{"id":303,"date":"2025-12-23T00:21:19","date_gmt":"2025-12-22T16:21:19","guid":{"rendered":"http:\/\/114.55.133.236\/?p=303"},"modified":"2026-03-03T08:27:13","modified_gmt":"2026-03-03T00:27:13","slug":"lqr%e6%8e%a7%e5%88%b6%e7%ae%97%e6%b3%95%e7%9a%84%e7%90%86%e8%ae%ba%e5%ad%a6%e4%b9%a0%e5%92%8c%e5%a4%a7%e5%b0%8fyaw%e4%ba%91%e5%8f%b0%e7%90%86%e8%ae%ba%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"http:\/\/qianmo.icu\/index.php\/2025\/12\/23\/lqr%e6%8e%a7%e5%88%b6%e7%ae%97%e6%b3%95%e7%9a%84%e7%90%86%e8%ae%ba%e5%ad%a6%e4%b9%a0%e5%92%8c%e5%a4%a7%e5%b0%8fyaw%e4%ba%91%e5%8f%b0%e7%90%86%e8%ae%ba%e5%ba%94%e7%94%a8\/","title":{"rendered":"\u9488\u5bf9\u5927\u5c0fyaw\u4e91\u53f0\u7684LQR\u63a7\u5236\u7b97\u6cd5\u7684\u7406\u8bba\u5b66\u4e60\u4e0e\u5e94\u7528"},"content":{"rendered":"\n
\n

\u60f3\u4e86\u89e3\u66f4\u591a\u6280\u672f\u5206\u4eab\u8bf7\u641c\u7d22\u201c\u6280\u672f\u201d\u6807\u7b7e\uff0c\u672c\u4eba\u6c34\u5e73\u6709\u9650\uff0c\u5185\u5bb9\u53ef\u80fd\u4e0d\u4e25\u8c28\u6216\u5b58\u5728\u9519\u8bef\uff0c\u5982\u6709\u53d1\u73b0\u9519\u8bef\u8bf7\u5728\u8bc4\u8bba\u533a\u5904\u7559\u8a00\uff0c\u6b22\u8fce\u6279\u8bc4\u6307\u6b63\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u63a8\u8350\u89c6\u9891<\/h2>\n\n\n\n

\u8df3\u51fa\u8bfe\u672c\u770bLQR\u63a7\u5236\uff0c\u4ece\u516c\u5f0f\u5230\u4ee3\u7801!_\u54d4\u54e9\u54d4\u54e9_bilibili<\/a><\/p>\n\n\n\n

\u3010\u624b\u628a\u624b\u6559\u505a\u5e73\u8861\u6b65\u5175\u8f6e\u8db3\u30117_LQR\u7cfb\u7edf\u5efa\u6a21_\u54d4\u54e9\u54d4\u54e9_bilibili<\/a><\/p>\n\n\n\n

\u4e00\u3001\u4ec0\u4e48LQR\u63a7\u5236\u7b97\u6cd5<\/h2>\n\n\n\n

LQR \u7684\u5168\u79f0\u662f Linear Quadratic Regulator<\/strong>\uff0c\u4e2d\u6587\u53eb\u7ebf\u6027\u4e8c\u6b21\u578b\u8c03\u8282\u5668<\/strong>\u3002\u5b83\u662f\u4e00\u79cd\u6700\u4f18\u63a7\u5236\u7b97\u6cd5\uff0c\u6838\u5fc3\u76ee\u6807\u5c31\u662f\uff1a\u8ba9\u7cfb\u7edf\u4ee5 \u201c\u6700\u5c0f\u7684\u63a7\u5236\u4ee3\u4ef7\u201d\uff0c\u7a33\u5b9a\u5730\u8fbe\u5230\u76ee\u6807\u72b6\u6001\u3002LQR\u662f\u73b0\u4ee3\u63a7\u5236\u7406\u8bba\u4e2d\u6700\u4f18\u53cd\u9988\u63a7\u5236\u7684\u6838\u5fc3\u7b97\u6cd5\uff0c\u5176\u672c\u8d28\u662f\u5728\u6ee1\u8db3\u7ebf\u6027\u7cfb\u7edf\u52a8\u529b\u5b66\u7ea6\u675f\u7684\u524d\u63d0\u4e0b\uff0c\u901a\u8fc7\u6700\u5c0f\u5316\u4e8c\u6b21\u578b\u6027\u80fd\u6307\u6807\uff0c\u5f97\u5230\u552f\u4e00\u7684\u6700\u4f18\u7ebf\u6027\u72b6\u6001\u53cd\u9988\u5f8b\uff0c\u5e76\u4ece\u6570\u5b66\u4e0a\u4e25\u683c\u4fdd\u8bc1\u95ed\u73af\u7cfb\u7edf\u7684\u6e10\u8fd1\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n\n

