{"id":397,"date":"2025-06-22T17:36:56","date_gmt":"2025-06-22T09:36:56","guid":{"rendered":"https:\/\/yin.nnneri.me\/?p=397"},"modified":"2025-06-25T23:54:19","modified_gmt":"2025-06-25T15:54:19","slug":"%e8%87%aa%e5%8a%a8%e6%8e%a7%e5%88%b6%e5%8e%9f%e7%90%86%e6%9c%9f%e6%9c%ab%e5%bf%ab%e9%80%9f%e5%a4%8d%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/yin.nnneri.me\/?p=397","title":{"rendered":"\u81ea\u52a8\u63a7\u5236\u539f\u7406\u671f\u672b\u5feb\u901f\u590d\u4e60"},"content":{"rendered":"<h2>\u4e8c\u9636\u7cfb\u7edf\u6b20\u963b\u5c3c\u54cd\u5e94\u8fc7\u7a0b\u5206\u6790<\/h2>\n<p>\u4e3b\u8981\u662f\u6c42\u56db\u4e2a\u53c2\u6570<\/p>\n<ul>\n<li>\u4e0a\u5347\u65f6\u95f4$t_r = \\frac{\\pi - \\theta}{\\omega_n \\sqrt{1-\\zeta^2}}$<\/li>\n<li>\u5cf0\u503c\u65f6\u95f4$t_p = \\frac{\\pi}{\\omega_n\\sqrt{1-\\zeta^2}}$<\/li>\n<li>\u8d85\u8c03\u91cf$\\sigma_p=e^{-\\frac{\\zeta}{\\sqrt{1-\\zeta^2}}\\pi} * 100\\%$<\/li>\n<li>\u8c03\u8282\u65f6\u95f4$t_s \\ge \\frac{1}{\\zeta\\omega_n}\\ln\\frac{1}{\\Delta\\sqrt{1-\\zeta^2}}$<br \/>\n\u5176\u4e2d $\\Delta = 0.05 \u6216 0.02$<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u8981\u83b7\u53d6\u4e09\u4e2a\u53c2\u6570<\/p>\n<ul>\n<li>\u963b\u5c3c\u89d2$\\theta$<\/li>\n<li>\u65e0\u963b\u5c3c\u81ea\u632f\u89d2\u9891\u7387$\\omega_n$<\/li>\n<li>\u76f8\u5bf9\u963b\u5c3c\u7cfb\u6570\uff08\u963b\u5c3c\u6bd4\uff09$\\zeta$<\/li>\n<\/ul>\n<p>\u5176\u4e2d<\/p>\n<ul>\n<li>$\\theta = \\arctan\\frac{\\sqrt{1-\\zeta^2}}{\\zeta}$<br \/>\n\u5982\u679c\u9898\u76ee\u7ed9\u4e86\u95ed\u73af\u4f20\u9012\u51fd\u6570<br \/>\n\u90a3\u4e48\u5316\u7b80\u4e3a$\\phi(s) = \\frac{C(s)}{R(s)} = \\frac{\\omega_n^2}{s^2+2\\zeta\\omega_ns+\\omega_n^2}$<\/li>\n<\/ul>\n<h2>\u52b3\u65af\u7a33\u5b9a\u5224\u636e<\/h2>\n<p>\u770b\u4e66P78<\/p>\n<h2>\u6839\u8f68\u8ff9<\/h2>\n<p>\u5f00\u73af\u4f20\u9012\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u5f62\u5f0f<\/p>\n<p>$$G(s)H(s) = K^*\\frac{(s-z_1)(s-z_2)...(s-z_m)}{(s-p_1)(s-p_2)...