1. 寮曡█
      PID锛堟瘮渚�-绌嶅垎-寰垎锛夋帶鍒跺櫒浣滅偤鏈€鏃╁(sh铆)鐢ㄥ寲鐨勬帶鍒跺櫒宸叉湁50澶氬勾姝峰彶锛屽洜鍏跺叿鏈夌畻娉曠啊(ji菐n)鍠�銆侀妫掓€уソ銆佸彲闈犳€ч珮銆佺洿瑙€鎬уソ绛夊劒(y艒u)榛�(di菐n)琚唬娉涚殑鎳�(y墨ng)鐢ㄤ簬宸ユキ(y猫)閬庣▼鎺у埗鍙婇亱(y霉n)鍕�(d貌ng)鎺у埗涓璠1]銆傚父瑕�(gu墨)PID鎺у埗鏁堟灉鐨勫劒(y艒u)鍔�锛屼笉鍍呭儏鍙栨焙浜庢帶鍒剁郴绲�(t菕ng)妯″瀷鐨勭簿纰虹▼搴︼紝閭勫繀闋堣(di脿o)鏁村ソ涓夊€�(g猫)鍙冩暩(sh霉)鐨勯棞(gu膩n)绯�锛岃€岄€欑ó闂�(gu膩n)绯讳笉涓€瀹氭槸绨�(ji菐n)鍠殑绶氭€х祫鍚�銆傚(sh铆)闅涚殑宸ユキ(y猫)閬庣▼鍙婇亱(y霉n)鍕�(d貌ng)閬庣▼寰€寰€鍏锋湁鏅�(sh铆)璁婃€�銆佽畩鍙冩暩(sh霉)銆佽畩绲�(ji茅)妲�(g貌u)绛変笉纰哄畾鎬у強寰堝挤(qi谩ng)鐨勯潪绶氭€э紝绮剧⒑鐨勬暩(sh霉)瀛�(xu茅)妯″瀷闆ｄ互寤虹珛锛屾澶栵紝甯歌(gu墨)PID閭勬湁瀵�(sh铆)鐝�(xi脿n)鍦ㄧ窔瑾�(di脿o)鏁村洶闆�锛屽弮鏁�(sh霉)闁撶浉浜掑奖闊匡紝鍙冩暩(sh霉)鏁村畾鏅�(sh铆)闁撻暦(zh菐ng)绛夌己榛�(di菐n)锛岄洠浠ュ彇寰楃悊鎯崇殑鎺у埗鏁堟灉銆�
      闅ㄨ憲鎺у埗鐞嗚珫鐨勭櫦(f膩)灞曪紝灏囨噳(y墨ng)鐢ㄥ唬娉涚殑PID鎺у埗鍣ㄨ垏鏅鸿兘鎺у埗鐞嗚珫鐩哥祼(ji茅)鍚圼2]鎴愮偤鏅鸿兘鎺у埗鐮旂┒鐨勬柊鏂瑰悜锛岀缍�(j墨ng)缍�(w菐ng)绲�(lu貌)绠楁硶鍏锋湁閫艰繎浠绘剰闈炵窔鎬ц〃閬�(d谩)鑳藉姏锛屽緢寮�(qi谩ng)鐨勮嚜瀛�(xu茅)缈�(x铆)鑳藉姏鍜屾鎷帹寤ｈ兘鍔�锛屽湪瑙ｆ焙楂樺害闈炵窔鎬у拰涓嶇⒑瀹氱郴绲�(t菕ng)鏂归潰鏈夊緢澶х殑鐨勬經鑳�锛屾噳(y墨ng)鐢ㄧ缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛屽彲浠ュ緸寰�(f霉)闆滅殑PID涓夊€�(g猫)鍙冩暩(sh霉)绲勫悎涓皨姹傛渶浣崇殑绶氭€х祫鍚�锛屼娇绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鍜孭ID鏈唱(zh矛)绲�(ji茅)鍚�銆傚緸鑰屼娇寰楁帶鍒跺櫒鍏锋湁杓冨ソ鐨勮嚜閬╂噳(y墨ng)鎬�锛屽(sh铆)鐝�(xi脿n)鍙冩暩(sh霉)鐨勮嚜鍕�(d貌ng)瀵�(sh铆)鏅�(sh铆)瑾�(di脿o)绡€(ji茅)锛岄仼鎳�(y墨ng)閬庣▼鐨勮畩鍖�锛屾彁楂樼郴绲�(t菕ng)浜嗙殑榄鎬у拰鍙潬鎬с€�
2. BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)
2.1 BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勬(g貌u)鎴愬強瑷�(sh猫)瑷�(j矛)[3]
      BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鏄竴绋叿鏈変笁灞ゆ垨涓夊堡浠ヤ笂鐨勭缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛屽寘鎷几鍏ュ堡銆侀毐鍚堡銆佽几鍑哄堡锛屼笂涓嬪堡涔嬮枔瀵�(sh铆)鐝�(xi脿n)鍏ㄩ€ｆ帴锛岃€屾瘡灞ょ缍�(j墨ng)鍏冧箣闁撶劇閫ｆ帴銆傜暥(d膩ng)涓€灏�(du矛)瀛�(xu茅)缈�(x铆)妯ｆ湰鎻愪緵绲︾恫(w菐ng)绲�(lu貌)鍚�锛岀缍�(j墨ng)鍏冪殑婵€娲诲€煎緸杓稿叆灞ょ稉(j墨ng)鍚勪腑闁撳堡鍚戣几鍑哄堡鍌虫挱锛屽湪杓稿嚭灞ょ殑鍚勭缍�(j墨ng)鍏冪嵅寰楃恫(w菐ng)绲�(lu貌)鐨勮几鍏ラ熆鎳�(y墨ng)銆傛帴涓嬩締锛屾寜鐓ф笡灏戠洰妯�(bi膩o)杓稿嚭鑸囧(sh铆)闅涜宸殑鏂瑰悜锛屽緸杓稿嚭灞ょ稉(j墨ng)閬庡悇涓枔灞ら€愬堡淇鍚勯€ｆ帴娆�(qu谩n)鍊�锛屾渶鍚庡洖鍒拌几鍏ュ堡锛岄€欑ó绠楁硶鍗矪P绠楁硶銆傞毃钁楅€欑ó瑾ゅ樊閫嗙殑鍌虫挱淇涓嶆柗閫�(j矛n)琛�锛岀恫(w菐ng)绲�(lu貌)灏�(du矛)杓稿叆妯″紡闊挎噳(y墨ng)鐨勬纰虹巼涔熶笉鏂蜂笂鍗�銆�
锛�1锛夎几鍏ヨ几鍑哄堡鐨勮ō(sh猫)瑷�(j矛)
      杓稿叆灞ょ殑瑷�(sh猫)瑷�(j矛)鍙互鏍规摎(j霉)闇€瑕佹眰瑙ｇ殑鍟忛鍜屾暩(sh霉)鎿�(j霉)琛ㄧず鏂瑰紡纰哄畾锛岃嫢杓稿叆淇¤櫉(h脿o)鐐烘ā鎿尝褰�锛岄偅涔堣几鍏ュ堡鍙互鏍规摎(j霉)娉㈠舰鐨勯噰妯ｉ粸(di菐n)鏁�(sh霉)鐩拝鑵氳几鍏ュ柈鍏冪殑缍暩(sh霉)锛屼篃鍙互鐢ㄤ竴鍊�(g猫)鍠厓杓稿叆锛岄€欐槸杓稿叆妯ｆ湰鐐洪噰妯ｇ殑鏅�(sh铆)闁撳簭鍒�銆傝几鍑哄堡鐨勭董鏁�(sh霉)鍙互鏍规摎(j霉)浣跨敤鑰呯殑瑕佹眰纰哄畾銆傚鏋淏P缍�(w菐ng)绲�(lu貌)鐢ㄤ綔鍒嗛鍣�锛岄鍒ユā寮忎竴鍏辨湁m鍊�(g猫)锛岄偅涔堣几鍑哄堡绁炵稉(j墨ng)鍏冪殑鍊�(g猫)鏁�(sh霉)鐐簃鎴栬€�銆�
锛�2锛夐毐灞ょ殑瑷�(sh猫)瑷�(j矛)
      闅卞堡鍠厓鐨勬暩(sh霉)鐩垏鍟忛鐨勮姹�銆佽几鍏�/杓稿嚭鍠厓鐨勬暩(sh霉)鐩兘鏈夌洿鎺ョ殑闂�(gu膩n)绯�锛岄毐鍠厓鐨勬暩(sh霉)鐩お澶氭渻(hu矛)灏�(d菐o)鑷村(xu茅)缈�(x铆)鏅�(sh铆)闁撻亷闀�(zh菐ng)銆佽宸笉涓€瀹氭渶浣�锛屼篃鏈�(hu矛)灏�(d菐o)鑷村閷�(cu貌)鎬у樊銆佷笉鑳借瓨(sh铆)鍒ヤ互鍓嶆矑鏈夌殑妯ｆ湰绛夌瓑锛屽洜姝わ紝涓€瀹氬瓨鍦ㄤ竴鍊�(g猫)鏈€浣崇殑闅卞柈鍏冩暩(sh霉)锛岄€氬父鐢ㄤ互涓嬩笁鍊�(g猫)鍏紡渚嗛伕鎿囨渶浣抽毐鍠厓鏁�(sh霉)锛�
1锛�锛屽叾涓璳鐐烘ǎ鏈暩(sh霉)锛宯鐐鸿几鍏ュ柈鍏冩暩(sh霉)銆�
2锛�锛屽叾涓璵鐐鸿几鍑虹缍�(j墨ng)鍏冩暩(sh霉)锛宯鐐鸿几鍏ュ柈鍏冩暩(sh霉)锛宎鐐篬1,10]涔嬮枔鐨勫父鏁�(sh霉)銆�
3锛�锛屽叾涓璶鐐鸿几鍏ュ柈鍏冩暩(sh霉)銆�
2.2 鍏稿瀷绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)
涓€鍊�(g猫)鍏稿瀷鐨勪笁灞ょ缍�(j墨ng)缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)濡備笅鍦栨墍绀猴細