\u5178\u578b\u9002\u7528\u573a\u666f\uff1a<\/h3>\n\n\n\n
    \n
  • \u591a\u53d8\u91cf\u8026\u5408\u7cfb\u7edf\uff08\u5982\u65e0\u4eba\u673a\u59ff\u6001\u63a7\u5236\uff1a\u4fef\u4ef0 \/ \u6a2a\u6eda \/ \u504f\u822a\u8026\u5408\uff09\uff1b<\/li>\n\n\n\n
  • \u9ad8\u9636\u7cfb\u7edf\uff08\u5982\u673a\u68b0\u81c2\u591a\u5173\u8282\u3001\u98de\u884c\u5668\u516d\u81ea\u7531\u5ea6\u63a7\u5236\uff09\uff1b<\/li>\n\n\n\n
  • \u5bf9 \u201c\u63a7\u5236\u4ee3\u4ef7\u201d \u654f\u611f\u7684\u573a\u666f\uff08\u5982\u536b\u661f\u63a8\u8fdb\u5668\u71c3\u6599\u6d88\u8017\u3001\u7535\u673a\u529f\u8017\u9650\u5236\uff09\u3002<\/li>\n<\/ul>\n\n\n\n

    1.\u7ebf\u6027\u7cfb\u7edf\uff08Linear\uff09<\/strong>\uff1a<\/h3>\n\n\n\n

    \u5c31\u662f\u7cfb\u7edf\u7684 \u201c\u8f93\u5165\u201d \u548c \u201c\u8f93\u51fa\u201d \u662f\u6210\u6b63\u6bd4\u7684\u7b80\u5355\u5173\u7cfb\u3002
    \u6bd4\u5982\uff1a\u4f60\u8e29\u6cb9\u95e8\u7684\u529b\u5ea6\uff08\u8f93\u5165\uff09\uff0c\u548c\u6c7d\u8f66\u52a0\u901f\u7684\u5feb\u6162\uff08\u8f93\u51fa\uff09\uff0c\u5927\u6982\u662f\u6210\u6b63\u6bd4\u7684 \u2014\u2014 \u8e29\u5f97\u8d8a\u72e0\uff0c\u52a0\u901f\u8d8a\u5feb\uff08\u5ffd\u7565\u590d\u6742\u56e0\u7d20\uff09\u3002
    \u53cd\u4e4b\uff0c\u975e\u7ebf\u6027\u7cfb\u7edf\u5c31\u662f\u8f93\u5165\u8f93\u51fa\u4e0d\u6210\u6b63\u6bd4\uff0c\u6bd4\u5982\uff1a\u4f60\u8e29\u6cb9\u95e8\u592a\u731b\uff0c\u8f6e\u80ce\u6253\u6ed1\u4e86\uff0c\u518d\u8e29\u6cb9\u95e8\u901f\u5ea6\u4e5f\u4e0d\u6da8\u4e86\u3002<\/p>\n\n\n\n

    LQR \u7684\u63a7\u5236\u5bf9\u8c61\u5fc5\u987b\u662f\u7ebf\u6027\u65f6\u4e0d\u53d8\uff08LTI\uff09\u7cfb\u7edf\uff0c\u5176\u52a8\u529b\u5b66\u7279\u6027\u7531\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b\u63cf\u8ff0\uff0c\u5206\u4e3a\u8fde\u7eed\u65f6\u95f4\u548c\u79bb\u6563\u65f6\u95f4\u4e24\u79cd\u5f62\u5f0f\u3002<\/p>\n\n\n\n

    \u8fde\u7eed\u65f6\u95f4\u7ebf\u6027\u7cfb\u7edf\uff1a<\/h4>\n\n\n\n
    \"\"<\/div><\/figure>\n\n\n\n
    \"\"<\/div><\/figure>\n\n\n\n

    \u79bb\u6563\u65f6\u95f4\u7ebf\u6027\u7cfb\u7edf\uff1a<\/h4>\n\n\n\n
    \"\"<\/div><\/figure>\n\n\n\n

    2.\u4e8c\u6b21\u578b\u6307\u6807\uff08Quadratic\uff09<\/strong>\uff1a<\/h3>\n\n\n\n