(s-p_n)},n\\ge m$$<br \/>\n\u5f0f\u4e2d\uff0c$z_i(i=1,2,...,m),p_j(j=1,2,...,n)$\u5206\u522b\u4e3a\u5f00\u73af\u96f6\u70b9\u4e0e\u5f00\u73af\u6781\u70b9<\/p>\n<h3>\u7ed8\u5236180\u00b0\u6839\u8f68\u8ff9\u7684\u57fa\u672c\u89c4\u5219<\/h3>\n<p>\u5bf9\u4e8e\u9898\u7ed9\u4fe1\u606f\uff0c\u5982\u4e00\u4e2a\u5f00\u73af\u4f20\u9012\u51fd\u6570$G(s)H(s)=\\frac{K^*}{s(s+1)(s+2)}$<br \/>\n\u9898\u76ee\u4e00\u822c\u8981\u6c42\u6c42\u89e3<\/p>\n<ul>\n<li>\u7cfb\u7edf\u6839\u8f68\u8ff9\u7684\u8d77\u70b9\u3001\u7ec8\u70b9\u548c\u5206\u652f\u60c5\u51b5<\/li>\n<li>\u6839\u8f68\u8ff9\u7684\u6e10\u8fd1\u7ebf<\/li>\n<li>\u6839\u8f68\u8ff9\u4e0e\u5b9e\u8f74\u7684\u4ea4\u70b9<\/li>\n<li>\u6839\u8f68\u8ff9\u4e0e\u865a\u8f74\u7684\u7126\u70b9<\/li>\n<li>\u53c2\u53d8\u91cf\u7684\u4e34\u754c\u503c<\/li>\n<\/ul>\n<p>\u89e3\u9898\u6b65\u9aa4<\/p>\n<ol>\n<li>\u6c42\u51fa\n<ul>\n<li>\u5f00\u73af\u6781\u70b9<\/li>\n<li>\u5f00\u73af\u96f6\u70b9<\/li>\n<li>\u65e0\u9650\u5f00\u73af\u96f6\u70b9<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<blockquote><p>\n  \u5bf9\u4e8e\u4f8b\u9898\uff0c\u4e0d\u96be\u770b\u51fa\uff0c\u6709$p_1=0,p_2=-1,p_3=-2$\uff0c\u4e09\u4e2a\u5f00\u73af\u6781\u70b9<br \/>\n  \u6ca1\u6709\u5f00\u73af\u96f6\u70b9<br \/>\n  \u65e0\u9650\u5f00\u73af\u96f6\u70b9\u5c31\u662f$n-m=3-0=3$\u4e2a<br \/>\n  \u6240\u4ee5\uff0c\u6709\u4e09\u4e2a\u8d77\u70b9\uff0c\u5206\u522b\u4f4d\u4e8e$(0,j0),(-1,j0),(-2,j0)$<br \/>\n  \u6e10\u8fd1\u7ebf\u7684\u6570\u91cf\u4e3a$n-m$\uff0c\u5c31\u662f\u4e09\u4e2a\n<\/p><\/blockquote>\n<ol start=\"2\">\n<li>\u6c42\u89e3\u6e10\u8fd1\u7ebf\u4e0e\u5b9e\u8f74\u7684\u4ea4\u70b9\u4ee5\u53ca\u5939\u89d2\u60c5\u51b5\n<ul>\n<li>\u5750\u6807\u4e3a\uff1a<\/li>\n<\/ul>\n<p>$$(\\frac{\\sum\\limits_{j=1}^np_j-\\sum\\limits_{i=1}^mz_i}{n-m},j0)$$<\/p>\n<ul>\n<li>\u5939\u89d2\u4e3a\uff1a<\/li>\n<\/ul>\n<p>$$\\frac{(2l+1)\\pi}{n-m},l=0,1,...,n-m-1$$<\/p>\n<\/li>\n<\/ol>\n<blockquote>\n<p>\u5bf9\u4f8b\u9898\u6c42\u89e3\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u5750\u6807\u4e3a$(\\frac{0-1-2}{3},j0) = (-1,j0)$<br \/>\n    \u6e10\u8fd1\u7ebf\u6709\u4e09\u4e2a\u65b9\u5411\uff0c\u4e3a$\\frac{\\pi}{3},\\frac{3\\pi}{3},\\frac{5\\pi}{3}$\n<\/p><\/blockquote>\n<ol