{"id":2160,"date":"2024-03-21T19:34:21","date_gmt":"2024-03-21T11:34:21","guid":{"rendered":"https:\/\/luckytian.cn\/?p=2160"},"modified":"2024-03-22T19:50:39","modified_gmt":"2024-03-22T11:50:39","slug":"%e4%b8%bb%e8%a2%ab%e5%8a%a8%e9%9a%94%e6%8c%af%e7%a0%94%e7%a9%b6%e8%83%8c%e6%99%af","status":"publish","type":"post","link":"https:\/\/luckytian.cn\/?p=2160","title":{"rendered":"\u4e3b\u88ab\u52a8\u9694\u632f\u7814\u7a76\u80cc\u666f"},"content":{"rendered":"\n
Journal of Mechanical Science and Technology(4\u533a)\uff1aModeling identification and control of a 6-DOF active vibration isolation system driving by voice coil motors with a Halbach array magnet<\/h5>\n\n\n\n

1. \u672c\u6587\u5b58\u5728\u7684\u95ee\u9898\uff1a<\/p>\n\n\n\n

\u867d\u7136\u91c7\u7528HFs\u65b9\u6cd5\u5b9e\u73b0\u4e86\u72b6\u6001\u65b9\u7a0b\u4e2d\u72b6\u6001\u77e9\u9635A\u7684\u53c2\u6570\u8bc6\u522b\uff08\u5373\u5bf9\u65bd\u52a0\u7684\u4e09\u4e2a\u7ebf\u6027\u529b\u548c\u4e09\u4e2a\u529b\u77e9\u5230\u9694\u632f\u53f0\u7684\u4f5c\u7528\u77e9\u9635\u8fdb\u884c\u6821\u6b63\uff09\uff0c\u4f46\u4e3b\u52a8\u63a7\u5236\u56de\u8def\u4e2d\u632f\u52a8\u4f20\u611f\u5668\u632f\u52a8\u4fe1\u53f7\u5230\u653e\u5927\u7535\u8def\u548c\u63a7\u5236\u5668\u63a7\u5236\u4f5c\u7528\u529b\u7ecf\u538b\u6d41\u8f6c\u6362\u5230\u97f3\u5708\u7535\u673a\u7684\u975e\u7ebf\u6027\u4f20\u9012\u7279\u6027\u5e76\u672a\u8003\u8651\uff0c\u5728\u9ad8\u7cbe\u5ea6\u4e3b\u52a8\u9694\u632f\u4e2d\uff0c\u4f20\u611f\u5668\u3001\u7535\u8def\u548c\u6267\u884c\u5668\u7684\u4f20\u9012\u7279\u6027\u5747\u4f1a\u5f71\u54cd\u6700\u7ec8\u7684\u632f\u52a8\u6291\u5236\u6548\u679c\u3002<\/p>\n\n\n\n

2.\u672c\u6587\u8d21\u732e\uff1a<\/p>\n\n\n\n

\u5c06\u8003\u8651\u7aef\u90e8\u6548\u5e94\u7684\u7247\u6d41\u6a21\u578b\u5e94\u7528\u4e8e\u97f3\u5708\u7535\u673a\u7684\u8bbe\u8ba1\uff1b\u9996\u6b21\u5c06\u590d\u5408\u975e\u7ebf\u6027\u53cd\u9988\u63a7\u5236\u5668\u5f15\u5165\u9694\u632f\u7cfb\u7edf\u7684\u63a7\u5236\u4e2d\uff1b\u901a\u8fc7HF\u65b9\u6cd5\u57fa\u4e8e\u8bc6\u522b\u53c2\u6570\u6765\u8bbe\u8ba1CNF\u63a7\u5236\u5668\u3002<\/p>\n\n\n\n