    \u53ef\u4ee5\u7406\u89e3\u6210 \u201c\u54b1\u4eec\u8981\u4ed8\u51fa\u7684\u603b\u4ee3\u4ef7\u201d\u3002\u8fd9\u4e2a\u4ee3\u4ef7\u5206\u4e24\u90e8\u5206\uff1a
    \u2460\u72b6\u6001\u504f\u5dee\u4ee3\u4ef7\uff1a\u7cfb\u7edf\u5b9e\u9645\u72b6\u6001\u548c\u76ee\u6807\u72b6\u6001\u7684\u5dee\u8ddd\u3002\u6bd4\u5982\uff1a\u4f60\u60f3\u8ba9\u5c0f\u8f66\u505c\u572810\u7c73\u5904\uff0c\u7ed3\u679c\u505c\u5728\u4e868\u7c73\uff0c\u5dee\u8ddd\u662f2\u7c73\uff0c\u8fd9\u4e2a\u5dee\u8ddd\u8d8a\u5927\uff0c\u4ee3\u4ef7\u8d8a\u9ad8\u3002
    \u2461\u63a7\u5236\u91cf\u4ee3\u4ef7\uff1a\u4e3a\u4e86\u8c03\u6574\u7cfb\u7edf\uff0c\u54b1\u4eec\u4ed8\u51fa\u7684 \u201c\u529b\u6c14\u201d\u3002\u6bd4\u5982\uff1a\u4e3a\u4e86\u8ba9\u5c0f\u8f66\u4ece8\u7c73\u523010\u7c73\uff0c\u4f60\u9700\u8981\u8e29\u6cb9\u95e8\uff0c\u8e29\u5f97\u8d8a\u72e0\uff08\u63a7\u5236\u91cf\u8d8a\u5927\uff09\uff0c\u6cb9\u8017\u8d8a\u9ad8\uff0c\u4ee3\u4ef7\u8d8a\u9ad8\u3002
    \u4e8c\u6b21\u578b\u7684\u610f\u601d\u5c31\u662f\uff1a\u8fd9\u4e9b\u4ee3\u4ef7\u4f1a\u88ab\u5e73\u65b9\u8ba1\u7b97\uff08\u6bd4\u5982\u5dee\u8ddd\u7684\u5e73\u65b9\u3001\u63a7\u5236\u91cf\u7684\u5e73\u65b9\uff09\uff0c\u76ee\u7684\u662f\u60e9\u7f5a\u5927\u7684\u504f\u5dee\u548c\u5927\u7684\u63a7\u5236\u91cf\u2014\u2014 \u6bd5\u7adf\u504f\u5dee\u592a\u5927\u3001\u63a7\u5236\u592a\u731b\uff0c\u7cfb\u7edf\u5bb9\u6613\u51fa\u95ee\u9898\u3002<\/p>\n\n\n\n

    \"\"<\/div><\/figure>\n\n\n\n
      \n
    • Q<\/strong>\uff1a\u72b6\u6001\u6743\u91cd\u77e9\u9635\uff08\u4e91\u53f0\u4e2d\u89d2\u5ea6\u6743\u91cd\u8bbe\u5927\uff0c\u4f18\u5148\u4fdd\u8bc1\u5bf9\u51c6\uff09\uff1b<\/li>\n\n\n\n
    • R<\/strong>\uff1a\u63a7\u5236\u6743\u91cd\u77e9\u9635\uff08\u8bbe\u5927\u5219\u9650\u5236\u7535\u673a\u7535\u538b\uff0c\u907f\u514d\u8fc7\u8f7d\uff09\uff1b<\/li>\n\n\n\n
    • J<\/strong>\u8d8a\u5c0f\uff0c\u4e91\u53f0\u65e2\u51c6\u53c8\u7701\u7535\u3002<\/li>\n<\/ul>\n\n\n\n

      \u901a\u8fc7\u6c42\u89e3\u79bb\u6563\u4ee3\u6570\u9ece\u5361\u63d0\u65b9\u7a0b\uff0c\u5f97\u5230\u552f\u4e00\u7684\u6b63\u5b9a\u77e9\u9635P<\/strong>\uff1a<\/p>\n\n\n\n

      \"\"<\/div><\/figure>\n\n\n\n

      \u518d\u7528P\u7b97\u51fa\u6700\u4f18\u53cd\u9988\u589e\u76ca\u77e9\u9635Kd<\/strong>\uff1a<\/p>\n\n\n\n

      \"\"<\/div><\/figure>\n\n\n\n

      3.\u8c03\u8282\u5668\uff08Regulator\uff09<\/strong>\uff1a<\/h3>\n\n\n\n

      \u6838\u5fc3\u4f5c\u7528\u662f \u201c\u7ef4\u7a33\u201d \u2014\u2014 \u8ba9\u7cfb\u7edf\u5f85\u5728\u4e00\u4e2a\u56fa\u5b9a\u7684\u76ee\u6807\u72b6\u6001\uff0c\u5c31\u7b97\u53d7\u5230\u5e72\u6270\uff0c\u4e5f\u80fd\u5feb\u901f\u62c9\u56de\u6765\u3002
      \u6bd4\u5982\uff1a\u8ba9\u65e0\u4eba\u673a\u60ac\u505c\u57285\u7c73\u9ad8\u5ea6\uff0c\u5c31\u7b97\u6709\u98ce\u522e\u5b83\uff0c\u4e5f\u80fd\u901a\u8fc7\u8c03\u6574\u87ba\u65cb\u6868\u8f6c\u901f\uff0c\u4fdd\u6301\u57285\u7c73\u3002<\/p>\n\n\n\n

      LQR \u7684\u6700\u4f18\u63a7\u5236\u6307\u4ee4\u662f\u72b6\u6001\u53cd\u9988\u5f62\u5f0f\uff0c\u76f4\u63a5\u7528\u5f53\u524d\u72b6\u6001\u504f\u5dee\u8ba1\u7b97\uff1a<\/p>\n\n\n\n

