)<span class="ff1">为<span class="ff6">防止单</span>级火箭在<span class="ff6">拐弯</span>时断<span class="ff6">裂而诞生</span>的<span class="ff6">柔</span>性火箭</span>(<span class="ff1">多级火箭</span>)<span class="ff1">，</span></div><div class="t m0 x5 h7 y29 ff1 fs3 fc0 sc1 ls0 ws0">其飞行<span class="ff6">姿态</span>的控制也可以用多级倒立摆系统进行研究。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62751d119221806f9d1e8d0d/bg4.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4 h7 yf ff1 fs3 fc0 sc1 ls0 ws0">由于倒立摆系统与双<span class="ff6">足</span>机器人、火箭飞行控制和各类<span class="ff6">伺服云</span>台</div><div class="t m0 x5 h6 y10 ff1 fs3 fc0 sc1 ls0 ws0">稳定有很大相似性，因此对倒立摆控制机理的研究具有重要的理论</div><div class="t m0 x5 h6 y11 ff1 fs3 fc0 sc1 ls0 ws0">和实践意义。</div><div class="t m0 x3 h5 y2a ff3 fs2 fc0 sc1 ls0 ws0">1.2 <span class="ff1 sc0">倒立摆的控制方法</span></div><div class="t m0 x4 h7 y2b ff1 fs3 fc0 sc1 ls0 ws0">倒立摆有多种控制方法。<span class="ff6">当</span>前，倒立摆的控制方法可<span class="ff6">分</span>为以下</div><div class="t m0 x5 h7 y2c ff1 fs3 fc0 sc1 ls0 ws0">几类<span class="ff6"> </span>：</div><div class="t m0 x4 h6 y2d ff5 fs3 fc0 sc1 ls0 ws0">(1)<span class="ff1">线性理论控制方法</span></div><div class="t m0 x4 h7 y2e ff1 fs3 fc0 sc1 ls0 ws0">将倒立摆系统的非线性<span class="ff6">模</span>型进行<span class="ff6">近</span>似线性<span class="ff6">化</span>处理，获得系统在</div><div class="t m0 x5 h7 y2f ff1 fs3 fc0 sc1 ls0 ws0">平<span class="ff6">衡</span>点<span class="ff6">附近</span>的线性<span class="ff6">化模</span>型，<span class="ff6">然后再利</span>用各种线性系统控制器<span class="ff6">设</span>计方</div><div class="t m0 x5 h7 y30 ff1 fs3 fc0 sc1 ls0 ws0">法，得到<span class="ff6">期望</span>的控制器。<span class="ff5">PID<span class="_ _0"> </span></span>控制、<span class="ff6">状态</span>反<span class="ff6">馈</span>控制、<span class="ff5">LQR<span class="_ _0"> </span></span>控制算法</div><div class="t m0 x5 h7 y31 ff1 fs3 fc0 sc1 ls0 ws0">是其典型代<span class="ff6">表</span>。</div><div class="t m0 x4 h7 y32 ff5 fs3 fc0 sc1 ls0 ws0">(2)<span class="ff6">预测<span class="ff1">控制和变</span>结构<span class="ff1">控制方法</span></span></div><div class="t m0 x4 h7 y33 ff6 fs3 fc0 sc1 ls0 ws0">预测<span class="ff1">控制：是一种优</span>化<span class="ff1">控制方法，强</span>调<span class="ff1">的是</span>模<span class="ff1">型的</span>功<span class="ff1">能</span>而<span class="ff1">不是</span></div><div class="t m0 x5 h7 y34 ff6 fs3 fc0 sc1 ls0 ws0">结构<span class="ff1">。变</span>结构<span class="ff1">控制：是一种非</span>连续<span class="ff1">控制，可将控制对象从</span>任<span class="ff1">意</span>位<span class="ff1">置</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
倒立摆LQR控制