3.\u5f15\u8a00\u90e8\u5206\uff1a<\/p>\n\n\n\n

\u5c06\u5de5\u4f5c\u73af\u5883\u7684\u5916\u90e8\u632f\u52a8\u548c\u5e72\u6270\u63a7\u5236\u5728\u5408\u7406\u8303\u56f4\u5185\u5bf9\u9ad8\u7aef\u4ea7\u54c1\u5236\u9020\u5177\u6709\u91cd\u8981\u610f\u4e49\uff0c\u7279\u522b\u662f\u5728\u7eb3\u7c73\u8ba1\u91cf\u3001\u9ad8\u7cbe\u5ea6\u5b9a\u4f4d\u7cfb\u7edf\u548c\u8d85\u7cbe\u5bc6\u5236\u9020\u4e2d[1-3]\u3002
\u8bbe\u8ba1\u4e86\u5305\u62ec\u6b63\u521a\u5ea6\u548c\u8d1f\u521a\u5ea6\u5143\u4ef6\u7684\u51c6\u96f6\u521a\u5ea6\uff08QZS\uff09\u9694\u632f\u7cfb\u7edf\uff0c\u4e0e\u7ebf\u6027\u65b9\u6848\u76f8\u6bd4\uff0c\u8be5\u7cfb\u7edf\u63d0\u4f9b\u4e86\u66f4\u4f4e\u7684\u8c10\u632f\u9891\u7387\u548c\u66f4\u5bbd\u7684\u9891\u5e26[6]\u3002\u9694\u632f\u65b9\u5f0f\u53ef\u5206\u4e3a\u88ab\u52a8\u9694\u632f\u65b9\u5f0f\u548c\u4e3b\u52a8\u9694\u632f\u65b9\u5f0f\u4e24\u7c7b\u3002
\u88ab\u52a8\u6cd5\u5728\u9ad8\u9891\u632f\u52a8\u60c5\u51b5\u4e0b\u6548\u679c\u826f\u597d\u3002\u7136\u800c\uff0c\u5b83\u5bf9\u4f4e\u9891\u60c5\u51b5\u51e0\u4e4e\u6ca1\u6709\u5f71\u54cd\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u4e3b\u52a8\u9694\u632f\u7684\u5e94\u7528\u53ef\u4ee5\u63d0\u9ad8\u4f4e\u9891\u60c5\u51b5\u4e0b\u7684\u6027\u80fd[8]\u3002
\u7531\u4e8e\u97f3\u5708\u7535\u673a\uff08VCM\uff09\u7684\u9ad8\u52a0\u901f\u5ea6\u3001\u9ad8\u901f\u548c\u5feb\u901f\u9a71\u52a8\u7279\u6027\uff0c\u7814\u7a76\u5176\u7279\u6027\u5438\u5f15\u4e86\u8bb8\u591a\u7814\u7a76\u4eba\u5458[9\uff0c10]\u3002\u7136\u800c\uff0cVCM\u7684\u8f93\u51fa\u529b\u5e76\u4e0d\u5bc6\u96c6\uff0c\u8fd9\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u9650\u5236\u4e86VCM\u7684\u4f7f\u7528\u3002
\u7814\u7a76\u4e86\u4e8c\u81ea\u7531\u5ea6\u88ab\u52a8\u548c\u4e3b\u52a8\u9694\u632f\u7cfb\u7edf\u4e2d\u7684\u60ef\u6027\u5143\u4ef6\u3002\u56e0\u4e3a\u65e0\u6e90\u9694\u79bb\u5668\u4e2d\u5305\u542b\u7684\u60ef\u6027\u5143\u4ef6\u53ef\u4ee5\u6269\u5927\u8d1f\u53cd\u9988\u589e\u76ca\u548c\u4e3b\u52a8\u963b\u5c3c\uff0c\u5373\u60ef\u6027\u5143\u4ef6\u80fd\u591f\u5b9e\u73b0\u66f4\u5927\u7684\u7a33\u5b9a\u88d5\u5ea6\uff0c\u8fd9\u6709\u5229\u4e8e\u4e9a\u4e34\u754c\u9694\u632f\u95ee\u9898[15]\u3002<\/p>\n\n\n\n