      \"\"<\/div><\/figure>\n\n\n\n

      \u4ec5\u53cd\u9988\u4f1a\u6709\u5c0f\u504f\u5dee\uff0c\u52a0\u7a33\u6001\u524d\u9988\u9879u0<\/strong>\uff0c\u6700\u7ec8\u63a7\u5236\u5f8b\uff1a<\/p>\n\n\n\n

      \"\"<\/div><\/figure>\n\n\n\n

      \u4e8c\u3001LQR\u63a7\u5236\u6d41\u7a0b(\u4ee5\u5927\u5c0fyaw\u4e91\u53f0\u4e3a\u4f8b\u5b50)<\/h2>\n\n\n\n

      \u5148\u79bb\u7ebf\u5efa\u6a21\u6c42\u89e3\u589e\u76ca\uff0c\u518d\u5728\u7ebf\u5b9e\u65f6\u95ed\u73af\u63a7\u5236\u3002\u6700\u6700\u91cd\u8981\u7684\u662f\u8981\u5bf9\u7cfb\u7edf\u8fdb\u884c\u6570\u5b66\u5efa\u6a21\u6216\u7cfb\u7edf\u8fa8\u8bc6\u6c42\u51fa\u72b6\u6001\u5411\u91cf\u4e0e\u63a7\u5236\u8f93\u5165\u4e4b\u95f4\u7684\u51fd\u6570\u5173\u7cfb\u3002
      <\/strong>(\u6570\u5b66\u5efa\u6a21\u9700\u8981\u5927\u91cf\u7684\u7269\u7406\u77e5\u8bc6\uff0c\u672c\u6587\u7565\u8fc7\u7269\u7406\u77e5\u8bc6\u7684\u8bb2\u89e3\uff0c\u8bf7\u81ea\u884c\u5b66\u4e60\u3002)<\/p>\n\n\n\n

      1.\u660e\u786e\u63a7\u5236\u76ee\u6807\u4e0e\u7cfb\u7edf\u53d8\u91cf\uff1a<\/h3>\n\n\n\n
      \"\"<\/div><\/figure>\n\n\n\n
      \"\"<\/div><\/figure>\n\n\n\n
        \n
      • \u63a7\u5236\u76ee\u6807\uff1a\n
          \n
        • \u53cc\u5c42 Yaw \u4e91\u53f0\u53cc\u8f74\u7cbe\u51c6\u8ddf\u8e2a\u76ee\u6807\u89d2\u5ea6\u03b81r\u3001\u03b82r\uff0c\u6291\u5236\u8f74\u95f4\u8026\u5408\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • \u72b6\u6001\u5411\u91cf\u5b9a\u4e49\uff1a\n
            \n
          • \u5305\u542b\u6240\u6709\u9700\u8981\u63a7\u5236\u7684\u6838\u5fc3\u72b6\u6001\uff0cn\u4e3a\u72b6\u6001\u7ef4\u5ea6\uff08\u4e91\u53f0 n=4\uff09 <\/li>\n\n\n\n
          • \u03b81\/\u03b8 2= \u5927 \/ \u5c0f Yaw \u8f74\u89d2\u5ea6\uff0c\u03c9 1\/\u03c9 2= \u5927 \/ \u5c0f Yaw \u8f74\u89d2\u901f\u5ea6\u3002 <\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • \u63a7\u5236\u8f93\u5165\u5b9a\u4e49\uff1a\u9a71\u52a8\u7cfb\u7edf\u7684\u6267\u884c\u91cf\uff0cp\u4e3a\u8f93\u5165\u7ef4\u5ea6\uff08\u4e91\u53f0p=2\uff09\n
              \n
            • u1\/u2= \u5927 \/ \u5c0f Yaw \u8f74\u7535\u673a\u63a7\u5236\u8f93\u5165\uff08\u7535\u538b \/ \u529b\u77e9 \/ \u901f\u5ea6\u6307\u4ee4\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

              2.\u7cfb\u7edf\u77e9\u9635Ad\u3001\u8f93\u5165\u77e9\u9635Bd<\/h3>\n\n\n\n

              \u628a\u7cfb\u7edf\u89c4\u5f8b\u5199\u6210\u4e00\u79cd\u6807\u51c6\u7684\u8868\u8fbe\u5f62\u5f0f\u3002<\/p>\n\n\n\n