start=\"3\">\n<li>\u6c42\u89e3\u6839\u8f68\u8ff9\u4e0e\u5b9e\u8f74\u7684\u4ea4\u70b9\n<ul>\n<li>\u4ea4\u70b9\u901a\u8fc7\u65b9\u7a0b\u786e\u5b9a\uff1a<\/li>\n<\/ul>\n<p>$$\\frac{d}{ds}[\\frac{K^\\ast}{G(s)H(s)}]\\vert_{s=\\alpha} = 0$$<\/p>\n<ul>\n<li>\u53d6\u5176\u53f3\u4fa7\u5f00\u73af\u6781\u70b9\u4e0e\u5f00\u73af\u96f6\u70b9\u6570\u91cf\u548c\u4e3a\u5947\u6570\u7684\u503c<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<blockquote><p>\n  \u5bf9\u4f8b\u9898\u6c42\u89e3\uff0c\u5f97\u51fa$\\frac{K^\\ast}{G(s)H(s)}=s(s+1)(s+2)$<br \/>\n     \u66ff\u6362\u7b26\u53f7\u5e76\u6c42\u5bfc\u5f97$3\\alpha^2+6\\alpha+2=0$<br \/>\n     \u6c42\u89e3\u5f97$\\alpha_1=-0.423,\\alpha_2=-1.577$<br \/>\n    \u5df2\u77e5\u4e09\u4e2a\u5750\u6807\u5206\u522b\u4e3a$(0,j0),(-1,j0),(-2,j0)$<br \/>\n     \u90a3\u4e48\u5bf9\u4e8e\u7ed3\u679c$-0.423$\uff0c\u5176\u53f3\u65b9\u5b58\u5728\u4e00\u4e2a\u6781\u70b9\uff0c\u6240\u4ee5\u7559\u4e0b<br \/>\n     \u5bf9\u4e8e\u7ed3\u679c$-1.577$\uff0c\u53f3\u65b9\u5b58\u5728\u4e24\u4e2a\u6781\u70b9\uff0c\u820d\u53bb<br \/>\n    \u56e0\u6b64\u6700\u7ec8\u7ed3\u679c\u4e3a$(-0.423,j0)$\n<\/p><\/blockquote>\n<ol>\n<li>\u6c42\u89e3\u6839\u8f68\u8ff9\u4e0e\u865a\u8f74\u4ea4\u70b9\n<ul>\n<li>\u4ee4$s=j\\omega$\uff0c\u4ee3\u5165\u65b9\u7a0b\u5e76\u6c42\u89e3<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>$$<br \/>\n\\begin{cases}<br \/>\nRe[1+G(j\\omega)H(j\\omega)]=0&#92;\\<br \/>\nIm[1+G(j\\omega)H(j\\omega)]=0<br \/>\n\\end{cases}<br \/>\n$$<\/p>\n<blockquote><p>\n  \u4ee3\u5165\u4f8b\u9898\uff0c\u5f97<\/p>\n<p>  $$<br \/>\n  \\begin{cases}<br \/>\n  -3\\omega^2+K^\\ast=0&#92;\\<br \/>\n  -\\omega^3+2\\omega=0<br \/>\n  \\end{cases}<br \/>\n  $$<\/p>\n<p>  \u6c42\u89e3<\/p>\n<p>  $^\\varepsilon\\omega^\\varepsilon$\n<\/p><\/blockquote>\n<h3>\u7ed8\u52360\u00b0\u6839\u8f68\u8ff9\u7684\u57fa\u672c\u89c4\u5219<\/h3>\n<p>\u6b65\u9aa4\u57fa\u672c\u4e0e\u4e0a\u8ff0\u76f8\u540c\uff0c\u4f46\u662f\u6709\u90e8\u5206\u516c\u5f0f\u53d8\u52a8<\/p>\n<ul>\n<li>\u6e10\u8fd1\u7ebf\u5939\u89d2<\/li>\n<\/ul>\n<p>$$\\frac{2l\\pi}{n-m},l=0,1,...,n-m-1$$<\/p>\n<ul>\n<li>\u6c42\u89e3\u6839\u8f68\u8ff9\u4e0e\u5b9e\u8f74\u7684\u4ea4\u70b9\n<ul>\n<li>\u53d6\u5176\u53f3\u4fa7\u5f00\u73af\u6781\u70b9\u4e0e\u5f00\u73af\u96f6\u70b9\u6570\u91cf\u548c\u4e3a\u5076\u6570\u7684\u503c<\/li>\n<\/ul>\n<\/li>\n<li>\u6c42\u89e3\u6839\u8f68\u8ff9\u4e0e\u865a\u8f74\u4ea4\u70b9<\/p>\n<\/li>\n<\/ul>\n<p>$$<br \/>\n  \\begin{cases}<br \/>\n        Re[1-G(j\\omega)H(j\\omega)]=0&#92;\\<br \/>\n        Im[1-G(j\\omega)H(j\\omega)]=0<br \/>\n    \\end{cases}<br \/>\n$$<\/p>\n<h1>\u7ebf\u6027\u7cfb\u7edf\u7684\u9891\u57df\u5206\u6790<\/h1>\n<h2>Bode\u56fe<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u73af\u8282<\/th>\n<th>\u9891\u7387\u7279\u6027<\/th>\n<th>\u8f6c\u6298\u9891\u7387\/\u76f8\u9891\u7279\u6027<\/th>\n<th>\u659c\u7387<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u653e\u5927\u73af\u8282<\/td>\n<td>$G(j\\omega)=K$<\/td>\n<td>$L(\\omega)=20\\lg K$<\/td>\n<td>$0$<\/td>\n<\/tr>\n<tr>\n<td>\u79ef\u5206\u73af\u8282<\/td>\n<td>$G(j\\omega)=\\frac{1}{j\\omega}$<\/td>\n<td>$0$<\/td>\n<td>$-20dB$<\/td>\n<\/tr>\n<tr>\n<td>\u5fae\u5206\u73af\u8282<\/td>\n<td>$G(j\\omega)=j\\omega$<\/td>\n<td>$0$<\/td>\n<td>$20dB$<\/td>\n<\/tr>\n<tr>\n<td>\u60ef\u6027\u73af\u8282<\/td>\n<td>$G(j\\omega)=\\frac{1}{1+jT\\omega}$<\/td>\n<td>$\\frac{1}{T}$<\/td>\n<td>$-20dB$<\/td>\n<\/tr>\n<tr>\n<td>\u4e00\u9636\u5fae\u5206\u73af\u8282<\/td>\n<td>$G(j\\omega)=1+j\\tau\\omega$<\/td>\n<td>$\\frac{1}{\\tau}$<\/td>\n<td>$20dB$<\/td>\n<\/tr>\n<tr>\n<td>\u632f\u8361\u73af\u8282<\/td>\n<td>$G(j\\omega)=\\frac{1}{1-T^2\\omega^2+j2T\\zeta\\omega}$<\/td>\n<td>$\\frac{1}{T}$<\/td>\n<td>$-40dB$<\/td>\n<\/tr>\n<tr>\n<td>\u4e8c\u9636\u5fae\u5206\u73af\u8282<\/td>\n<td>$G(j\\omega)=1-\\tau^2\\omega^2+j2\\tau\\zeta\\omega$<\/td>\n<td>$\\frac{1}{\\tau}$<\/td>\n<td>$40dB$<\/td>\n<\/tr>\n<tr>\n<td>\u4e0d\u7a33\u5b9a\u60ef\u6027\u73af\u8282<\/td>\n<td>$G(j\\omega)=\\frac{-1}{-1+jT\\omega}$<\/td>\n<td>$\\frac{1}{T}$<\/td>\n<td>$-20dB$<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u5df2\u77e5\u5f00\u73af\u4f20\u9012\u51fd\u6570\u6c42\u89e3Bode\u56fe<\/h3>\n<p>\u4f8b\u5982<\/p>\n<blockquote><p>\n  $G(s)=\\frac{64(s+2)}{s(s+0.5)(s^2+3.2s+64)}$\n<\/p><\/blockquote>\n<ol>\n<li>\u5316\u7b80<\/li>\n<\/ol>\n<blockquote><p>\n  $G(s)=\\frac{4(\\frac{s}{2}+1)}{s(2s+1)(\\frac{s^2}{64}+\\frac{s}{20}+1)}$\n<\/p><\/blockquote>\n<ol start=\"2\">\n<li>\u8fa8\u8bc6\u51fa\u5178\u578b\u73af\u8282<\/li>\n<\/ol>\n<blockquote><p>\n  \u5bf9\u4e8e\u4f8b\u9898\uff0c\u53ef\u4ee5\u62c6\u5206\u6210<br \/>\n  $4$\uff0c\u653e\u5927\u73af\u8282\u4e3a4<br \/>\n  $\\frac{s}{2}+1$\uff0c\u4e00\u9636\u5fae\u5206\u73af\u8282\uff0c$\\omega=2rad\/s$\u540e$+20dB$<br \/>\n  $\\frac{1}{s}$\uff0c\u79ef\u5206\u73af\u8282\uff0c\u8fc7\u70b9$(1,20\\lg K)$\u4f5c\u659c\u7387$-20dB$\u7ebf<br \/>\n  $\\frac{1}{2s+1}$\uff0c\u4e00\u9636\u79ef\u5206\u73af\u8282\uff0c$\\omega=0.5rad\/s$\u540e$-20dB$<br \/>\n  $\\frac{1}{\\frac{s^2}{64}+\\frac{s}{20}+1}$\u632f\u8361\u73af\u8282\uff0c$\\omega=8rad\/s$\u540e$-40dB$\n<\/p><\/blockquote>\n<ol start=\"3\">\n<li>\u753b\u56fe<\/li>\n<\/ol>\n<h3>\u5df2\u77e5\uff08\u5e26\u6709\u4fee\u6b63\u7684\uff09Bode\u56fe\u6c42\u5f00\u73af\u4f20\u9012\u51fd\u6570<\/h3>\n<p>\u5bf9\u4e8e\u4e8c\u9636\u5fae\u5206\/\u632f\u8361\u73af\u8282\uff0c\u9700\u8981\u6c42\u89e3$\\zeta$<br \/>\n\u5728\u5176\u8f6c\u6298\u9891\u7387\u5904\u5b58\u5728\u4fee\u6b63\u8bef\u5dee\u6709\u516c\u5f0f$\\Delta=20\\lg\\frac{1}{2\\zeta}$<\/p>\n<h3>\u7a33\u6001\u8bef\u5dee\u548c\u76f8\u89d2\u88d5\u5ea6<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u9636\u7cfb\u7edf\u6b20\u963b\u5c3c\u54cd\u5e94\u8fc7\u7a0b\u5206\u6790 \u4e3b\u8981\u662f\u6c42\u56db\u4e2a\u53c2\u6570 \u4e0a\u5347\u65f6\u95f4$t_r = \\frac{\\pi &#8211; \\theta}{\\omega_n \\s &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[2],"tags":[],"class_list":["post-397","post","type-post","status-publish","format-standard","hentry","category-schoolwork"],"_links":{"self":[{"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/posts\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=397"}],"version-history":[{"count":16,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/posts\/397\/revisions"}],"predecessor-version":[{"id":414,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=\/wp\/v2\/posts\/397\/revisions\/414"}],"wp:attachment":[{"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yin.nnneri.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}