4.\u672c\u6587\u65b9\u6cd5\u8bbe\u8ba1\uff1a
\uff081\uff09\u672c\u6587\u91c7\u7528\u4e86\u4e00\u79cdHalbach\u78c1\u94c1\u9635\u5217\u7684\u97f3\u5708\u7535\u673a\u6a21\u578b\uff0c\u5728\u672c\u6587\u7b2c\u4e8c\u8282\u7ed9\u51fa\u4e86\u8be5\u97f3\u5708\u7535\u673a\u7684\u78c1\u573a\u6a21\u578b\uff1b
\uff082\uff09\u4e3a\u4e86\u8bc6\u522b\u4f5c\u7528\u529b$F_u$\u81f3\u9694\u632f\u53f0\u516d\u81ea\u7531\u5ea6\u72b6\u6001\u7684\u53d8\u5316\u5173\u7cfb\uff0c\u91c7\u7528\u6df7\u5408\u51fd\u6570(hybrid funtions, HFs)\u7684\u65b9\u6cd5\u5bf9\u7cfb\u7edf\u7684\u591a\u8f93\u5165\u591a\u8f93\u51fa(MIMO)\u7cfb\u7edf\u8fdb\u884c\u8bc6\u522b\u3002
\u65f6\u4e0d\u53d8\u7cfb\u7edf\u7684\u72b6\u6001\u7a7a\u95f4\u88ab\u63cf\u8ff0\u4e3a\uff1a$\\dot{x}(t)=A x(t)+B u(t)$<\/p>\n\n\n\n

\u5728\u6570\u5b66\u4e0a\uff0c\u4efb\u4f55\u5e73\u65b9\u53ef\u79ef\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u6df7\u5408\u51fd\u6570\uff08HFs\uff09\u96c6\u8868\u793a\uff0c\u6df7\u5408\u51fd\u6570\u96c6\u7531\u91c7\u6837\u4fdd\u6301\u51fd\u6570\uff08SHF\uff09\u548c\u4e09\u89d2\u51fd\u6570\uff08TF\uff09\u7ec4\u6210[22, 23]\u3002HF\u65b9\u6cd5\u53ef\u5e94\u7528\u4e8e\u8bb8\u591a\u7ebf\u6027\u8fde\u7eed\u65f6\u95f4<\/mark>\u9f50\u6b21\u548c\u975e\u9f50\u6b21\u7cfb\u7edf\u7684\u5408\u6210\u548c\u8bc6\u522b\u3002HF\u65b9\u6cd5\u7528\u4e8e\u53c2\u8003\u6587\u732e\u4e2d\u5355\u8f93\u5165\u5355\u8f93\u51fa\uff08SISO\uff09\u7cfb\u7edf\u7684\u5206\u6790[24]\u3002\u73b0\u5728\uff0c\u8be5\u65b9\u6cd5\u5c06\u8fdb\u4e00\u6b65\u63a8\u5bfc\u5e76\u5e94\u7528\u4e8eMIMO\u7cfb\u7edf\u7684\u8bc6\u522b\u3002\uff08\u8bc6\u522b\u7cfb\u7edf\u72b6\u6001\u65b9\u7a0b\u7684\u72b6\u6001\u77e9\u9635$A$\uff09<\/p>\n\n\n\n

\uff083\uff09\u4e3b\u52a8\u9694\u632f\u7cfb\u7edf\u7684\u590d\u5408\u975e\u7ebf\u6027\u53cd\u9988\u63a7\u5236(Composite nonlinear feedback control, CNF)<\/p>\n\n\n\n

CNF\u63a7\u5236\u5f8b\u901a\u8fc7\u52a8\u6001\u963b\u5c3c\u6bd4\u5b9e\u73b0\u4e86\u5feb\u901f\u54cd\u5e94\u548c\u5c0f\u8d85\u8c03\u7684\u4f18\u70b9\uff0c<\/p>\n\n\n\n

\"\"<\/figure>
\n

\u5de6\u56fe\u6240\u793a\u4e3b\u52a8\u9694\u632f\u7cfb\u7edf\u52a8\u529b\u5b66\u6a21\u578b\u4e3a\uff1a
$\\left[M_p\\right] \\ddot{P}+\\left[C_p\\right] \\dot{P}+\\left[K_p\\right] P=\\left[C_B\\right] \\dot{B}+\\left[K_B\\right] B+F_u+F_d$
\u5176\u4e2d, $P=\\left[x_p, y_p, z_p, \\theta_{x p}, \\theta_{y p}, \\theta_{z p}\\right]^T$\u4e3a\u9694\u632f\u53f0\u8fd0\u52a8\u77e2\u91cf\uff0c$B$\u4e3a\u5bf9\u5e94\u7684\u5730\u9762\u632f\u52a8\u77e2\u91cf\uff0c$F_u=\\left[F_x, F_x, F_x, M_{\\theta x}, M_{\\theta y}, M_{\\theta z}\\right]^T$\u4e3a\u9a71\u52a8\u529b\uff0c$F_d=\\left[F_{d x}, F_{d y}, F_{d z}, M_{d \\theta x}, M_{d \\theta y}, M_{d \\theta z}\\right]^T$\u4e3a\u5916\u90e8\u6270\u52a8\u529b\uff0c$\\left[M_p\\right]=\\operatorname{diag}\\left[m, m, m, I_x, I_y, I_z\\right]$\u4e3a\u53c2\u6570\u77e9\u9635\uff0c$C_p$, $K_p$, $C_B$, $K_B$\u4e3a\u7cfb\u7edf\u8f6c\u77e9\u5230\u7cfb\u7edf\u5148\u8fd0\u52a8\u8f6c\u6362\u7684\u53c2\u6570\u77e9\u9635\uff0c\u9664$z$\u8f74\u5916\uff0c\u6c34\u5e73\u65b9\u5411\u7684\u8f6c\u52a8\u548c\u5e73\u52a8\u5747\u5177\u6709\u8026\u5408<\/p>\n<\/div><\/div>\n\n\n\n