              \u65b9\u6cd5 1\uff1a\u8fde\u7eed\u6a21\u578b\u79bb\u6563\u5316\uff08\u7406\u8bba\u5efa\u6a21\u6cd5\uff0c\u6700\u5e38\u7528\uff09\uff1a<\/strong><\/h4>\n\n\n\n
                \n
              • \u79bb\u6563\u72b6\u6001\u65b9\u7a0b\u4e3a\uff1a\n
                  \n
                • \"\"<\/div><\/li>\n<\/ul>\n<\/li>\n\n\n\n
                • \u5176\u4e2d\uff1a\uff08\u4ee5\u4e0b\u4ec5\u4e3a\u53c2\u8003\uff0c\u5b9e\u9645\u4e0a\u8981\u6839\u636e\u6570\u5b66\u5efa\u6a21\u5f97\u51fa\u7684\u51fd\u6570\u5173\u7cfb\u8f6c\u6362\u5f97\u5230A\u548cB\uff09<\/strong>\n
                    \n
                  • \"\"<\/div><\/li>\n\n\n\n
                  • J1\/J2<\/strong>\uff1a\n
                      \n
                    • \u5927 \/ \u5c0f Yaw \u8f74\u7b49\u6548\u60ef\u91cf\uff08\u7535\u673a + \u8d1f\u8f7d\uff09\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                    • B1\/B2<\/strong>\uff1a\n
                        \n
                      • \u5927 \/ \u5c0f Yaw \u8f74\u7b49\u6548\u963b\u5c3c\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • J12\/J21<\/strong>\uff1a\n
                          \n
                        • \u8f74\u95f4\u8026\u5408\u60ef\u91cf\uff08\u5c0f\u8f74\u8f6c\u52a8\u5bf9\u5927\u8f74\u7684\u5f71\u54cd\uff09\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                        • Kt1\/Kt2<\/strong>\uff1a\n
                            \n
                          • \u7535\u673a\u529b\u77e9\u5e38\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                            \u65b9\u6cd5 2\uff1a\u7cfb\u7edf\u8fa8\u8bc6\uff08\u5b9e\u9a8c\u6cd5\uff0c\u65e0\u6a21\u578b\u65f6\u7528\uff09\uff1a<\/strong><\/h4>\n\n\n\n

                            \u82e5\u4e91\u53f0\u7ed3\u6784\u590d\u6742\u3001\u65e0\u6cd5\u63a8\u5bfc\u7406\u8bba\u6a21\u578b\uff0c\u6216\u8005\u8981\u5f97\u5230\u50cf\u963b\u5c3c\u7cfb\u6570\u8fd9\u6837\u4e0d\u80fd\u901a\u8fc7\u8ba1\u7b97\u7684\u6765\u7684\u53c2\u6570\uff0c\u8003\u8651\u76f4\u63a5\u901a\u8fc7\u6d4b\u8bd5\u5b9e\u9a8c\u7684\u6570\u636e\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u5206\u6790\u8ba1\u7b97\u5f97\u51fa\u60f3\u8981\u7684\u53c2\u6570\uff1a<\/p>\n\n\n\n

                              \n
                            • \u7ed9\u53cc\u7535\u673a\u65bd\u52a0\u4f2a\u968f\u673a\u6fc0\u52b1\u4fe1\u53f7\uff08\u5982\u767d\u566a\u58f0\u7535\u538b\uff09\uff1b<\/li>\n\n\n\n
                            • \u7528\u7f16\u7801\u5668\u91c7\u96c6\u53cc\u8f74\u7684\u89d2\u5ea6 \/ \u89d2\u901f\u5ea6\u6570\u636e\uff1b<\/li>\n\n\n\n
                            • \u7528\u5de5\u5177\u62df\u5408\u79bb\u6563\u6a21\u578b\uff1a\n
                                \n
                              • Matlab\uff1a\u7528System Identification Toolbox\uff0c\u5bfc\u5165\u8f93\u5165\u8f93\u51fa\u6570\u636e\uff0c\u9009\u62e9 \u201c\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\u201d\uff0c\u76f4\u63a5\u8f93Ad\/Bd\uff1b<\/li>\n\n\n\n
                              • \u4f18\u52bf\uff1a\u65e0\u9700\u77e5\u9053\u4efb\u4f55\u673a\u68b0\u53c2\u6570\uff0c\u76f4\u63a5\u8d34\u5408\u5b9e\u9645\u7cfb\u7edf\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                3.\u72b6\u6001\u6743\u91cd\u77e9\u9635Q\u3001\u63a7\u5236\u6743\u91cd\u77e9\u9635R\u3002<\/h3>\n\n\n\n

                                Q\u60e9\u7f5a\u72b6\u6001\u504f\u5dee\uff0cR\u60e9\u7f5a\u63a7\u5236\u8f93\u5165\u4ee3\u4ef7\uff0c\u65e0\u901a\u7528\u516c\u5f0f\uff0c\u9760\u5de5\u7a0b\u7ecf\u9a8c\u6574\u5b9a\uff0c\u6838\u5fc3\u539f\u5219\u662f \u201c\u8ddf\u8e2a\u7cbe\u5ea6\u201d \u4e0e \u201c\u63a7\u5236\u4ee3\u4ef7\u201d \u7684\u6743\u8861 \u3002<\/p>\n\n\n\n

