{"id":91,"date":"2024-10-12T08:34:01","date_gmt":"2024-10-12T00:34:01","guid":{"rendered":"https:\/\/www.rwr.ink\/?p=91"},"modified":"2025-11-14T17:32:43","modified_gmt":"2025-11-14T09:32:43","slug":"%e6%a8%a1%e7%b3%8apid%e6%8e%a7%e5%88%b6%e5%8a%a0%e7%83%ad%e5%99%a8%e7%b3%bb%e7%bb%9f%e4%bb%bf%e7%9c%9f","status":"publish","type":"post","link":"https:\/\/www.rwr.ink\/index.php\/2024\/10\/12\/%e6%a8%a1%e7%b3%8apid%e6%8e%a7%e5%88%b6%e5%8a%a0%e7%83%ad%e5%99%a8%e7%b3%bb%e7%bb%9f%e4%bb%bf%e7%9c%9f\/","title":{"rendered":"\u6a21\u7ccaPID\u63a7\u5236\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f"},"content":{"rendered":"<h1>\u6a21\u7ccaPID\u63a7\u5236\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f<\/h1>\n<h2>\u76ee\u5f55<\/h2>\n<ul>\n<li><a href=\"#\u6a21\u7ccapid\u63a7\u5236\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f\" target=\"_blank\"  rel=\"nofollow\" >\u6a21\u7ccaPID\u63a7\u5236\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f<\/a>\n<ul>\n<li><a href=\"#\u76ee\u5f55\" target=\"_blank\"  rel=\"nofollow\" >\u76ee\u5f55<\/a><\/li>\n<li><a href=\"#\u5f15\u8a00\" target=\"_blank\"  rel=\"nofollow\" >\u5f15\u8a00<\/a><\/li>\n<li><a href=\"#\u7cfb\u7edf\u6982\u8ff0\" target=\"_blank\"  rel=\"nofollow\" >\u7cfb\u7edf\u6982\u8ff0<\/a><\/li>\n<li><a href=\"#\u6570\u5b66\u6a21\u578b\" target=\"_blank\"  rel=\"nofollow\" >\u6570\u5b66\u6a21\u578b<\/a><\/li>\n<li><a href=\"#\u96b6\u5c5e\u5ea6\u51fd\u6570\" target=\"_blank\"  rel=\"nofollow\" >\u96b6\u5c5e\u5ea6\u51fd\u6570<\/a>\n<ul>\n<li><a href=\"#s\u5f62\u51fd\u6570\" target=\"_blank\"  rel=\"nofollow\" >S\u5f62\u51fd\u6570<\/a><\/li>\n<li><a href=\"#z\u5f62\u51fd\u6570\" target=\"_blank\"  rel=\"nofollow\" >Z\u5f62\u51fd\u6570<\/a><\/li>\n<li><a href=\"#\u4e09\u89d2\u5f62\u51fd\u6570\" target=\"_blank\"  rel=\"nofollow\" >\u4e09\u89d2\u5f62\u51fd\u6570<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#\u6a21\u7ccapid\u63a7\u5236\u5668\" target=\"_blank\"  rel=\"nofollow\" >\u6a21\u7ccaPID\u63a7\u5236\u5668<\/a>\n<ul>\n<li><a href=\"#\u6a21\u7cca\u5316\" target=\"_blank\"  rel=\"nofollow\" >\u6a21\u7cca\u5316<\/a><\/li>\n<li><a href=\"#\u89c4\u5219\u5e93\" target=\"_blank\"  rel=\"nofollow\" >\u89c4\u5219\u5e93<\/a><\/li>\n<li><a href=\"#\u89e3\u6a21\u7cca\" target=\"_blank\"  rel=\"nofollow\" >\u89e3\u6a21\u7cca<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#pid\u63a7\u5236\u5668\" target=\"_blank\"  rel=\"nofollow\" >PID\u63a7\u5236\u5668<\/a><\/li>\n<li><a href=\"#\u52a0\u70ed\u5668\u7cfb\u7edf\u52a8\u529b\u5b66\" target=\"_blank\"  rel=\"nofollow\" >\u52a0\u70ed\u5668\u7cfb\u7edf\u52a8\u529b\u5b66<\/a><\/li>\n<li><a href=\"#smith\u9884\u4f30\u5668\" target=\"_blank\"  rel=\"nofollow\" >Smith\u9884\u4f30\u5668<\/a><\/li>\n<li><a href=\"#\u4eff\u771f\u6d41\u7a0b\" target=\"_blank\"  rel=\"nofollow\" >\u4eff\u771f\u6d41\u7a0b<\/a><\/li>\n<li><a href=\"#\u6027\u80fd\u6307\u6807\" target=\"_blank\"  rel=\"nofollow\" >\u6027\u80fd\u6307\u6807<\/a><\/li>\n<li><a href=\"#\u7528\u6237\u754c\u9762\" target=\"_blank\"  rel=\"nofollow\" >\u7528\u6237\u754c\u9762<\/a><\/li>\n<li><a href=\"#\u7ed3\u8bba\" target=\"_blank\"  rel=\"nofollow\" >\u7ed3\u8bba<\/a><\/li>\n<li>\n<h2><a href=\"#\u9644\u4ef6\" target=\"_blank\"  rel=\"nofollow\" >\u9644\u4ef6<\/a><\/h2>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\u5f15\u8a00<\/h2>\n<p>\u672c\u6587\u63d0\u4f9b\u4e86\u7531\u81ea\u9002\u5e94\u6a21\u7ccaPID\u63a7\u5236\u5668\u548cSmith\u9884\u4f30\u5668\u63a7\u5236\u7684\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f\u6a21\u578b\u7684\u5b8c\u6574\u7b97\u6cd5\u4eff\u771f\u3002\u8be5\u7cfb\u7edf\u65e8\u5728\u901a\u8fc7\u6839\u636e\u8bbe\u5b9a\u503c\u53d8\u5316\u8c03\u6574\u52a0\u70ed\u5668\u7684\u529f\u7387\u8f93\u51fa\uff0c\u6700\u5c0f\u5316\u8d85\u8c03\u91cf\u3001\u7a33\u6001\u8bef\u5dee\u548c\u7a33\u5b9a\u65f6\u95f4\u6765\u8c03\u8282\u52a0\u70ed\u5668\u7684\u6e29\u5ea6\u3002<\/p>\n<hr \/>\n<h2>\u7cfb\u7edf\u6982\u8ff0<\/h2>\n<p>\u8be5\u4eff\u771f\u5305\u542b\u51e0\u4e2a\u76f8\u4e92\u8fde\u63a5\u7684\u7ec4\u4ef6\uff1a<\/p>\n<ol>\n<li><strong>\u52a0\u70ed\u5668\u7cfb\u7edf<\/strong>: \u6a21\u62df\u52a0\u70ed\u5668\u7684\u70ed\u529b\u5b66\u7279\u6027\uff0c\u5305\u62ec\u70ed\u8f93\u5165\u3001\u73af\u5883\u70ed\u635f\u5931\u548c\u529f\u7387\u9650\u5236\u3002<\/li>\n<li><strong>PID\u63a7\u5236\u5668<\/strong>: \u4f20\u7edf\u7684\u6bd4\u4f8b-\u79ef\u5206-\u5fae\u5206\u63a7\u5236\u5668\uff0c\u6839\u636e\u8bef\u5dee\u53cd\u9988\u8ba1\u7b97\u63a7\u5236\u4fe1\u53f7\u3002<\/li>\n<li><strong>\u6a21\u7ccaPID\u63a7\u5236\u5668<\/strong>: \u901a\u8fc7\u4f7f\u7528\u6a21\u7cca\u903b\u8f91\u6839\u636e\u5f53\u524d\u8bef\u5dee\u548c\u8bef\u5dee\u7387\u81ea\u9002\u5e94\u8c03\u6574PID\u53c2\u6570\uff08Kp\u3001Ki\u3001Kd\uff09\u6765\u589e\u5f3aPID\u63a7\u5236\u5668\u3002<\/li>\n<li><strong>Smith\u9884\u4f30\u5668<\/strong>: \u8865\u507f\u7cfb\u7edf\u5ef6\u8fdf\uff0c\u5e76\u5728\u5b58\u5728\u6b7b\u533a\u65f6\u95f4\u7684\u60c5\u51b5\u4e0b\u63d0\u9ad8\u63a7\u5236\u5668\u7684\u6027\u80fd\u3002<\/li>\n<li><strong>\u4eff\u771f\u6846\u67b6<\/strong>: \u534f\u8c03\u8fd9\u4e9b\u7ec4\u4ef6\u4e4b\u95f4\u7684\u4ea4\u4e92\uff0c\u5e94\u7528\u8bbe\u5b9a\u503c\u66f4\u6539\u5e76\u8bb0\u5f55\u7cfb\u7edf\u6027\u80fd\u6307\u6807\u3002<\/li>\n<li><strong>\u7528\u6237\u754c\u9762<\/strong>: \u53ef\u89c6\u5316\u7cfb\u7edf\u54cd\u5e94\u3001\u63a7\u5236\u4fe1\u53f7\u3001PID\u53c2\u6570\u548c\u6027\u80fd\u6307\u6807\uff0c\u5e76\u5141\u8bb8\u901a\u8fc7\u4ea4\u4e92\u5f0f\u6ed1\u5757\u8fdb\u884c\u5b9e\u65f6\u8c03\u6574\u3002<\/li>\n<\/ol>\n<hr \/>\n<h2>\u6570\u5b66\u6a21\u578b<\/h2>\n<h3>\u96b6\u5c5e\u5ea6\u51fd\u6570<\/h3>\n<p>\u96b6\u5c5e\u5ea6\u51fd\u6570\uff08MFs\uff09\u662f\u6a21\u7cca\u903b\u8f91\u7684\u57fa\u7840\uff0c\u5b9a\u4e49\u4e86\u6bcf\u4e2a\u8f93\u5165\u5728\u6bcf\u4e2a\u6a21\u7cca\u96c6\u4e2d\u7684\u96b6\u5c5e\u7a0b\u5ea6\u3002\u8be5\u4eff\u771f\u4f7f\u7528\u4e09\u79cd\u7c7b\u578b\u7684\u96b6\u5c5e\u5ea6\u51fd\u6570\uff1aS\u5f62\u3001Z\u5f62\u548c\u4e09\u89d2\u5f62\u3002<\/p>\n<h4>S\u5f62\u51fd\u6570<\/h4>\n<p><strong>\u5b9a\u4e49:<\/strong><\/p>\n<p>S\u5f62\u51fd\u6570\u7528\u4e8e\u6a21\u62df\u4ece\u4f4e\u96b6\u5c5e\u5ea6\u503c\u9010\u6e10\u589e\u52a0\u5230\u9ad8\u96b6\u5c5e\u5ea6\u503c\u7684\u6a21\u7cca\u96c6\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u8f93\u5165 [latex]x[\/latex]\uff0c\u53c2\u6570 [latex]a[\/latex] \u548c [latex]b[\/latex] \u5b9a\u4e49\u4e86\u8fc7\u6e21\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\text{s_shaped}(x, a, b) =\\begin{cases} 0 &amp; \\text{if } x \\leq a \\<br \/>\n2 \\left( \\frac{x - a}{b - a} \\right)^2 &amp; \\text{if } a &lt; x \\leq \\frac{a + b}{2} \\1 - 2 \\left( \\frac{b - x}{b - a} \\right)^2 &amp; \\text{if } \\frac{a + b}{2} &lt; x &lt; b \\1 &amp; \\text{if } x \\geq b<br \/>\n\\end{cases}<br \/>\n[\/latex]<\/p>\n<h4>Z\u5f62\u51fd\u6570<\/h4>\n<p><strong>\u5b9a\u4e49:<\/strong><\/p>\n<p>Z\u5f62\u51fd\u6570\u6a21\u62df\u4ece\u9ad8\u96b6\u5c5e\u5ea6\u503c\u5e73\u6ed1\u9012\u51cf\u5230\u4f4e\u96b6\u5c5e\u5ea6\u503c\u7684\u6a21\u7cca\u96c6\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u8f93\u5165 [latex]x[\/latex]\uff0c\u53c2\u6570 [latex]a[\/latex] \u548c [latex]b[\/latex] \u5b9a\u4e49\u4e86\u8fc7\u6e21\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\text{z_shaped}(x, a, b) =<br \/>\n\\begin{cases}<br \/>\n1 &amp; \\text{if } x \\leq a \\<br \/>\n1 - 2 \\left( \\frac{x - a}{b - a} \\right)^2 &amp; \\text{if } a &lt; x \\leq \\frac{a + b}{2} \\<br \/>\n2 \\left( \\frac{b - x}{b - a} \\right)^2 &amp; \\text{if } \\frac{a + b}{2} &lt; x &lt; b \\<br \/>\n0 &amp; \\text{if } x \\geq b<br \/>\n\\end{cases}<br \/>\n[\/latex]<\/p>\n<h4>\u4e09\u89d2\u5f62\u51fd\u6570<\/h4>\n<p><strong>\u5b9a\u4e49:<\/strong><\/p>\n<p>\u4e09\u89d2\u5f62\u51fd\u6570\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u3001\u5bf9\u79f0\u7684\u6a21\u7cca\u96c6\uff0c\u5728\u4e2d\u5fc3\u70b9\u8fbe\u5230\u5cf0\u503c\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u8f93\u5165 [latex]x[\/latex]\uff0c\u53c2\u6570 [latex]a[\/latex], [latex]b[\/latex], \u548c [latex]c[\/latex] \u5b9a\u4e49\u4e86\u4e09\u89d2\u5f62\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\text{tri}(x, a, b, c) =<br \/>\n\\begin{cases}<br \/>\n0 &amp; \\text{if } x \\leq a \\text{ or } x \\geq c \\<br \/>\n\\frac{x - a}{b - a} &amp; \\text{if } a &lt; x \\leq b \\<br \/>\n\\frac{c - x}{c - b} &amp; \\text{if } b &lt; x &lt; c \\<br \/>\n0 &amp; \\text{otherwise}<br \/>\n\\end{cases}<br \/>\n[\/latex]<\/p>\n<h3>\u6a21\u7ccaPID\u63a7\u5236\u5668<\/h3>\n<p>\u6a21\u7ccaPID\u63a7\u5236\u5668\u4f7f\u7528\u6a21\u7cca\u903b\u8f91\u6839\u636e\u5f53\u524d\u8bef\u5dee ([latex]E[\/latex]) \u548c\u8bef\u5dee\u5bfc\u6570 ([latex]dE[\/latex]) \u81ea\u9002\u5e94\u5730\u8c03\u6574PID\u53c2\u6570\u3002<\/p>\n<h4>\u6a21\u7cca\u5316<\/h4>\n<p><strong>\u8fc7\u7a0b:<\/strong><\/p>\n<ol>\n<li>\n<p><strong>\u8f93\u5165\u53d8\u91cf<\/strong>:<\/p>\n<ul>\n<li><strong>\u8bef\u5dee ([latex]E[\/latex])<\/strong>: \u8bbe\u5b9a\u503c\u4e0e\u8fc7\u7a0b\u53d8\u91cf\u4e4b\u95f4\u7684\u504f\u5dee\u3002<\/li>\n<li><strong>\u8bef\u5dee\u5bfc\u6570 ([latex]dE[\/latex])<\/strong>: \u8bef\u5dee\u7684\u53d8\u5316\u7387\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u6a21\u7cca\u5316<\/strong>:<\/p>\n<ul>\n<li>\u6bcf\u4e2a\u8f93\u5165\u53d8\u91cf\u90fd\u88ab\u5206\u914d\u5230\u4e03\u4e2a\u6a21\u7cca\u96c6\u7684\u96b6\u5c5e\u5ea6\uff1aNB\uff08\u8d1f\u5927\uff09\u3001NM\uff08\u8d1f\u4e2d\uff09\u3001NS\uff08\u8d1f\u5c0f\uff09\u3001ZE\uff08\u96f6\uff09\u3001PS\uff08\u6b63\u5c0f\uff09\u3001PM\uff08\u6b63\u4e2d\uff09\u3001PB\uff08\u6b63\u5927\uff09\u3002<\/li>\n<li>\u4f7f\u7528\u4e0a\u9762\u5b9a\u4e49\u7684\u96b6\u5c5e\u5ea6\u51fd\u6570\u8ba1\u7b97\u96b6\u5c5e\u5ea6\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p><strong>\u6570\u5b66\u8868\u793a:<\/strong><\/p>\n<p>[latex]\\displaystyle<br \/>\n\\mu<em>E(\\text{Label}) = \\text{MembershipFunction}(E, \\text{parameters})<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\mu<\/em>{dE}(\\text{Label}) = \\text{MembershipFunction}(dE, \\text{parameters})<br \/>\n[\/latex]<\/p>\n<h4>\u89c4\u5219\u5e93<\/h4>\n<p><strong>\u7ed3\u6784:<\/strong><\/p>\n<p>\u4e00\u4e2a 7x7 \u89c4\u5219\u77e9\u9635\u5b9a\u4e49\u4e86 [latex]E[\/latex] \u548c [latex]dE[\/latex] \u7684\u7ec4\u5408\u5982\u4f55\u6620\u5c04\u5230 PID \u53c2\u6570\u7684\u8c03\u6574 ([latex]\\Delta K_p[\/latex], [latex]\\Delta K_i[\/latex], [latex]\\Delta K_d[\/latex])\u3002<\/p>\n<p><strong>\u89c4\u5219\u793a\u4f8b:<\/strong><\/p>\n<p>\u5982\u679c [latex]E[\/latex] \u4e3a NB \u4e14 [latex]dE[\/latex] \u4e3a PB\uff0c\u5219\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\Delta K_p &amp;= \\text{output_map_Kp}['PB'] \\<br \/>\n&amp;= 0.5<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\Delta K_i &amp;= \\text{output_map_Ki}['ZE'] \\<br \/>\n&amp;= 0.0<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\Delta K_d &amp;= \\text{output_map_Kd}['NS'] \\<br \/>\n&amp;= -0.05<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n<strong>\u89c4\u5219\u5e94\u7528:<\/strong><\/p>\n<p>\u5bf9\u4e8e [latex]E[\/latex] \u548c [latex]dE[\/latex] \u7684\u6bcf\u4e2a\u7ec4\u5408\uff1a<\/p>\n<ol>\n<li>\u786e\u5b9a\u96b6\u5c5e\u5ea6 [latex]\\mu<em>E[\\text{Label}][\/latex] \u548c [latex]\\mu<\/em>{dE}[\\text{Label}][\/latex]\u3002<\/li>\n<li>\u5e94\u7528\u6700\u5c0f\u8fd0\u7b97\u7b26\u8ba1\u7b97\u89e6\u53d1\u5f3a\u5ea6<\/li>\n<\/ol>\n<p>[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\alpha &amp;= \\min\\Bigl(\\mu_E[\\text{Label}<em>E], \\<br \/>\n&amp;\\quad \\mu<\/em>{dE}[\\text{Label}_{dE}]\\Bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<\/p>\n<ol start=\"3\">\n<li>\u5c06\u5bf9 [latex]\\Delta K_p[\/latex], [latex]\\Delta K_i[\/latex], \u548c [latex]\\Delta K_d[\/latex] \u7684\u8d21\u732e\u52a0\u6743 [latex]\\alpha[\/latex] \u5e76\u805a\u5408\u3002<\/li>\n<\/ol>\n<h4>\u89e3\u6a21\u7cca<\/h4>\n<p><strong>\u65b9\u6cd5: \u52a0\u6743\u5e73\u5747<\/strong><\/p>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a PID \u53c2\u6570\u8c03\u6574\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\Delta K_p = \\frac{\\sum (\\Delta K_p^{(i)} \\cdot \\alpha_i)}{\\sum \\alpha_i}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\Delta K_i = \\frac{\\sum (\\Delta K_i^{(i)} \\cdot \\alpha_i)}{\\sum \\alpha_i}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\Delta K_d = \\frac{\\sum (\\Delta K_d^{(i)} \\cdot \\alpha_i)}{\\sum \\alpha_i}<br \/>\n[\/latex]<br \/>\n\u5982\u679c\u5206\u6bcd\u4e3a\u96f6\uff08\u6ca1\u6709\u89e6\u53d1\u89c4\u5219\uff09\uff0c\u5219\u8c03\u6574\u9ed8\u8ba4\u4e3a\u96f6\u3002<\/p>\n<h3>PID\u63a7\u5236\u5668<\/h3>\n<p>\u4f20\u7edf\u7684PID\u63a7\u5236\u5668\u6839\u636e\u8bef\u5dee\u53cd\u9988\u8ba1\u7b97\u63a7\u5236\u4fe1\u53f7\u3002<\/p>\n<p><strong>\u63a7\u5236\u5f8b:<\/strong><\/p>\n<p>[latex]\\displaystyle<br \/>\nu(t) = K_p \\cdot e(t) + K<em>i \\cdot \\int<\/em>{0}^{t} e(\\tau) d\\tau + K_d \\cdot \\frac{de(t)}{dt}<br \/>\n[\/latex]<br \/>\n<strong>\u79bb\u6563\u5b9e\u73b0:<\/strong><\/p>\n<p>\u7ed9\u5b9a\u91c7\u6837\u65f6\u95f4\u4e3a [latex]\\Delta t[\/latex] \u7684\u79bb\u6563\u65f6\u95f4\u6b65\u957f\uff1a<\/p>\n<p>[latex]\\displaystyle<br \/>\n\\text{\u79ef\u5206\u9879} += e(t) \\cdot \\Delta t<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\text{\u5fae\u5206\u9879} = \\frac{e(t) - e(t-1)}{\\Delta t}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\nu(t) = K_p \\cdot e(t) + K_i \\cdot \\text{\u79ef\u5206\u9879} + K_d \\cdot \\text{\u5fae\u5206\u9879}<br \/>\n[\/latex]<br \/>\n<strong>\u53c2\u6570\u7ea6\u675f:<\/strong><\/p>\n<p>\u6bcf\u4e2a PID \u53c2\u6570\u90fd\u88ab\u9650\u5236\u5728\u6307\u5b9a\u7684\u6700\u5c0f\u548c\u6700\u5927\u8fb9\u754c\u5185\uff0c\u4ee5\u786e\u4fdd\u7a33\u5b9a\u6027\u3002<\/p>\n<p>[latex]\\displaystyle<br \/>\nK<em>p \\in [Kp<\/em>{\\text{min}}, Kp_{\\text{max}}]<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\nK<em>i \\in [Ki<\/em>{\\text{min}}, Ki_{\\text{max}}]<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\nK<em>d \\in [Kd<\/em>{\\text{min}}, Kd_{\\text{max}}]<br \/>\n[\/latex]<\/p>\n<h3>\u52a0\u70ed\u5668\u7cfb\u7edf\u52a8\u529b\u5b66<\/h3>\n<p>\u6a21\u62df\u52a0\u70ed\u5668\u7684\u70ed\u884c\u4e3a\uff0c\u8003\u8651\u70ed\u8f93\u5165\u3001\u73af\u5883\u635f\u5931\u548c\u7cfb\u7edf\u7ea6\u675f\u3002<\/p>\n<p><strong>\u53c2\u6570:<\/strong><\/p>\n<ul>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<\/ul>\n<p><strong>\u72b6\u6001\u53d8\u91cf:<\/strong><\/p>\n<ul>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>[latex]\\text{delay_buffer}[\/latex]: FIFO \u7f13\u51b2\u533a\uff0c\u7528\u4e8e\u6a21\u62df\u6b7b\u533a\u65f6\u95f4\u3002<\/li>\n<\/ul>\n<p><strong>\u52a8\u6001\u65b9\u7a0b (\u6b27\u62c9\u79bb\u6563\u5316):<\/strong><\/p>\n<p>[latex]\\displaystyle<br \/>\n\\frac{dy}{dt} = \\frac{K \\cdot u_{\\text{delayed}}(t) - y(t)}{\\tau} - h \\cdot (y(t) - T<em>a)<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\ny(t+1) = y(t) + \\left( \\frac{K \\cdot u<\/em>{\\text{delayed}}(t) - y(t)}{\\tau} - h \\cdot (y(t) - T_a) \\right) \\cdot T_s<br \/>\n[\/latex]<br \/>\n<strong>\u63a7\u5236\u4fe1\u53f7\u5904\u7406:<\/strong><\/p>\n<ol>\n<li><strong>\u9650\u5e45<\/strong>: \u786e\u4fdd [latex]u(t)[\/latex] \u4f4d\u4e8e [latex][P<em>{\\text{min}}, P<\/em>{\\text{max}}][\/latex] \u5185\u3002<\/li>\n<li><strong>\u901f\u7387\u9650\u5236<\/strong>: \u9650\u5236\u529f\u7387\u53d8\u5316\uff1a<\/li>\n<\/ol>\n<p>[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nu(t) = \\text{clip}\\Bigl(&amp;u(t), \\<br \/>\n&amp;u(t-1) - \\Delta P<em>{\\text{max}}, \\<br \/>\n&amp;u(t-1) + \\Delta P<\/em>{\\text{max}}\\Bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<\/p>\n<ol start=\"3\">\n<li><strong>\u6b7b\u533a\u65f6\u95f4<\/strong>: \u5c06 [latex]u(t)[\/latex] \u63d2\u5165\u5ef6\u8fdf\u7f13\u51b2\u533a\u5e76\u68c0\u7d22 [latex]u_{\\text{delayed}}(t)[\/latex]\u3002<\/li>\n<\/ol>\n<h3>Smith\u9884\u4f30\u5668<\/h3>\n<p>Smith\u9884\u4f30\u5668\u901a\u8fc7\u4f7f\u7528\u65e0\u6b7b\u533a\u65f6\u95f4\u7684\u7cfb\u7edf\u6a21\u578b\u6765\u9884\u6d4b\u672a\u6765\u72b6\u6001\u5e76\u76f8\u5e94\u5730\u8c03\u6574\u63a7\u5236\u4fe1\u53f7\uff0c\u4ece\u800c\u9884\u6d4b\u7cfb\u7edf\u5ef6\u8fdf\u3002<\/p>\n<p><strong>\u53c2\u6570:<\/strong><\/p>\n<ul>\n<li>\u4e0e\u52a0\u70ed\u5668\u7cfb\u7edf\u5171\u4eab\u76f8\u540c\u7684\u53c2\u6570\uff0c\u9664\u4e86 [latex]T_d = 0[\/latex]\uff08\u65e0\u6b7b\u533a\u65f6\u95f4\uff09\u3002<\/li>\n<\/ul>\n<p><strong>\u9884\u6d4b\u65b9\u7a0b:<\/strong><\/p>\n<p>[latex]\\displaystyle<br \/>\n\\frac{dy<em>{\\text{model}}}{dt} = \\frac{K \\cdot u(t) - y<\/em>{\\text{model}}(t)}{\\tau} - h \\cdot (y_{\\text{model}}(t) - T<em>a)<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\ny<\/em>{\\text{model}}(t+1) = y<em>{\\text{model}}(t) + \\left( \\frac{K \\cdot u(t) - y<\/em>{\\text{model}}(t)}{\\tau} - h \\cdot (y_{\\text{model}}(t) - T_a) \\right) \\cdot T_s<br \/>\n[\/latex]<br \/>\n<strong>\u8865\u507f\u673a\u5236:<\/strong><\/p>\n<p>[latex]\\displaystyle<br \/>\nu<em>{\\text{compensated}}(t) = u<\/em>{\\text{PID}}(t) + (SV(t) - y<em>{\\text{model}}(t))<br \/>\n[\/latex]<br \/>\n\u5176\u4e2d [latex]SV(t)[\/latex] \u662f\u5f53\u524d\u8bbe\u5b9a\u503c\uff0c[latex]y<\/em>{\\text{model}}(t)[\/latex] \u662f\u9884\u6d4b\u6e29\u5ea6\u3002<\/p>\n<hr \/>\n<h2>\u4eff\u771f\u6d41\u7a0b<\/h2>\n<p>\u4eff\u771f\u7a0b\u5e8f\u534f\u8c03\u52a0\u70ed\u5668\u7cfb\u7edf\u3001\u6a21\u7ccaPID\u63a7\u5236\u5668\u548cSmith\u9884\u4f30\u5668\u5728\u79bb\u6563\u65f6\u95f4\u6b65\u957f\u4e0a\u7684\u4ea4\u4e92\u3002<\/p>\n<p><strong>\u6b65\u9aa4:<\/strong><\/p>\n<ol>\n<li>\n<p><strong>\u521d\u59cb\u5316<\/strong>:<\/p>\n<ul>\n<li>\u8bbe\u7f6e\u521d\u59cb PID \u53c2\u6570 ([latex]K<em>{p0}, K<\/em>{i0}, K_{d0}[\/latex])\u3002<\/li>\n<li>\u5b9a\u4e49\u8bbe\u5b9a\u503c\u66f2\u7ebf\uff0c\u4ee5\u56fa\u5b9a\u95f4\u9694\u66f4\u6539\u3002<\/li>\n<li>\u521d\u59cb\u5316\u52a0\u70ed\u5668\u7cfb\u7edf\u3001Smith \u9884\u4f30\u5668\u3001\u6a21\u7cca PID \u63a7\u5236\u5668\u548c PID \u63a7\u5236\u5668\u3002<\/li>\n<li>\u521d\u59cb\u5316\u6027\u80fd\u6307\u6807\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u65f6\u95f4\u6b65\u8fdb\u5faa\u73af<\/strong> ([latex]t = 0[\/latex] \u5230 [latex]t = \\text{TIME_STEPS} - 1[\/latex]):<\/p>\n<ul>\n<li><strong>\u8bbe\u5b9a\u503c\u5206\u914d<\/strong>: \u5206\u914d\u5f53\u524d\u8bbe\u5b9a\u503c [latex]SV(t)[\/latex]\u3002<\/li>\n<li><strong>\u8fc7\u7a0b\u53d8\u91cf (PV)<\/strong>: \u68c0\u7d22\u5f53\u524d\u6e29\u5ea6 [latex]y(t)[\/latex]\u3002<\/li>\n<li><strong>\u8bef\u5dee\u8ba1\u7b97<\/strong>:<br \/>\n[latex]\\displaystyle<br \/>\ne(t) = SV(t) - PV(t)<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\ndE(t) = e(t) - e(t-1) \\quad \\text{(\u5982\u679c } t &gt; 0 \\text{)}<br \/>\n[\/latex]<\/li>\n<li><strong>\u6027\u80fd\u6307\u6807\u66f4\u65b0<\/strong>: \u5728\u8bbe\u5b9a\u503c\u66f4\u6539\u95f4\u9694\uff0c\u8ba1\u7b97\u8d85\u8c03\u91cf\u3001\u7a33\u6001\u8bef\u5dee\u548c\u7a33\u5b9a\u65f6\u95f4\u3002<\/li>\n<li><strong>\u6a21\u7cca\u5316<\/strong>: \u4f7f\u7528\u96b6\u5c5e\u5ea6\u51fd\u6570\u8ba1\u7b97 [latex]\\mu<em>E[\/latex] \u548c [latex]\\mu<\/em>{dE}[\/latex]\u3002<\/li>\n<li><strong>\u63a8\u7406<\/strong>: \u5e94\u7528\u6a21\u7cca\u89c4\u5219\u786e\u5b9a [latex]\\Delta K_p, \\Delta K_i, \\Delta K_d[\/latex]\u3002<\/li>\n<li><strong>\u81ea\u9002\u5e94 PID \u8c03\u6574<\/strong>: \u66f4\u65b0 PID \u53c2\u6570\uff1a<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nK_p(t) &amp;= \\text{clip}\\bigl(K_p(t-1) + \\Delta K<em>p, \\<br \/>\n&amp;\\quad