\"\"<\/figure>
\n

\u4e3b\u52a8\u9694\u632f\u7cfb\u7edf\u5177\u5907\u56db\u4e2a\u6c34\u5e73\u9a71\u52a8\u5668AH\u548c\u56db\u4e2a\u5782\u76f4\u9a71\u52a8\u5668AV\uff0c\u57fa\u4e8e\u6267\u884c\u5668\u4e0e\u632f\u52a8\u4e4b\u95f4\u7684\u529b\u548c\u529b\u77e9\u5e73\u8861\u539f\u7406\uff0c\u6267\u884c\u5668\u7684\u52a8\u529b\u5b66\u6a21\u578b\u4e3a\uff1a$F M=\\left[T_A\\right] A V H$\uff0c\u5176\u4e2d\uff0c$F M=\\left[F_x, F_y, F_z, M_{\\theta x}, M_{\\theta y}, M_{\\theta z}\\right]^T$\u4e3a\u529b\u548c\u529b\u77e9\uff0c$A V H=[A V_1, A V_2, A V_3, A V_4, A H_1,A H_2,A H_3,A H_4$\u4e3a\u9a71\u52a8\u529b\u77e2\u3002<\/p>\n<\/div><\/div>\n\n\n\n

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

\u57fa\u4e8e\u5de6\u56fe\u6240\u793a\u9635\u5217\u653e\u7f6e\u4f20\u611f\u5668\uff0c\u53ef\u4ee5\u5f97\u5230\u4f20\u611f\u5668\u6570\u636e\u548c\u9694\u632f\u53f0\u8fd0\u52a8\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a$S=\\left[T_s\\right] P o S$\uff0c\u5176\u4e2d$S=\\left[S H_1, S H_2, S H_3, S V_1, S V_2, S V_3\\right]^T$\u8868\u793a\u4f20\u611f\u5668\u7684\u4f4d\u7f6e\u77e2\u91cf\uff0c$\\operatorname{Pos}=\\left[x_p, y_p, z_p, \\theta_{x p}, \\theta_{y p}, \\theta_{z p}\\right]^T$\u4e3a\u8fd0\u52a8\u77e2\u91cf<\/p>\n<\/div><\/div>\n\n\n\n

\uff084\uff09CNF\u63a7\u5236\u5668\u8bbe\u8ba1\uff1a<\/p>\n\n\n\n

\u591a\u81ea\u7531\u5ea6\u7cfb\u7edf\u666e\u904d\u5b58\u5728\u6a21\u6001\u8026\u5408\uff0c\u6a21\u6001\u5206\u89e3\u5bf9\u63a7\u5236\u65b9\u6cd5\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002
\u5728\u4e0d\u8003\u8651\u5730\u9762\u632f\u52a8\u4e0b\uff0c\u4e3b\u52a8\u9694\u632f\u7cfb\u7edf\u6a21\u578b\u4e3a\uff1a$\\left[M_p\\right] \\ddot{P}+\\left[C_p\\right] \\dot{P}+\\left[K_p\\right] P=F_u$
\u672c\u6587\u4e2d\u7684\u53c2\u6570\u8fa8\u8bc6\u5373\u4e3a\u5bf9\u6b64\u516c\u5f0f\u4e2d\u7684\u53c2\u6570\u8fdb\u884c\u8fa8\u8bc6\uff0c$\\left[\\begin{array}{l}\\dot{x}_1 \\ \\dot{x}_2\\end{array}\\right]=\\left[\\begin{array}{cc}\\mathbf{0} & \\mathbf{I} \\ -\\left[M_p\\right]^{-1}\\left[K_p\\right] & -\\left[M_p\\right]^{-1}\\left[C_p\\right]\\end{array}\\right]\\left[\\begin{array}{l}x_1 \\ x_2\\end{array}\\right]+\\left[\\begin{array}{c}\\mathbf{0} \\ {\\left[M_p\\right]^{-1}}\\end{array}\\right] F_u$<\/p>\n\n\n\n