                                \u2460\u72b6\u6001\u6743\u91cd\u77e9\u9635 Q<\/em><\/strong>\uff08n<\/em>\u00d7n<\/em> \u5bf9\u79f0\u534a\u6b63\u5b9a\uff0c\u4e91\u53f0 n<\/em>=4\uff09\uff1a<\/h4>\n\n\n\n
                                  \n
                                • \u7ed3\u6784\u9009\u62e9\uff1a<\/strong>\n
                                    \n
                                  • \u4f18\u5148\u9009\u5bf9\u89d2\u77e9\u9635\uff08\u975e\u5bf9\u89d2\u5143\u7d20\u4e3a 0\uff0c\u7b80\u5316\u6574\u5b9a\uff09\uff0c\u5bf9\u89d2\u5143\u7d20\u5bf9\u5e94\u6bcf\u4e2a\u72b6\u6001\u7684\u60e9\u7f5a\u6743\u91cd\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                  • \u53d6\u503c\u539f\u5219<\/strong>\uff1a\n
                                      \n
                                    • \u5bf9\u8f85\u52a9\u72b6\u6001\uff08\u5982\u89d2\u901f\u5ea6\u03c91,\u03c92\uff09\uff0c\u6743\u91cd\u53d6\u5c0f\uff08\u598210\u223c50\uff09\uff0c\u6291\u5236\u9707\u8361\u5373\u53ef\uff1b<\/li>\n\n\n\n
                                    • \u82e5\u8f74\u95f4\u8026\u5408\u4e25\u91cd\uff0c\u53ef\u589e\u5927\u975e\u5bf9\u89d2\u5143\u7d20\uff08\u5982\u03b81\u4e0e\u03c92\u7684\u8026\u5408\u9879\uff09\uff0c\u4e3b\u52a8\u6291\u5236\u8026\u5408\u6270\u52a8\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                    • \u4e91\u53f0\u793a\u4f8b<\/strong>\uff1a\n
                                        \n
                                      • Q=diag{Q\u03b81,Q\u03c91,Q\u03b82,Q\u03c92}=diag{200,20,200,20}<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                        \u2461\u63a7\u5236\u6743\u91cd\u77e9\u9635R\uff08p\u00d7p\u5bf9\u79f0\u6b63\u5b9a\uff0c\u4e91\u53f0p=2\uff09\uff1a<\/strong><\/p>\n\n\n\n

                                          \n
                                        • \u7ed3\u6784\u9009\u62e9\uff1a<\/strong>\n
                                            \n
                                          • \u4f18\u5148\u9009\u5bf9\u89d2\u77e9\u9635\uff0c\u5bf9\u89d2\u5143\u7d20\u5bf9\u5e94\u6bcf\u4e2a\u63a7\u5236\u8f93\u5165\u7684\u60e9\u7f5a\u6743\u91cd\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                          • \u53d6\u503c\u539f\u5219\uff1a<\/strong>\n
                                              \n
                                            • \u6743\u91cd\u8d8a\u5927\uff0c\u63a7\u5236\u8f93\u5165\u8d8a\u5c0f\uff08\u907f\u514d\u7535\u673a\u8fc7\u8f7d\uff09\uff0c\u4f46\u8ddf\u8e2a\u901f\u5ea6\u8d8a\u6162\uff1b<\/li>\n\n\n\n
                                            • \u6743\u91cd\u8d8a\u5c0f\uff0c\u63a7\u5236\u8f93\u5165\u8d8a\u5927\uff0c\u8ddf\u8e2a\u901f\u5ea6\u8d8a\u5feb\uff0c\u4f46\u6613\u8d85\u8c03 \/ \u8fc7\u8f7d\uff1b<\/li>\n\n\n\n
                                            • \u53cc\u7535\u673a\u6027\u80fd\u4e00\u81f4\u65f6\uff0c\u6743\u91cd\u53d6\u76f8\u540c\u503c\uff1b\u6027\u80fd\u4e0d\u540c\u65f6\uff0c\u5f31\u7535\u673a\u6743\u91cd\u53d6\u5927\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                            • \u4e91\u53f0\u793a\u4f8b<\/strong>\uff1a\n
                                                \n
                                              • R<\/em>=diag{R<\/em>1\u200b,R<\/em>2\u200b}=diag{1,1}<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                                \u2462\u6574\u5b9a\u6280\u5de7\uff08\u8bd5\u51d1\u6cd5\uff0c\u5de5\u7a0b\u901a\u7528\uff09\uff1a<\/strong><\/h4>\n\n\n\n
                                                  \n
                                                • \u521d\u59cb\u503c\uff1a<\/strong>\n
                                                    \n
                                                  • Q\u5bf9\u89d2\u5143\u7d20\u8bbe\u4e3adiag{100,10,100,10}\uff0cR=diag{1,1}\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                                  • \u4eff\u771f\u6d4b\u8bd5<\/strong>\uff1a\n
                                                      \n
                                                    • \u82e5\u8ddf\u8e2a\u6162 \u2192 \u589e\u5927Q\u89d2\u5ea6\u6743\u91cd\uff1b\u82e5\u7535\u673a\u8fc7\u8f7d \u2192 \u589e\u5927R\uff1b\u82e5\u9707\u8361 \u2192 \u589e\u5927Q\u89d2\u901f\u5ea6\u6743\u91cd\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                                    • \u8fed\u4ee3\u4f18\u5316<\/strong>\uff1a\n
                                                        \n
                                                      • \u9010\u6b65\u8c03\u6574\uff0c\u76f4\u5230\u6ee1\u8db3 \u201c\u8ddf\u8e2a\u7cbe\u5ea6 + \u63a7\u5236\u7ea6\u675f\u201d \u7684\u8981\u6c42\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                                        4.\u6c42\u89e3\u6700\u4f18\u53cd\u9988\u589e\u76caKd\u3002<\/h3>\n\n\n\n