Kp<\/em>{\\text{min}}, Kp_{\\text{max}}\\bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nK_i(t) &amp;= \\text{clip}\\bigl(K_i(t-1) + \\Delta K<em>i, \\<br \/>\n&amp;\\quad Ki<\/em>{\\text{min}}, Ki_{\\text{max}}\\bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nK_d(t) &amp;= \\text{clip}\\bigl(K_d(t-1) + \\Delta K<em>d, \\<br \/>\n&amp;\\quad Kd<\/em>{\\text{min}}, Kd_{\\text{max}}\\bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<\/li>\n<li><strong>PID \u63a7\u5236\u8f93\u51fa<\/strong>:<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nu_{\\text{PID}}(t) &amp;= K_p(t) \\cdot e(t) \\<br \/>\n&amp;\\quad + K_i(t) \\cdot \\text{Integral}_e \\<br \/>\n&amp;\\quad + K_d(t) \\cdot dE(t)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<\/li>\n<li><strong>Smith \u9884\u4f30\u5668<\/strong>: \u9884\u6d4b\u65e0\u5ef6\u8fdf\u7684 PV [latex]\\hat{y}(t)[\/latex]\u3002<\/li>\n<li><strong>\u63a7\u5236\u8865\u507f<\/strong>:<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\nu<em>{\\text{compensated}}(t) &amp;= u<\/em>{\\text{PID}}(t) \\<br \/>\n&amp;\\quad + \\bigl(SV(t) - \\hat{y}(t)\\bigr)<br \/>\n\\end{aligned}<br \/>\n[\/latex]<\/li>\n<li><strong>\u52a0\u70ed\u5668\u66f4\u65b0<\/strong>: \u5c06 [latex]u_{\\text{compensated}}(t)[\/latex] \u5e94\u7528\u4e8e\u52a0\u70ed\u5668\u7cfb\u7edf\u4ee5\u83b7\u5f97 [latex]y(t+1)[\/latex] \u548c [latex]u(t+1)[\/latex]\u3002<\/li>\n<li><strong>\u6570\u636e\u8bb0\u5f55<\/strong>: \u5b58\u50a8 PV\u3001SV\u3001\u63a7\u5236\u8f93\u51fa\u3001PID \u53c2\u6570\u548c\u6027\u80fd\u6307\u6807\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u6700\u7ec8\u6027\u80fd\u6307\u6807<\/strong>: \u5faa\u73af\u7ed3\u675f\u540e\uff0c\u8ba1\u7b97\u6700\u540e\u4e00\u4e2a\u8bbe\u5b9a\u503c\u5468\u671f\u7684\u6307\u6807\u3002<\/p>\n<\/li>\n<\/ol>\n<hr \/>\n<h2>\u6027\u80fd\u6307\u6807<\/h2>\n<p>\u4e3a\u4e86\u8bc4\u4f30\u63a7\u5236\u5668\u7684\u6709\u6548\u6027\uff0c\u4eff\u771f\u8ddf\u8e2a\u6bcf\u6b21\u8bbe\u5b9a\u503c\u66f4\u6539\u7684\u4ee5\u4e0b\u6307\u6807\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u8d85\u8c03\u91cf (%)<\/strong>:<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\text{\u8d85\u8c03\u91cf} &amp;= \\left( \\frac{\\max(PV(t)) - SV}{SV} \\right) \\<br \/>\n&amp;\\times 100<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n\u6d4b\u91cf PV \u8d85\u8fc7\u8bbe\u5b9a\u503c\u7684\u7a0b\u5ea6\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7a33\u6001\u8bef\u5dee<\/strong>:<br \/>\n[latex]\\displaystyle<br \/>\n\\begin{aligned}<br \/>\n\\text{\u7a33\u6001\u8bef\u5dee} &amp;= \\frac{1}{N} \\sum_{t=T-N}^{T} (SV(t) - PV(t))<br \/>\n\\end{aligned}<br \/>\n[\/latex]<br \/>\n\u54cd\u5e94\u6700\u540e [latex]N[\/latex] \u6b65\u7684\u5e73\u5747\u8bef\u5dee\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7a33\u5b9a\u65f6\u95f4 (\u6b65\u957f)<\/strong>:<br \/>\nPV \u4fdd\u6301\u5728\u8bbe\u5b9a\u503c\u7684 [latex]\\pm2\\%[\/latex] \u4ee5\u5185\u4e14\u4e4b\u540e\u4e0d\u518d\u8d85\u51fa\u6b64\u8303\u56f4\u6240\u9700\u7684\u6b65\u6570\u3002<\/p>\n<\/li>\n<\/ol>\n<hr \/>\n<h2>\u7528\u6237\u754c\u9762<\/h2>\n<p>\u4ea4\u4e92\u5f0f\u56fe\u5f62\u754c\u9762\uff0c\u5177\u6709\u4ee5\u4e0b\u529f\u80fd\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u56fe\u8868<\/strong>:<\/p>\n<ul>\n<li><strong>\u7cfb\u7edf\u54cd\u5e94<\/strong>: \u663e\u793a PV \u548c SV \u968f\u65f6\u95f4\u7684\u53d8\u5316\u3002<\/li>\n<li><strong>\u63a7\u5236\u4fe1\u53f7<\/strong>: \u663e\u793a\u63a7\u5236\u8f93\u51fa [latex]u(t)[\/latex]\u3002<\/li>\n<li><strong>\u52a0\u70ed\u5668\u529f\u7387<\/strong>: \u53ef\u89c6\u5316\u5e94\u7528\u4e8e\u52a0\u70ed\u5668\u7684\u5b9e\u9645\u529f\u7387\u3002<\/li>\n<li><strong>\u81ea\u9002\u5e94 PID \u53c2\u6570<\/strong>: \u8ddf\u8e2a [latex]K_p, K_i, K_d[\/latex] \u968f\u65f6\u95f4\u7684\u53d8\u5316\u3002<\/li>\n<li><strong>\u6027\u80fd\u6307\u6807<\/strong>: \u7ed8\u5236\u6bcf\u6b21\u8bbe\u5b9a\u503c\u66f4\u6539\u7684\u8d85\u8c03\u91cf\u3001\u7a33\u6001\u8bef\u5dee\u548c\u7a33\u5b9a\u65f6\u95f4\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u6ed1\u5757<\/strong>:<\/p>\n<ul>\n<li><strong>\u521d\u59cb PID \u53c2\u6570<\/strong>:\n<ul>\n<li><strong>Kp0<\/strong>: \u521d\u59cb\u6bd4\u4f8b\u589e\u76ca (0 \u5230 50)\u3002<\/li>\n<li><strong>Ki0<\/strong>: \u521d\u59cb\u79ef\u5206\u589e\u76ca (0 \u5230 10)\u3002<\/li>\n<li><strong>Kd0<\/strong>: \u521d\u59cb\u5fae\u5206\u589e\u76ca (0 \u5230 10)\u3002<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u6700\u5927\u529f\u7387<\/strong>: \u8c03\u6574\u6700\u5927\u52a0\u70ed\u529f\u7387 (50 \u5230 12,000)\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u4ea4\u4e92\u6027<\/strong>:<\/p>\n<ul>\n<li>\u8c03\u6574\u6ed1\u5757\u4f1a\u89e6\u53d1\u4eff\u771f\u7a0b\u5e8f\u4f7f\u7528\u66f4\u65b0\u7684\u53c2\u6570\u91cd\u65b0\u8fd0\u884c\u3002<\/li>\n<li>\u56fe\u8868\u52a8\u6001\u66f4\u65b0\u4ee5\u53cd\u6620\u65b0\u7684\u4eff\u771f\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<hr \/>\n<h2>\u7ed3\u8bba<\/h2>\n<p>\u672c\u6587\u6982\u8ff0\u4e86\u4e0e Smith \u9884\u4f30\u5668\u96c6\u6210\u7684\u6a21\u7cca PID \u63a7\u5236\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f\u7684\u7b97\u6cd5\u7ed3\u6784\u548c\u6570\u5b66\u57fa\u7840\u3002\u8be5\u7cfb\u7edf\u5229\u7528\u6a21\u7cca\u903b\u8f91\u8fdb\u884c\u81ea\u9002\u5e94 PID \u53c2\u6570\u6574\u5b9a\uff0c\u5728\u5b58\u5728\u7cfb\u7edf\u5ef6\u8fdf\u548c\u8bbe\u5b9a\u503c\u53d8\u5316\u7684\u60c5\u51b5\u4e0b\u589e\u5f3a\u63a7\u5236\u6027\u80fd\u3002\u4ea4\u4e92\u5f0f\u4eff\u771f\u4fc3\u8fdb\u4e86\u63a7\u5236\u52a8\u529b\u5b66\u548c\u6027\u80fd\u6307\u6807\u7684\u5b9e\u65f6\u5b9e\u9a8c\u548c\u53ef\u89c6\u5316\u3002<\/p>\n<p>TODO\uff1a<\/p>\n<ul>\n<li><strong>\u5176\u4ed6\u6027\u80fd\u6307\u6807<\/strong>: \u4f8b\u5982\u7edd\u5bf9\u8bef\u5dee\u79ef\u5206 (IAE) \u6216\u5e73\u65b9\u8bef\u5dee\u79ef\u5206 (ISE)\u3002<\/li>\n<li><strong>\u9ad8\u7ea7\u96b6\u5c5e\u5ea6\u51fd\u6570<\/strong>: \u7ed3\u5408\u9ad8\u65af\u6216\u6837\u6761\u57fa\u96b6\u5c5e\u5ea6\u51fd\u6570\u4ee5\u5b9e\u73b0\u66f4\u5e73\u6ed1\u7684\u8fc7\u6e21\u3002<\/li>\n<li><strong>\u4f18\u5316\u7b97\u6cd5<\/strong>: \u4f7f\u7528\u4f18\u5316\u7b97\u6cd5\u6765\u5fae\u8c03\u6a21\u7cca\u89c4\u5219\u5e93\u6216 PID \u53c2\u6570\u8303\u56f4\u3002<\/li>\n<li><strong>\u6dfb\u52a0\u66f4\u591a\u73af\u5883\u53c2\u6570<\/strong>: \u4f8b\u5982\u771f\u7a7a\u503c\u3001\u6c29\u6c14\/\u6c1f\u5229\u6602\u7b49\u6c14\u4f53\u6d41\u91cf<\/li>\n<\/ul>\n<hr \/>\n<h2>\u9644\u4ef6<\/h2>\n<pre><code class=\"language-python\">import numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.widgets import Slider\nimport matplotlib.gridspec as gridspec\n\n# \u5b9a\u4e49\u4f1a\u5458\u51fd\u6570\ndef s_shaped(x, a, b):\n    if x &lt;= a:\n        return 0\n    elif a &lt; x &lt;= (a + b) \/ 2:\n        return 2 * ((x - a) \/ (b - a)) ** 2\n    elif (a + b) \/ 2 &lt; x &lt; b:\n        return 1 - 2 * ((b - x) \/ (b - a)) ** 2\n    else:\n        return 1\n\ndef z_shaped(x, a, b):\n    if x &lt;= a:\n        return 1\n    elif a &lt; x &lt;= (a + b) \/ 2:\n        return 1 - 2 * ((x - a) \/ (b - a)) ** 2\n    elif (a + b) \/ 2 &lt; x &lt; b:\n        return 2 * ((b - x) \/ (b - a)) ** 2\n    else:\n        return 0\n\ndef tri(x, a, b, c):\n    if x &lt;= a or x &gt;= c:\n        return 0\n    elif a &lt; x &lt;= b:\n        return (x - a) \/ (b - a)\n    elif b &lt; x &lt; c:\n        return (c - x) \/ (c - b)\n    else:\n        return 0\n\n# \u5b9a\u4e49\u6a21\u7cca\u63a7\u5236\u5668\nclass FuzzyPIDController:\n    def __init__(self, E_max=100, dE_max=50):\n        self.E_max = E_max\n        self.dE_max = dE_max\n        # \u5b9a\u4e49\u8f93\u51fa\u7684\u72ec\u7acb\u6620\u5c04\u6570\u503c\n        self.output_map_Kp = {\n            &#039;NB&#039;: -0.5,\n            &#039;NM&#039;: -0.25,\n            &#039;NS&#039;: -0.1,\n            &#039;ZE&#039;: 0.0,\n            &#039;PS&#039;: 0.1,\n            &#039;PM&#039;: 0.25,\n            &#039;PB&#039;: 0.5\n        }\n        self.output_map_Ki = {\n            &#039;NB&#039;: -0.3,\n            &#039;NM&#039;: -0.15,\n            &#039;NS&#039;: -0.05,\n            &#039;ZE&#039;: 0.0,\n            &#039;PS&#039;: 0.05,\n            &#039;PM&#039;: 0.15,\n            &#039;PB&#039;: 0.3\n        }\n        self.output_map_Kd = {\n            &#039;NB&#039;: -0.2,\n            &#039;NM&#039;: -0.1,\n            &#039;NS&#039;: -0.05,\n            &#039;ZE&#039;: 0.0,\n            &#039;PS&#039;: 0.05,\n            &#039;PM&#039;: 0.1,\n            &#039;PB&#039;: 0.2\n        }\n        # \u5b9a\u4e49\u89c4\u5219\u8868\n        self.rules = [\n            # NB row\n            [(&#039;PB&#039;, &#039;ZE&#039;, &#039;NS&#039;), (&#039;PM&#039;, &#039;PS&#039;, &#039;ZE&#039;), (&#039;PM&#039;, &#039;PS&#039;, &#039;PS&#039;),\n             (&#039;PM&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;PS&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;),\n             (&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;)],\n            # NM row\n            [(&#039;PM&#039;, &#039;PS&#039;, &#039;NS&#039;), (&#039;PM&#039;, &#039;PS&#039;, &#039;PS&#039;), (&#039;PM&#039;, &#039;PM&#039;, &#039;PS&#039;),\n             (&#039;PS&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;), (&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;),\n             (&#039;NS&#039;, &#039;ZE&#039;, &#039;PM&#039;)],\n            # NS row\n            [(&#039;PM&#039;, &#039;PS&#039;, &#039;PS&#039;), (&#039;PM&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;PS&#039;, &#039;PM&#039;, &#039;PS&#039;),\n             (&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;), (&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;), (&#039;NS&#039;, &#039;ZE&#039;, &#039;PM&#039;),\n             (&#039;NM&#039;, &#039;NS&#039;, &#039;PB&#039;)],\n            # ZE row\n            [(&#039;PM&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;PS&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;),\n             (&#039;ZE&#039;, &#039;ZE&#039;, &#039;ZE&#039;), (&#039;ZE&#039;, &#039;NS&#039;, &#039;PM&#039;), (&#039;NM&#039;, &#039;NS&#039;, &#039;PB&#039;),\n             (&#039;NM&#039;, &#039;NM&#039;, &#039;PB&#039;)],\n            # PS row\n            [(&#039;PS&#039;, &#039;PM&#039;, &#039;PS&#039;), (&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;), (&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;),\n             (&#039;NS&#039;, &#039;ZE&#039;, &#039;PM&#039;), (&#039;NM&#039;, &#039;NS&#039;, &#039;PB&#039;), (&#039;NM&#039;, &#039;NM&#039;, &#039;PB&#039;),\n             (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;)],\n            # PM row\n            [(&#039;ZE&#039;, &#039;PM&#039;, &#039;PM&#039;), (&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;), (&#039;NS&#039;, &#039;ZE&#039;, &#039;PM&#039;),\n             (&#039;NM&#039;, &#039;NS&#039;, &#039;PB&#039;), (&#039;NM&#039;, &#039;NM&#039;, &#039;PB&#039;), (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;),\n             (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;)],\n            # PB row\n            [(&#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;), (&#039;NS&#039;, &#039;ZE&#039;, &#039;PM&#039;), (&#039;NM&#039;, &#039;NS&#039;, &#039;PB&#039;),\n             (&#039;NM&#039;, &#039;NM&#039;, &#039;PB&#039;), (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;), (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;),\n             (&#039;NB&#039;, &#039;NB&#039;, &#039;PB&#039;)]\n        ]\n        self.E_labels = [&#039;NB&#039;, &#039;NM&#039;, &#039;NS&#039;, &#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;, &#039;PB&#039;]\n        self.dE_labels = [&#039;NB&#039;, &#039;NM&#039;, &#039;NS&#039;, &#039;ZE&#039;, &#039;PS&#039;, &#039;PM&#039;, &#039;PB&#039;]\n\n    def fuzzify(self, E, dE):\n        mu_E = {}\n        mu_dE = {}\n        # Fuzzify E\n        mu_E[&#039;NB&#039;] = z_shaped(E, -self.E_max, -self.E_max \/ 2)\n        mu_E[&#039;NM&#039;] = tri(E, -self.E_max, -self.E_max \/ 2, 0)\n        mu_E[&#039;NS&#039;] = tri(E, -self.E_max \/ 2, 0, self.E_max \/ 4)\n        mu_E[&#039;ZE&#039;] = tri(E, -self.E_max \/ 4, 0, self.E_max \/ 4)\n        mu_E[&#039;PS&#039;] = tri(E, 0, self.E_max \/ 4, self.E_max \/ 2)\n        mu_E[&#039;PM&#039;] = tri(E, self.E_max \/ 3, self.E_max \/ 2, 2 * self.E_max \/ 3)\n        mu_E[&#039;PB&#039;] = s_shaped(E, self.E_max \/ 2, self.E_max)\n        # Fuzzify dE\n        mu_dE[&#039;NB&#039;] = z_shaped(dE, -self.dE_max, -self.dE_max \/ 2)\n        mu_dE[&#039;NM&#039;] = tri(dE, -self.dE_max, -self.dE_max \/ 2, 0)\n        mu_dE[&#039;NS&#039;] = tri(dE, -self.dE_max \/ 2, 0, self.dE_max \/ 2)\n        mu_dE[&#039;ZE&#039;] = tri(dE, -self.dE_max \/ 4, 0, self.dE_max \/ 4)\n        mu_dE[&#039;PS&#039;] = tri(dE, 0, self.dE_max \/ 4, self.dE_max \/ 2)\n        mu_dE[&#039;PM&#039;] = tri(dE, self.dE_max \/ 3, self.dE_max \/ 2, 2 * self.dE_max \/ 3)\n        mu_dE[&#039;PB&#039;] = s_shaped(dE, self.dE_max \/ 2, self.dE_max)\n        return