\u4ee3\u5165\u6a21\u6001\u77e9\u9635\u8fdb\u884c\u6a21\u6001\u5206\u89e3\uff0c\u53ef\u5f97\uff1a$\\left(V_1^{\\prime}\\left[M_p\\right] V_1 s^2+V_1^{\\prime}\\left[C_p\\right] V_1 s+V_1^{\\prime}\\left[K_p\\right] V_1\\right) \\eta=V_1^{\\prime} F_u(s)$\uff0c\u5176\u4e2d\uff1a$\\eta=\\left[\\begin{array}{llllll}\\eta_1 & \\eta_2 & \\eta_3 & \\eta_4 & \\eta_5 & \\eta_6\\end{array}\\right]^T$\uff0c$V_1^{\\prime} F_u(s) \\triangleq f=\\left[\\begin{array}{llllll}f_1 & f_2 & f_3 & f_4 & f_5 & f_6\\end{array}\\right]^T$\uff0c
\u91cd\u5199\u6a21\u6001\u89e3\u8026\u540e\u7684\u65b9\u7a0b\u4e3a\uff1a$\\left[M_\\eta\\right] \\ddot{\\eta}+\\left[C_\\eta\\right] \\dot{\\eta}+\\left[K_\\eta\\right] \\eta=f$\uff0c\u5176\u4e2d\uff1a$\\left[M_\\eta\\right]=V_1^{\\prime}\\left[M_p\\right] V_1=I$\uff0c$\\left[C_\\eta\\right]=V_1^{\\prime}\\left[C_p\\right] V_1$\u548c$\\left[K_\\eta\\right]=V_1^{\\prime}\\left[K_p\\right] V_1$\u5747\u4e3a\u5bf9\u89d2\u9635\u3002<\/p>\n\n\n\n

\u8003\u8651\u5230\u963b\u5c3c\u77e9\u9635\u4e2d\u4e3b\u8981\u5bf9\u89d2\u5143\u7d20\u548c\u5176\u4f59\u5143\u7d20\u4e4b\u95f4\u7684\u5927\u5c0f\u987a\u5e8f\uff0c\u53ef\u4ee5\u5c06\u975e\u5bf9\u89d2\u5143\u7d20\u89c6\u4e3a\u96f6\uff0c\u5373\u5b9e\u73b0\u5b8c\u5168\u7684\u6a21\u6001\u5206\u89e3\u3002\u56e0\u6b64\uff0cCNF\u63a7\u5236\u5668\u53ef\u4ee5\u8bbe\u8ba1\u4e3aSISO\u7cfb\u7edf\u3002\u4f8b\u5982\uff0c\u4ece\u7b2c\u4e00\u8f93\u5165\u5230\u7b2c\u4e00\u8f93\u51fa\uff0c\u5fae\u5206\u65b9\u7a0b\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a$\\ddot{\\eta}_1+9.24 \\dot{\\eta}_1+965.52 \\eta_1=f_1$<\/p>\n","protected":false},"excerpt":{"rendered":"

Journal of Mechanical Science and Technology(4\u533a)\uff1aModeli […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[19,31],"tags":[22],"special":[],"_links":{"self":[{"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/posts\/2160"}],"collection":[{"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/luckytian.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2160"}],"version-history":[{"count":28,"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/posts\/2160\/revisions"}],"predecessor-version":[{"id":2212,"href":"https:\/\/luckytian.cn\/index.php?rest_route=\/wp\/v2\/posts\/2160\/revisions\/2212"}],"wp:attachment":[{"href":"https:\/\/luckytian.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/luckytian.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/luckytian.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2160"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/luckytian.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=2160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}