                                                        \u5728\u83b7\u53d6Ad\u3001Bd\u3001Q\u3001R\u540e\uff0c\u6c42\u89e3\u6700\u4f18\u53cd\u9988\u589e\u76caKd\uff08\u7b80\u79f0 K\uff09\u7684\u6838\u5fc3\u662f\u5148\u89e3\u79bb\u6563\u9ece\u5361\u63d0\u65b9\u7a0b\u5f97\u77e9\u9635P\uff0c\u518d\u4ee3\u5165\u516c\u5f0f\u7b97Kd\uff0c\u5de5\u7a0b\u4e2d\u51e0\u4e4e\u4e0d\u7528\u624b\u52a8\u7b97\uff0c\u4f18\u5148\u7528\u5de5\u5177\u51fd\u6570\uff0c\u4ee5\u4e0b\u662f\u6700\u7b80\u5b9e\u64cd\u65b9\u6cd5\uff1a<\/p>\n\n\n\n

                                                        \u5de5\u7a0b\u5b9e\u64cd\uff08Matlab \u4e00\u884c\u641e\u5b9a\uff0c\u6700\u5e38\u7528\uff09\uff1a<\/h4>\n\n\n\n

                                                        matlab\u4ee3\u7801\uff1a<\/p>\n\n\n\n

                                                        % \u524d\u9762\u8981\u5b9a\u4e49\u597dAd\uff084\u00d74\uff09\u3001Bd\uff084\u00d72\uff09\u3001Q\uff084\u00d74\uff09\u3001R\uff082\u00d72\uff09\u77e9\u9635\u3002\n[Kd, P, E] = dlqr(Ad, Bd, Q, R); % \u79bb\u6563LQR\u6c42\u89e3\u6838\u5fc3\u51fd\u6570<\/code><\/pre>\n\n\n\n
                                                          \n
                                                        • Kd\uff1a\u5c31\u662f\u4f60\u8981\u7684\u6700\u4f18\u53cd\u9988\u589e\u76ca\u77e9\u9635\uff082\u00d74\uff09\uff0c\u76f4\u63a5\u7528\u4e8e\u540e\u7eed\u5b9e\u65f6\u63a7\u5236\uff1b<\/li>\n\n\n\n
                                                        • P\uff1a\u9ece\u5361\u63d0\u65b9\u7a0b\u7684\u89e3\uff084\u00d74\uff09\uff0c\u53ef\u9a8c\u8bc1\u662f\u5426\u6b63\u5b9a\uff08\u5de5\u7a0b\u4e2d\u4e00\u822c\u4e0d\u7528\u7ba1\uff09\uff1b<\/li>\n\n\n\n
                                                        • E\uff1a\u95ed\u73af\u7cfb\u7edf\u7279\u5f81\u503c\uff0c\u82e5\u6240\u6709\u7279\u5f81\u503c\u6a21 < 1 \u2192 \u7cfb\u7edf\u7a33\u5b9a\uff08\u5173\u952e\u9a8c\u8bc1\uff09\u3002<\/li>\n<\/ul>\n\n\n\n
                                                          5.\u9488\u5bf9\u5927\u5c0fyaw\u4e91\u53f0\u8fdb\u884c\u5b9e\u8df5<\/h3>\n\n\n\n
                                                          \u4ee5\u4e0b\u5c06\u91c7\u7528\u6570\u5b66\u5efa\u6a21\u7684\u65b9\u5f0f\u8fdb\u884c\u521d\u6b65\u7406\u8bba\u5b9e\u64cd<\/p>\n\n\n\n
                                                          \"\"<\/div><\/figure>\n\n\n\n
                                                          \"\"<\/div><\/figure>\n\n\n\n
                                                          \"\"<\/div><\/figure>\n\n\n\n
                                                          \u5bf9\u4e8e\u5176\u4e2d\u7684\u963b\u5c3c\u7cfb\u6570b\u5c31\u5fc5\u987b\u8981\u7528\u7cfb\u7edf\u8fa8\u8bc6\u6cd5\u6765\u83b7\u5f97\u4e86\uff0c\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u672c\u6587\u7565\uff0c\u611f\u5174\u8da3\u8bf7\u81ea\u884c\u641c\u7d22\u3002<\/p>\n\n\n\n
