自动控制原理 选择题第80题,已知系统开环传递函数G(s)=8/(s(s-1)) 怎么求N+, N 已知系统的开环传递函数为G(s)=K/s(s+2)(s+4)...
\u5df2\u77e5\u5355\u4f4d\u8d1f\u53cd\u9988\u7cfb\u7edf\u7684\u5f00\u73af\u4f20\u9012\u51fd\u6570\u4e3aG(s)\uff0c\u8bd5\u6c42\u8be5\u7cfb\u7edf\u7684\u5355\u4f4d\u9636\u8dc3\u54cd\u5e94\uff0c\u5e76\u6c42\u8be5\u7cfb\u7edf\u8bb2\u5230\u5355\u4f4d\u8d1f\u53cd\u9988\uff0c\u77e5\u9053G(s)=4/s(s+1)\u3002\u90a3\u4e48Y(s)/X(s)=G(s)/(1+G(s))=4/(S^2+S+4)
\u4e8c\u9636\u7cfb\u7edf\u7684G(s)\u6709\u4e2a\u901a\u5f0f\uff1a
\u03c9n^2
G(s) = --------------------------------
S^2 + 2*\u03b6*\u03c9n S+ \u03c9n^2
\u5bf9\u5e94\u4e0a\u9762\u7684\u5f0f\u5b50\u5c31\u5f88\u5bb9\u6613\u6c42\u51fa\u03c9n\u548c\u03b6\uff0c\u03c9n=2\uff0c\u03b6=0.25
\u5cf0\u503c\u65f6\u95f4 tp=\u03c0/\u03c9d=\u03c0/(\u03c9n*sqrt(1-\u03b6^2))=1.622 s
\u4e0a\u5347\u65f6\u95f4 tr=(\u03c0-\u03b8)/\u03c9d =(\u03c0-\u03b8)/(\u03c9n*sqrt(1-\u03b6^2)) =0.9416 s
\u03b8=arctan(sqrt(1-\u03b6^2)/\u03b6)=1.318
\u8d85\u8c03\u91cf \u03c3p=exp(-\u03b6*\u03c0/sqrt(1-\u03b6^2))*100%=44.434%
\u8c03\u6574\u65f6\u95f4 ts \u5206\u4e24\u79cd\u4e0d\u540c\u7684\u8bef\u5dee\u8303\u56f4(\u0394) \u00b12%~\u00b15%
ts= -ln\u0394 /(\u03b6*\u03c9n) \u8fd9\u91cc\u5c31\u4e0d\u7ed9\u4f60\u7b97\u4e86
=========\u521a\u5b66\u81ea\u63a7\uff0c\u6c42\u63a2\u8ba8=====================
\u9996\u5148\u6839\u636e\u5f00\u73af\u4f20\u9012\u51fd\u6570G(S)\u753b\u51faG(s)H(s)\u95ed\u5408\u66f2\u7ebf\uff0c\u627e\u6b63\u7a7f\u8d8a\u7684\u6b21\u6570N+\u548c\u8d1f\u7a7f\u8d8a\u7684\u6b21\u6570N-\u3002R\u4e3as\u5e73\u9762\u95ed\u5408\u66f2\u7ebf\u5305\u56f4\u539f\u70b9\u5708\u6570\uff0cR=2\uff08N+\u2014 N-\uff09\u3002
\u9898\u76ee\u5df2\u7ecf\u7ed9\u5b9a\u5f00\u73af\u4f20\u9012\u51fd\u6570\u4e3aG\uff08s\uff09=2/\uff08\uff082s+1\uff09\uff088s+1\uff09\uff09\uff0c\u7ed8\u5236\u8be5\u7cfb\u7edf\u7684\u5f00\u73af\u5e45\u76f8\u66f2\u7ebf\u3002
\u7531\u5355\u4f4d\u53cd\u9988\u7cfb\u7edf\u7684\u5f00\u73af\u4f20\u9012\u51fd\u6570\u5f97\u95ed\u73af\u4f20\u9012\u51fd\u6570G0(s)\uff1d1/\uff081\uff0bG(s)\uff09\uff0c\u95ed\u73af\u4f20\u9012\u51fd\u6570\u7684\u5206\u6bcd\u7528\u52b3\u65af\u5224\u636e\u5224\u65ad\u7cfb\u7edf\u7a33\u5b9a\u6027\uff0c\u5f97\u51faK\u7684\u8303\u56f4\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5047\u8bbe\u7cfb\u7edf\u5355\u8f93\u5165R(s)\u3001\u5355\u8f93\u51faC(s)\uff0c\u524d\u5411\u901a\u9053\u4f20\u9012\u51fd\u6570G1(s)G2(s)\uff0c\u53cd\u9988\uff08\u53cd\u5411\u901a\u9053\uff09\u4e3a\u8d1f\u53cd\u9988H(s)\uff1a\u90a3\u4e48\u201c\u4eba\u4e3a\u201d\u65ad\u5f00\u7cfb\u7edf\u7684\u4e3b\u53cd\u9988\u901a\u8def\uff0c\u5c06\u524d\u5411\u901a\u9053\u4f20\u9012\u51fd\u6570\u4e0e\u53cd\u9988\u901a\u8def\u4f20\u9012\u51fd\u6570\u76f8\u4e58\uff0c\u5373\u5f97\u7cfb\u7edf\u7684\u5f00\u73af\u4f20\u9012\u51fd\u6570\uff0c\u90a3\u4e48\u5f00\u73af\u4f20\u9012\u51fd\u6570\u76f8\u5f53\u4e8eB(s)/R(s)\uff0c\u5373\u4e3aH(s)G1(s)G2(s)\uff0c\u524d\u9762\u6240\u8bf4\u7684\u201c\u65ad\u5f00\u201d\u5c31\u662f\u6307\u65ad\u5f00\u53cd\u9988\u4fe1\u53f7\u8fdb\u5165\u7684\u8282\u70b9 (\u53cd\u9988\u901a\u9053\u7684\u8f93\u51fa\u7aef)\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u5f00\u73af\u4f20\u9012\u51fd\u6570
根据题目已经给定开环传递函数为G(s)绘制该系统的开环幅相曲线。起点:A(0)=∞,ψ(0)=-270º;A(∞)=0,ψ(∞)=-180º。N + :半Nyquist曲线自上向下穿越 GH 平面 (-∞, - 1)区间的次数。N - :半Nyquist曲线自下向上穿越 GH 平面 (-∞, - 1)区间的次数。
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