已知反馈系统的开环传递函数如何求这个系统的单位阶跃响应 已知单位反馈系统的开环传递函数为G(s)=4/s(s+5),...
\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=====================
\u5148\u5224\u7a33\uff0c\u7136\u540e\u4e58\u4ee51/s\uff0c\u7b97\u4e09\u4e2a\u53c2\u6570\u3002\u5b66\u5b8c\u592a\u591a\u5e74\uff0c\u6211\u5df2\u7ecf\u60f3\u4e0d\u8d77\u6765\u4e86\uff0c\u4f60\u627e\u672c\u4e66\uff0c\u7167\u7740\u516c\u5f0f\u6765
根据开环传递函数求出闭环传递函数，例如开环传递函数为G(s),反馈支路为H(s)则闭环传递函数为T(S)=G(S)/(1+G(S)H(S)),然后系统的阶跃相应就是Y(S)=T(S)*（1/S）,其中1/S是阶跃信号的拉普拉斯变换H(s)=G(s)/(1+G(s)*H(s))
H(s)是反馈的传递函数
单位介跃响应是:H(s)*(K/S)的逆laplace运算
绛旓細鍗曚綅鍙嶉绯荤粺鐨勫紑鐜紶閫掑嚱鏁涓 G(s) = 10/s^2, 鍒欓棴鐜紶閫掑嚱鏁 = G(s)/{1+G(s)} = (s^2)/(s^2+10).
绛旓細瑙ｇ瓟濡備笅锛氶鍏堢郴缁熶负1鍨嬬郴缁燂紝鐞嗙敱锛氬垎姣嶄笂鑳芥彁鍒板椤瑰紡澶栭儴鐨剆涓轰竴娆★紝濡傛灉鏈変袱涓猻鐨勮瘽锛屽氨鏄簩鍨嬬郴缁燂紝浠ユ绫绘帹銆傚叾娆★紝鍗曚綅闃惰穬鍝嶅簲绋虫佸兼槸1锛岀悊鐢卞涓嬶細鏍规嵁鏄崟浣鍙嶉绯荤粺涓旀湁寮鐜浼犲嚱鏈夊叕寮徫=G/(1+G)锛屽緱鍒拔=K/(7s2+s+K);鑰岀郴缁熻緭鍑篊(s)=R(s)*桅(s)=(1/s)*K/(7s2+s+K...
绛旓細宸茬煡鍗曚綅鍙嶉绯荤粺鐨勫紑鐜紶閫掑嚱鏁G(s)H(s)=2.5(s+1)/(s(0.25s+1))璇曟眰鍦ㄥ弬鑰冭緭鍏ヤ綔鐢ㄤ笅鐨勭ǔ鎬佽宸?绛旓細鏃犵┓澶с傛绯荤粺寮鐜彧鏈変竴涓Н鍒嗙幆鑺傘傚畠鍙互鏃犺宸湴璺熻釜闃惰穬杈撳叆淇″彿锛屼篃鍙互鏈夎宸湴璺熻釜鏂滃潯杈撳叆淇″彿銆備絾璺熻釜鍔犻熷害淇″彿:t^2 鐨勯潤鎬佽宸槸鏃犵┓澶х殑銆
绛旓細鐢卞崟浣鍙嶉绯荤粺鐨勫紑鐜紶閫掑嚱鏁寰楅棴鐜紶閫掑嚱鏁癎0(s)锛1/锛1锛婫(s)锛夈傞棴鐜紶閫掑嚱鏁扮殑鍒嗘瘝鐢ㄥ姵鏂垽鎹垽鏂郴缁熺ǔ瀹氭э紝寰楀嚭K鐨勮寖鍥淬傚亣璁剧郴缁熺殑鍗曚竴杈撳叆R 锛坰锛夊拰鍗曡緭鍑篊 锛坰锛夛紝鍚戝墠閫氶亾浼犻掑嚱鏁癎1 锛坰锛 G2 锛坰锛夊拰鍙嶉鏄秷鏋佸弽棣圚 锛坰锛夛細涓昏绯荤粺鐨勫弽棣堣矾寰勬槸鈥滀汉涓衡濇柇寮杩炴帴锛屽拰杩滄湡閫氶亾...