                                                          \u56e0\u4e3a\u6761\u4ef6\u4e0d\u592a\u5141\u8bb8\uff0c\u6211\u53ea\u80fd\u5148\u5b9e\u8df5\u5230\u8fd9\u91cc\uff0c\u540e\u7eed\u7684\u53c2\u6570\u6d4b\u91cf\u3001\u6570\u503c\u8ba1\u7b97\u3001\u7cfb\u7edf\u6536\u655b\u6027\u6d4b\u8bd5\u548c\u6700\u7ec8\u6210\u679c\u65e0\u6cd5\u7ed9\u5927\u5bb6\u8fdb\u884c\u5c55\u793a\uff0c\u8fd9\u90e8\u5206\u7684\u5185\u5bb9\u63a8\u8350\u53bb\u89c2\u770b\u6587\u7ae0\u5f00\u5934\u63a8\u8350\u7684\u89c6\u9891\uff0c\u91cc\u9762\u6709\u8be6\u7ec6\u7684\u8bb2\u89e3\u3002<\/p>\n\n\n\n
                                                          \u4e09\u3001\u8c08\u8c08\u4e2a\u4eba\u5bf9LQR\u63a7\u5236\u7b97\u6cd5\u7684\u7406\u89e3<\/h2>\n\n\n\n
                                                            \n
                                                          • \u76f8\u6bd4\u4e8ePID\u8fd9\u79cd\u7eaf\u51ed\u501f\u7ecf\u9a8c\u8c03\u53c2\u7684\u63a7\u5236\u65b9\u5f0f\uff0cLQR\u7684\u63a7\u5236\u662f\u57fa\u4e8e\u771f\u5b9e\u7684\u7269\u7406\u6a21\u578b\u7684\uff0c\u5728\u6570\u5b66\u5efa\u6a21\u5b8c\u5907\u4e14\u7cbe\u786e\u7684\u524d\u63d0\u4e0b\uff0cLQR\u7684\u63a7\u5236\u4f1a\u66f4\u52a0\u7cbe\u51c6\uff0c\u63a7\u5236\u6027\u80fd\u4f1a\u66f4\u4f18\u79c0\u3002<\/li>\n\n\n\n
                                                          • LQR\u5bf9\u4e8e\u591a\u7ef4\u5ea6\u76f8\u4e92\u8026\u5408\u7684\u7cfb\u7edf\u6709\u5929\u7136\u7684\u4f18\u52bf\uff0c\u4e0d\u5fc5\u50cfPID\u90a3\u6837\u9700\u8981\u590d\u6742\u7684\u89e3\u8026\u5408\uff0c\u5546\u4e1a\u4e0a\u7684\u591a\u8fde\u6746\u7684\u673a\u68b0\u81c2\u90fd\u662f\u7528\u7684LQR\u8fdb\u884c\u63a7\u5236\u7684\uff0c\u5f53\u7136\u7b97\u6cd5\u4f1a\u66f4\u52a0\u7684\u590d\u6742\uff0c\u4ec5\u4ec5\u53ea\u6709LQR\u662f\u4e0d\u597d\u7528\u7684\uff0c\u5e76\u4e14LQR\u7684\u6bcf\u4e00\u4e2a\u53c2\u6570\u90fd\u662f\u6709\u660e\u786e\u610f\u4e49\u7684\uff0c\u5982\u679c\u66f4\u65b0\u4e86\u673a\u68b0\u7ed3\u6784\u4e0d\u5fc5\u50cfPID\u90a3\u6837\u4ece\u5934\u5f00\u59cb\u8c03\uff0c\u53ea\u9700\u8981\u4fee\u6539\u76f8\u5bf9\u5e94\u7684\u6570\u5b66\u5efa\u6a21\u6a21\u578b\u7684\u53c2\u6570\u5c31\u884c\u4e86\u3002<\/li>\n\n\n\n
                                                          • \u5bf9\u4e8e\u7b80\u5355\u7684\u7cfb\u7edf\u8fd8\u662f\u5efa\u8bae\u53bb\u4f7f\u7528PID\uff0c\u56e0\u4e3aLQR\u5bf9\u4e8e\u5355\u7535\u673a\u7684\u63a7\u5236\u6ca1\u6709\u5f88\u5927\u7684\u4f18\u52bf\uff0c\u53cd\u800c\u56e0\u4e3a\u5b83\u7684\u590d\u6742\u6027\uff0c\u548c\u5bf9\u6570\u5b66\u6a21\u578b\u7684\u4f9d\u8d56\u6027\uff0c\u4e0a\u624b\u95e8\u69db\u5f88\u9ad8\uff0c\u662f\u5f88\u5927\u7684\u52a3\u52bf\uff0c\u5982\u679c\u4e2d\u9014\u8ba1\u7b97\u51fa\u73b0\u9519\u8bef\uff0c\u90a3\u4e48LQR\u7cfb\u7edf\u5f88\u53ef\u80fd\u5c31\u5d29\u4e86\uff0c\u8bba\u4e0b\u9650\u5b8c\u5168\u6bd4\u4e0d\u8fc7PID\u3002<\/li>\n<\/ul>\n\n\n\n
                                                            <\/p>\n","protected":false},"excerpt":{"rendered":"
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