mu_E, mu_dE\n\n    def infer(self, mu_E, mu_dE):\n        # \u521d\u59cb\u5316\u8f93\u51fa\u4f1a\u5458\u5ea6\u5217\u8868\n        delta_Kp = []\n        delta_Ki = []\n        delta_Kd = []\n\n        # \u904d\u5386\u6240\u6709\u89c4\u5219\n        for i, E_label in enumerate(self.E_labels):\n            for j, dE_label in enumerate(self.dE_labels):\n                alpha = min(mu_E[E_label], mu_dE[dE_label])  # \u53d6\u6700\u5c0f\n                if alpha &gt; 0:\n                    rule = self.rules[i][j]\n                    delta_Kp.append((self.output_map_Kp[rule[0]], alpha))\n                    delta_Ki.append((self.output_map_Ki[rule[1]], alpha))\n                    delta_Kd.append((self.output_map_Kd[rule[2]], alpha))\n\n        # \u805a\u5408: \u5bf9\u6bcf\u4e2a\u8f93\u51fa\u53d8\u91cf\u53d6\u52a0\u6743\u5e73\u5747\n        def weighted_average(output):\n            numerator = sum([val * alpha for val, alpha in output])\n            denominator = sum([alpha for _, alpha in output])\n            if denominator == 0:\n                return 0\n            return numerator \/ denominator\n\n        delta_Kp_value = weighted_average(delta_Kp)\n        delta_Ki_value = weighted_average(delta_Ki)\n        delta_Kd_value = weighted_average(delta_Kd)\n\n        return delta_Kp_value, delta_Ki_value, delta_Kd_value\n\n# \u5b9a\u4e49PID\u63a7\u5236\u5668\nclass PIDController:\n    def __init__(self, Kp=2.0, Ki=0.5, Kd=0.1, \n                 Kp_min=0, Kp_max=10, \n                 Ki_min=0, Ki_max=10, \n                 Kd_min=0, Kd_max=10):\n        self.Kp = Kp\n        self.Ki = Ki\n        self.Kd = Kd\n        self.Kp_min = Kp_min\n        self.Kp_max = Kp_max\n        self.Ki_min = Ki_min\n        self.Ki_max = Ki_max\n        self.Kd_min = Kd_min\n        self.Kd_max = Kd_max\n        self.integral = 0\n        self.prev_error = 0\n\n    def update_parameters(self, delta_Kp, delta_Ki, delta_Kd):\n        self.Kp = np.clip(self.Kp + delta_Kp, self.Kp_min, self.Kp_max)\n        self.Ki = np.clip(self.Ki + delta_Ki, self.Ki_min, self.Ki_max)\n        self.Kd = np.clip(self.Kd + delta_Kd, self.Kd_min, self.Kd_max)\n\n    def compute(self, error, dt=1):\n        # \u79ef\u5206\n        self.integral += error * dt\n        # \u5fae\u5206\n        derivative = (error - self.prev_error) \/ dt\n        self.prev_error = error\n\n        return self.Kp * error + self.Ki * self.integral + self.Kd * derivative\n\n# \u5b9a\u4e49\u52a0\u70ed\u5668\u7cfb\u7edf\u6a21\u578b\uff0c\u5305\u542b\u73af\u5883\u70ed\u91cf\u6563\u5931\u3001\u52a0\u70ed\u529f\u7387\u9650\u5236\u548c\u52a0\u70ed\u529f\u7387\u53d8\u5316\u7387\u9650\u5236\nclass HeaterSystem:\n    def __init__(self, K=1.0, tau=10.0, Td=5, Ts=0.05, ambient_temperature=20.0, heat_loss_coefficient=0.1, \n                 max_power=100.0, min_power=0.0, power_rate_limit=10.0):\n        self.K = K\n        self.tau = tau\n        self.Td = Td  # \u6ede\u540e\u65f6\u95f4\uff08\u5ef6\u8fdf\u6b65\u6570\uff09\n        self.Ts = Ts    # \u91c7\u6837\u65f6\u95f4\n        self.ambient_temperature = ambient_temperature  # \u73af\u5883\u6e29\u5ea6\n        self.heat_loss_coefficient = heat_loss_coefficient  # \u70ed\u91cf\u6563\u5931\u7cfb\u6570\n        self.delay_buffer = [0] * Td  # \u6ede\u540e\u7f13\u51b2\u533a\n        self.y = ambient_temperature  # \u521d\u59cb\u6e29\u5ea6\n        self.max_power = max_power  # \u6700\u5927\u52a0\u70ed\u529f\u7387\n        self.min_power = min_power  # \u6700\u5c0f\u52a0\u70ed\u529f\u7387\n        self.power_rate_limit = power_rate_limit  # \u52a0\u70ed\u529f\u7387\u53d8\u5316\u7387\u9650\u5236\n        self.prev_delayed_u = 0.0  # \u8bb0\u5f55\u4e0a\u4e00\u4e2a\u5ef6\u8fdf\u7684\u52a0\u70ed\u529f\u7387\n\n    def update(self, u):\n        # \u9650\u5236\u63a7\u5236\u4fe1\u53f7\u5728\u52a0\u70ed\u529f\u7387\u8303\u56f4\u5185\n        u = np.clip(u, self.min_power, self.max_power)\n\n        # \u9650\u5236\u52a0\u70ed\u529f\u7387\u53d8\u5316\u7387\n        delta_u = u - self.prev_delayed_u\n        delta_u = np.clip(delta_u, -self.power_rate_limit, self.power_rate_limit)\n        u = self.prev_delayed_u + delta_u\n\n        # \u6dfb\u52a0\u63a7\u5236\u8f93\u5165\u5230\u5ef6\u8fdf\u7f13\u51b2\u533a\n        self.delay_buffer.append(u)\n        delayed_u = self.delay_buffer.pop(0)\n        self.prev_delayed_u = delayed_u  # \u66f4\u65b0\u4e0a\u4e00\u4e2a\u5ef6\u8fdf\u7684\u52a0\u70ed\u529f\u7387\n\n        # \u6b27\u62c9\u6cd5\u79bb\u6563\u5316\u4e00\u9636\u60ef\u6027\u73af\u8282\uff0c\u52a0\u4e0a\u73af\u5883\u70ed\u91cf\u6563\u5931\n        dy = (self.K * delayed_u - self.y) * self.Ts \/ self.tau\n        # \u73af\u5883\u70ed\u91cf\u6563\u5931\n        dy -= (self.y - self.ambient_temperature) * self.heat_loss_coefficient * self.Ts\n        self.y += dy\n\n        return self.y, delayed_u  # \u8fd4\u56de\u5ef6\u8fdf\u540e\u7684\u52a0\u70ed\u529f\u7387\n\n# \u5b9a\u4e49\u53f2\u5bc6\u65af\u9884\u6d4b\u5668\nclass SmithPredictor:\n    def __init__(self, model: HeaterSystem, Td=5):\n        self.model = model\n        self.Td = Td\n        self.model_delay_buffer = [0] * Td\n        self.model_output = self.model.ambient_temperature  # \u521d\u59cb\u9884\u6d4b\u8f93\u51fa\n\n    def predict(self, u):\n        # \u9650\u5236\u63a7\u5236\u4fe1\u53f7\u5728\u52a0\u70ed\u529f\u7387\u8303\u56f4\u5185\n        u = np.clip(u, self.model.min_power, self.model.max_power)\n\n        # \u9884\u6d4b\u6a21\u578b\u4e0d\u542b\u6ede\u540e\n        dy = (self.model.K * u - self.model_output) * self.model.Ts \/ self.model.tau\n        # \u73af\u5883\u70ed\u91cf\u6563\u5931\n        dy -= (self.model_output - self.model.ambient_temperature) * self.model.heat_loss_coefficient * self.model.Ts\n        self.model_output += dy\n        return self.model_output\n\n# \u5b9a\u4e49\u4eff\u771f\u51fd\u6570\ndef simulate(Kp0, Ki0, Kd0, E_max=100, dE_max=50, TIME_STEPS=2000, \n             SETPOINT_CHANGE_INTERVAL=500, max_power=12000.0, \n             min_power=0.0, power_rate_limit=100.0, heater_power=0):\n    # \u8bbe\u5b9a\u70b9\u914d\u7f6e\uff1a\u6bcfSETPOINT_CHANGE_INTERVAL\u6b65\u6539\u53d8\u4e00\u6b21\u8bbe\u5b9a\u70b9\n    SETPOINT_VALUES = [200, 400, 300, 600]\n    num_changes = TIME_STEPS \/\/ SETPOINT_CHANGE_INTERVAL\n    SETPOINT_PROFILE = np.concatenate([np.ones(SETPOINT_CHANGE_INTERVAL) * SETPOINT_VALUES[i % len(SETPOINT_VALUES)] for i in range(num_changes)])\n    if len(SETPOINT_PROFILE) &lt; TIME_STEPS:\n        SETPOINT_PROFILE = np.concatenate([SETPOINT_PROFILE, np.ones(TIME_STEPS - len(SETPOINT_PROFILE)) * SETPOINT_VALUES[-1]])\n\n    # \u521d\u59cb\u5316\u6a21\u5757\n    heater = HeaterSystem(K=1, tau=10.0, Td=1, Ts=0.1, ambient_temperature=20.0, \n                          heat_loss_coefficient=0.1, max_power=max_power, min_power=min_power, \n                          power_rate_limit=power_rate_limit)\n    smith_model = HeaterSystem(K=1, tau=10.0, Td=0, Ts=0.1, ambient_temperature=20.0, \n                               heat_loss_coefficient=0.1, max_power=max_power, min_power=min_power, \n                               power_rate_limit=power_rate_limit)  # \u6a21\u578b\u4e0d\u542b\u6ede\u540e\n    smith = SmithPredictor(model=smith_model, Td=1)\n    fuzzy_controller = FuzzyPIDController(E_max=E_max, dE_max=dE_max)\n    pid = PIDController(Kp=Kp0, Ki=Ki0, Kd=Kd0, \n                        Kp_min=0, Kp_max=50, \n                        Ki_min=0, Ki_max=10, \n                        Kd_min=0, Kd_max=10)\n\n    # \u521d\u59cb\u5316\u8bb0\u5f55\u53d8\u91cf\n    PV_history = []\n    SV_history = []\n    error_history = []\n    control_history = []\n    heater_power_history = []\n    Kp_history = []\n    Ki_history = []\n    Kd_history = []\n    overshoot_history = []\n    steady_state_error_history = []\n    settling_time_history = []\n\n    # \u521d\u59cb\u5316\u6027\u80fd\u6307\u6807\n    current_setpoint = SETPOINT_PROFILE[0]\n    response_start_index = 0\n    overshoot = 0\n    steady_state_error = 0\n    settling_time = 0\n    settling_time_threshold = 0.02  # 2%\n    within_settle = False\n\n    # \u4eff\u771f\u5faa\u73af\n    for t in range(TIME_STEPS):\n        SV = SETPOINT_PROFILE[t]\n        PV = heater.y\n        error = SV - PV\n        dE = error - (error_history[-1] if t &gt; 0 else 0)\n\n        # \u68c0\u6d4b\u8bbe\u5b9a\u70b9\u53d8\u5316\n        if t % SETPOINT_CHANGE_INTERVAL == 0 and t != 0:\n            # \u8ba1\u7b97\u5e76\u8bb0\u5f55\u6027\u80fd\u6307\u6807\n            # \u8d85\u8c03\u91cf\n            max_PV = max(PV_history[response_start_index:t]) if t &gt; response_start_index else PV\n            overshoot = ((max_PV - current_setpoint) \/ current_setpoint) * 100 if current_setpoint != 0 else 0\n            overshoot_history.append(overshoot)\n\n            # \u7a33\u6001\u8bef\u5dee (\u53d6\u6700\u540e50\u6b65\u7684\u5e73\u5747\u8bef\u5dee)\n            steady_state_error = np.mean(error_history[max(t-50, response_start_index):t]) if t &gt; response_start_index else error\n            steady_state_error_history.append(steady_state_error)\n\n            # \u8c03\u8282\u65f6\u95f4 (\u627e\u5230\u7b2c\u4e00\u6b21\u8fdb\u5165\u5e76\u4fdd\u6301\u5728\u00b12%\u8303\u56f4\u5185\u7684\u65f6\u95f4\u6b65)\n            target_min = current_setpoint * (1 - settling_time_threshold)\n            target_max = current_setpoint * (1 + settling_time_threshold)\n            settling_time = 0\n            for i in range(response_start_index, t):\n                if target_min &lt;= PV_history[i] &lt;= target_max:\n                    # Check if it stays within the range for the remaining steps\n                    if all(target_min &lt;= pv &lt;= target_max for pv in PV_history[i:t]):\n                        settling_time = i - response_start_index\n                        break\n            settling_time_history.append(settling_time)\n\n            # \u66f4\u65b0\u5f53\u524d\u8bbe\u5b9a\u70b9\u548c\u54cd\u5e94\u8d77\u59cb\u7d22\u5f15\n            current_setpoint = SV\n            response_start_index = t\n\n        # \u6a21\u7cca\u63a7\u5236\u5668\u8c03\u6574PID\u53c2\u6570\n        mu_E, mu_dE = fuzzy_controller.fuzzify(error, dE)\n        delta_Kp, delta_Ki, delta_Kd = fuzzy_controller.infer(mu_E, mu_dE)\n\n        if heater_power != 0:\n            delta_Kp *= (heater_power \/ max_power) # \u6839\u636e\u52a0\u70ed\u529f\u7387\u8c03\u6574PID\u53c2\u6570\n\n        pid.update_parameters(delta_Kp, delta_Ki, delta_Kd)\n\n        # PID\u8ba1\u7b97\u63a7\u5236\u8f93\u51fa\n        u_pid = pid.compute(error, dt=heater.Ts)\n\n        # \u53f2\u5bc6\u65af\u9884\u6d4b\u5668\u9884\u6d4bPV\n        predicted_PV = smith.predict(u_pid)\n\n        # \u63a7\u5236\u8f93\u51fa\u8865\u507f\n        u_compensated = u_pid + (SV - predicted_PV)\n\n        # \u66f4\u65b0\u52a0\u70ed\u5668\u7cfb\u7edf\uff0c\u5e76\u83b7\u53d6\u5ef6\u8fdf\u540e\u7684\u52a0\u70ed\u529f\u7387\n        y, heater_power = heater.update(u_compensated)\n\n        # \u8bb0\u5f55\u6570\u636e\n        PV_history.append(y)\n        SV_history.append(SV)\n        error_history.append(error)\n        control_history.append(u_compensated)\n        heater_power_history.append(heater_power)\n        Kp_history.append(pid.Kp)\n        Ki_history.append(pid.Ki)\n        Kd_history.append(pid.Kd)\n\n    # \u6700\u540e\u4e00\u4e2a\u8bbe\u5b9a\u70b9\u7684\u6027\u80fd\u6307\u6807\n    max_PV = max(PV_history[response_start_index:]) if TIME_STEPS &gt; response_start_index else PV_history[-1]\n    overshoot = ((max_PV - current_setpoint) \/ current_setpoint) * 100 if current_setpoint != 0 else 0\n    overshoot_history.append(overshoot)\n    steady_state_error = np.mean(error_history[response_start_index:]) if TIME_STEPS &gt; response_start_index else error_history[-1]\n    steady_state_error_history.append(steady_state_error)\n    settling_time = 0\n    target_min = current_setpoint * (1 - settling_time_threshold)\n    target_max = current_setpoint * (1 + settling_time_threshold)\n    for i in range(response_start_index, TIME_STEPS):\n        if target_min &lt;= PV_history[i] &lt;= target_max:\n            if all(target_min &lt;= pv &lt;= target_max for pv in PV_history[i:]):\n                settling_time = i - response_start_index\n                break\n    settling_time_history.append(settling_time)\n\n    return (PV_history, SV_history, control_history, heater_power_history, \n            Kp_history, Ki_history, Kd_history, \n            overshoot_history, steady_state_error_history, settling_time_history)\n\n# \u521d\u59cb\u5316\u4eff\u771f\u53c2\u6570\nINITIAL_Kp = 2.0\nINITIAL_Ki = 0.5\nINITIAL_Kd = 0.1\n\n# \u8fd0\u884c\u521d\u59cb\u4eff\u771f\nSETPOINT_CHANGE_INTERVAL=500\nresults = simulate(INITIAL_Kp, INITIAL_Ki, INITIAL_Kd, TIME_STEPS=2000, \n                   SETPOINT_CHANGE_INTERVAL=SETPOINT_CHANGE_INTERVAL, \n                   max_power=12000, min_power=0, power_rate_limit=10)\nPV_history, SV_history, control_history, heater_power_history, Kp_history, Ki_history, Kd_history, \\\novershoot_history, steady_state_error_history, settling_time_history = results\n\n# \u521b\u5efa\u56fe\u5f62\u548c\u5b50\u56fe\uff0c\u589e\u52a0\u4e00\u4e2a\u5b50\u56fe\u7528\u4e8e\u5c55\u793a\u52a0\u70ed\u529f\u7387\u548c\u6027\u80fd\u6307\u6807\nfig = plt.figure(figsize=(15, 20))\ngs = gridspec.GridSpec(5, 1, height_ratios=[2, 1, 1, 1, 1], hspace=0.4)\n\n# \u5b50\u56fe1\uff1a\u7cfb\u7edf\u54cd\u5e94\nax1 = plt.subplot(gs[0])\nline1_PV, = ax1.plot(PV_history, label=&#039;Process Variable (PV)&#039;, color=&#039;b&#039;)\nline1_SV, = ax1.plot(SV_history, label=&#039;Setpoint (SV)&#039;, linestyle=&#039;--&#039;, color=&#039;r&#039;)\nax1.set_ylabel(&#039;Temperature&#039;)\nax1.set_title(&#039;System Response&#039;)\nax1.legend()\nax1.grid(True)\n\n# \u5b50\u56fe2\uff1a\u63a7\u5236\u8f93\u51fa\nax2 = plt.subplot(gs[1], sharex=ax1)\nline2, = ax2.plot(control_history, label=&#039;Control Output (u)&#039;, color=&#039;g&#039;)\nax2.set_ylabel(&#039;Control Output&#039;)\nax2.set_title(&#039;Control Signal&#039;)\nax2.legend()\nax2.grid(True)\n\n# \u5b50\u56fe3\uff1a\u52a0\u70ed\u529f\u7387\nax3 = plt.subplot(gs[2], sharex=ax1)\nline3, = ax3.plot(heater_power_history, label=&#039;Heater Power (u)&#039;, color=&#039;orange&#039;)\nax3.set_ylabel(&#039;Heater Power&#039;)\nax3.set_title(&#039;Heater Power&#039;)\nax3.legend()\nax3.grid(True)\n\n# \u5b50\u56fe4\uff1aPID\u53c2\u6570\nax4 = plt.subplot(gs[3], sharex=ax1)\nline4_Kp, = ax4.plot(Kp_history, label=&#039;Kp&#039;, color=&#039;m&#039;)\nline4_Ki, = ax4.plot(Ki_history, label=&#039;Ki&#039;, color=&#039;c&#039;)\nline4_Kd, = ax4.plot(Kd_history, label=&#039;Kd&#039;, color=&#039;y&#039;)\nax4.set_ylabel(&#039;PID Parameters&#039;)\nax4.set_title(&#039;Adaptive PID Parameters&#039;)\nax4.legend()\nax4.grid(True)\n\n# \u5b50\u56fe5\uff1a\u6027\u80fd\u6307\u6807\nax5 = plt.subplot(gs[4])\nsteps = [SETPOINT_CHANGE_INTERVAL * i for i in range(len(overshoot_history))]\nax5.plot(steps, overshoot_history, label=&#039;Overshoot (%)&#039;, marker=&#039;o&#039;, color=&#039;purple&#039;)\nax5.plot(steps, steady_state_error_history, label=&#039;Steady-State Error&#039;, marker=&#039;x&#039;, color=&#039;brown&#039;)\nax5.plot(steps, settling_time_history, label=&#039;Settling Time (steps)&#039;, marker=&#039;^&#039;, color=&#039;black&#039;)\nax5.set_xlabel(&#039;Time Step&#039;)\nax5.set_ylabel(&#039;Performance Metrics&#039;)\nax5.set_title(&#039;Performance Metrics per Setpoint Change&#039;)\nax5.legend()\nax5.grid(True)\n\n# \u8c03\u6574\u5b50\u56fe\u95f4\u8ddd\u4ee5\u7559\u51fa\u6ed1\u5757\u7a7a\u95f4\nplt.subplots_adjust(bottom=0.35)\n\n# \u6dfb\u52a0\u6ed1\u5757\naxcolor = &#039;lightgoldenrodyellow&#039;\nax_Kp = plt.axes([0.15, 0.25, 0.65, 0.03], facecolor=axcolor)\nax_Ki = plt.axes([0.15, 0.18, 0.65, 0.03], facecolor=axcolor)\nax_Kd = plt.axes([0.15, 0.11, 0.65, 0.03], facecolor=axcolor)\nax_max_power = plt.axes([0.15, 0.04, 0.65, 0.03], facecolor=axcolor)\n\nslider_Kp = Slider(ax_Kp, &#039;Kp0&#039;, 0.0, 50.0, valinit=INITIAL_Kp, valstep=0.1)\nslider_Ki = Slider(ax_Ki, &#039;Ki0&#039;, 0.0, 10.0, valinit=INITIAL_Ki, valstep=0.1)\nslider_Kd = Slider(ax_Kd, &#039;Kd0&#039;, 0.0, 10.0, valinit=INITIAL_Kd, valstep=0.1)\nslider_max_power = Slider(ax_max_power, &#039;Max Power&#039;, 50.0, 12000.0, valinit=2000.0, valstep=1.0)\n\n# \u5b9a\u4e49\u66f4\u65b0\u51fd\u6570\ndef update(val):\n    Kp0 = slider_Kp.val\n    Ki0 = slider_Ki.val\n    Kd0 = slider_Kd.val\n    max_power = slider_max_power.val\n    min_power = 0.0  # \u53ef\u4ee5\u6839\u636e\u9700\u8981\u8c03\u6574\u6700\u5c0f\u52a0\u70ed\u529f\u7387\n    power_rate_limit = 500.0  # \u56fa\u5b9a\u53d8\u5316\u7387\u9650\u5236\uff0c\u53ef\u6269\u5c55\u4e3a\u53ef\u8c03\n\n    # \u91cd\u65b0\u8fd0\u884c\u4eff\u771f\n    results = simulate(Kp0, Ki0, Kd0, TIME_STEPS=2000, \n                      SETPOINT_CHANGE_INTERVAL=SETPOINT_CHANGE_INTERVAL, \n                      max_power=max_power, min_power=min_power, \n                      power_rate_limit=power_rate_limit)\n    PV, SV, u, heater_power, Kp, Ki, Kd, overshoot, steady_state_error, settling_time = results\n\n    # \u66f4\u65b0\u7cfb\u7edf\u54cd\u5e94\u56fe\n    line1_PV.set_ydata(PV)\n    line1_SV.set_ydata(SV)\n    ax1.relim()\n    ax1.autoscale_view()\n\n    # \u66f4\u65b0\u63a7\u5236\u8f93\u51fa\u56fe\n    line2.set_ydata(u)\n    ax2.relim()\n    ax2.autoscale_view()\n\n    # \u66f4\u65b0\u52a0\u70ed\u529f\u7387\u56fe\n    line3.set_ydata(heater_power)\n    ax3.relim()\n    ax3.autoscale_view()\n\n    # \u66f4\u65b0PID\u53c2\u6570\u56fe\n    line4_Kp.set_ydata(Kp)\n    line4_Ki.set_ydata(Ki)\n    line4_Kd.set_ydata(Kd)\n    ax4.relim()\n    ax4.autoscale_view()\n\n    # \u66f4\u65b0\u6027\u80fd\u6307\u6807\u56fe\n    steps = [500 * i for i in range(len(overshoot))]\n    ax5.clear()\n    ax5.plot(steps, overshoot, label=&#039;Overshoot (%)&#039;, marker=&#039;o&#039;, color=&#039;purple&#039;)\n    ax5.plot(steps, steady_state_error, label=&#039;Steady-State Error&#039;, marker=&#039;x&#039;, color=&#039;brown&#039;)\n    ax5.plot(steps, settling_time, label=&#039;Settling Time (steps)&#039;, marker=&#039;^&#039;, color=&#039;black&#039;)\n    ax5.set_xlabel(&#039;Time Step&#039;)\n    ax5.set_ylabel(&#039;Performance Metrics&#039;)\n    ax5.set_title(&#039;Performance Metrics per Setpoint Change&#039;)\n    ax5.legend()\n    ax5.grid(True)\n\n    fig.canvas.draw_idle()\n\n# \u6ce8\u518c\u6ed1\u5757\u66f4\u65b0\u4e8b\u4ef6\nslider_Kp.on_changed(update)\nslider_Ki.on_changed(update)\nslider_Kd.on_changed(update)\nslider_max_power.on_changed(update)\n\nplt.show()<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"\u52a0\u70ed\u5668\u7cfb\u7edf\u4eff\u771f\u91c7\u7528\u6a21\u7ccaPID\u63a7\u5236\u4ee5\u4f18\u5316\u6e29\u5ea6\u8c03\u8282\uff0c\u51cf\u5c11\u8bef\u5dee\u3002","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":[1],"tags":[],"class_list":["post-91","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/posts\/91","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/comments?post=91"}],"version-history":[{"count":6,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/posts\/91\/revisions"}],"predecessor-version":[{"id":107,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/posts\/91\/revisions\/107"}],"wp:attachment":[{"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/media?parent=91"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/categories?post=91"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rwr.ink\/index.php\/wp-json\/wp\/v2\/tags?post=91"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}