绛旓細G(s)=H(s)/(1+/-H(s))鍒嗘瘝閲屽姞鍑忔槸鐪嬫槸鍗曚綅璐鍙嶉杩樻槸姝ｅ弽棣堬紝璐熷弽棣堝氨鍙+ H鏄寮鐜紶閫掑嚱鏁
绛旓細s=tf('s'); %鐢熸垚鎷夋櫘鎷夋柉鍙橀噺s G=10/(s*(s+1)); %鐢熸垚寮鐜紶閫掑嚱鏁 [mag,phase,w]=bode(G); %鑾峰彇瀵规暟棰戠巼鐗规т笂姣忎釜棰戠巼w瀵瑰簲鐨勫箙鍊煎拰鐩镐綅瑙 [Gm,Pm]=margin(G); %璁＄畻寮鐜紶閫掑嚱鏁扮殑骞呭艰閲忓拰鐩镐綅瑁曢噺 DPm=45; %鏈熸湜鐨勭浉浣嶈閲 MPm=DPm-Pm+5; %鏍℃缃戠粶...
绛旓細G(s)=k/s(Ts+1)D(s)=Ts^2+s+k 閫氳繃鍔虫柉鍒ゆ嵁锛歍锛孠鍏ㄥぇ浜0锛绯荤粺绋冲畾
绛旓細璁插埌鍗曚綅璐鍙嶉锛岀煡閬揋(s)=4/s(s+1)銆傞偅涔圷(s)/X(s)=G(s)/(1+G(s))=4/(S^2+S+4)浜岄樁绯荤粺鐨G(s)鏈変釜閫氬紡锛毾塶^2 G(s) = --- S^2 + 2*味*蠅n S+ 蠅n^2 瀵瑰簲涓婇潰鐨勫紡瀛愬氨寰堝鏄撴眰鍑合塶鍜屛讹紝蠅n=2锛屛=0.25 宄板兼椂闂 tp=蟺/蠅d=蟺/(蠅n*sqrt(1-...
绛旓細宸茬煡鍗曚綅璐鍙嶉绯荤粺鐨勫紑鐜紶閫掑嚱鏁涓篏=K/S(1/2S+1)(1/6S+1),璇曠敤棰戠巼娉曡璁′覆鑱旀粸鍚庢牎姝ｈ缃,浣跨郴缁熺殑鐩镐綅瑁曞害涓簓=40,澧炵泭瑁曞害涓嶄綆浜10db,闈欐侀熷害璇樊绯绘暟K=1/7s,鍓垏棰戠巼涓嶄綆... 宸茬煡鍗曚綅璐熷弽棣堢郴缁熺殑寮鐜紶閫掑嚱鏁颁负G=K/S(1/2S+1)(1/6S+1),璇曠敤棰戠巼娉曡璁′覆鑱旀粸鍚庢牎姝ｈ缃,浣跨郴缁熺殑鐩镐綅瑁曞害涓簓...
绛旓細R(s)=2/(s^2+4)桅(s)=G(s)/(1+G(s))=1/(s+2)鎵浠ワ細C(s)=R(s)*桅(s)=2/(s^2+4)*1/(s+2)=2/[(s+2)*(s^2+4)]锛岃繖鏄痵鍩熺殑瑙ｏ紝鐢ㄩ儴鍒嗗垎寮忓睍寮娉曞皢澶氶」寮忓睍寮鎴愶細C(s)=0.25/(s+2)-0.25s/(s^2+4)+0.25*2/(s^2+4)鐒跺悗鐢ㄦ媺鏅媺鏂嗗彉鎹㈠皢杩欏嚑涓...