鍦�1  BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)鍦�

      鍏朵腑锛� 銆� 銆佲€�銆� 鐐� BP缍�(w菐ng)绲�(lu貌)鐨勮几鍏�锛� 銆� 銆佲€�銆� 鐐� BP缍�(w菐ng)绲�(lu貌)鐨勮几鍑猴紝灏�(du矛)鎳�(y墨ng)PID鎺у埗鍣ㄧ殑涓夊€�(g猫)鍙冩暩(sh霉)锛�鐐鸿几灞ゅ埌闅卞惈灞ょ殑閫ｆ帴娆�(qu谩n)鍊�锛�鐐洪毐鍚堡鍒拌几鍑哄堡鐨勯€ｆ帴娆�(qu谩n)鍊�銆傞€氶亷绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勮嚜瀛�(xu茅)缈�(x铆)銆佸姞娆�(qu谩n)绯绘暩(sh霉)鐨勮(di脿o)鏁�锛屼娇绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)杓稿嚭灏�(du矛)鎳�(y墨ng)浜庢煇绋渶鍎�(y艒u)鎺у埗瑕�(gu墨)寰嬩笅鐨凱ID鎺у埗鍣ㄥ弮鏁�(sh霉)銆� 
鍦栦竴涓悇鍙冩暩(sh霉)涔嬮枔鐨勯棞(gu膩n)绯籟4]濡備笅锛�
杓稿叆灞わ細

闅卞惈灞わ細    
杓稿嚭灞わ細    
鍙栨€ц兘鎸囨(bi膩o)鐐猴細锛屾寜鐓ф搴︿笅闄嶆硶淇缍�(w菐ng)绲�(lu貌)鐨勬瑠(qu谩n)鍊�锛屼娇鏈€灏忥紝淇鏂规硶濡備笅锛�
闅卞惈灞わ細     
杓稿嚭灞わ細     
3. 绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗鍣ㄥ強鎺у埗绠楁硶
1銆丅P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗鍣ㄧ祼(ji茅)妲�(g貌u)濡備笅鍦栨墍绀猴細

鍦�2  绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鎺у埗鍣ㄧ祼(ji茅)妲�(g貌u)鍦�

      鐢卞湒鍙煡锛氭帶鍒跺櫒鐢卞叐閮ㄥ垎绲勬垚锛屽垎鍒ョ偤甯歌(gu墨)PID鎺у埗鍜岀缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛屽叾涓�锛屽父瑕�(gu墨)PID鐩存帴灏�(du矛)琚帶灏�(du矛)璞￠€�(j矛n)琛岄枆鐠�(hu谩n)鎺у埗锛屽苟涓斿叾鎺у埗鍙冩暩(sh霉)Kp銆並i銆並d鐐哄湪绶氳(di脿o)鏁存柟寮�锛涚缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛屾牴鎿�(j霉)绯荤当(t菕ng)鐨勯亱(y霉n)琛岀媭鎱�(t脿i)锛岃(di脿o)绡€(ji茅)PID鎺у埗鍣ㄧ殑鍙冩暩(sh霉)锛屼互鏈熼仈(d谩)鍒版煇绋€ц兘鎸囨(bi膩o)鐨勬渶鍎�(y艒u)鍖�锛屼娇杓稿嚭灞ょ缍�(j墨ng)鍏冪殑杓稿嚭灏�(du矛)鎳�(y墨ng)浜嶱ID鎺у埗鍣ㄧ殑涓夊€�(g猫)鍙(di脿o)鍙冩暩(sh霉)銆傞€氶亷绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勮嚜瀛�(xu茅)缈�(x铆)銆佸姞娆�(qu谩n)绯绘暩(sh霉)鐨勮(di脿o)鏁�锛屼娇绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)杓稿嚭灏�(du矛)鎳�(y墨ng)浜庢煇绋渶鍎�(y艒u)鎺у埗瑕�(gu墨)寰嬩笅鐨凱ID鎺у埗鍣ㄥ弮鏁�(sh霉)銆�
2銆佹帶鍒剁畻娉�
绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鐨勬帶鍒剁畻娉昜5]濡備笅锛�
(1).  纰哄畾绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勭祼(ji茅)妲�(g貌u)锛屽嵆纰哄畾杓稿叆绡€(ji茅)榛�(di菐n)鏁�(sh霉)鍜岄毐鍚堡绡€(ji茅)榛�(di菐n)鏁�(sh霉),骞剁郸鍑哄悇灞ゅ姞娆�(qu谩n)绯绘暩(sh霉)鐨勫垵鍊�鍜�锛屽苟閬稿畾瀛�(xu茅)缈�(x铆)閫熺巼 鍜屾叄鎬х郴鏁�(sh霉) 锛屼护k =1锛�
(2).  閲囨ǎ寰楀埌r(k)鍜寉(k)锛岃▓(j矛)绠楃暥(d膩ng)鍓嶆檪(sh铆)鍒昏宸甧rror(k)= r(k)-y(k)锛�
(3).  瑷�(j矛)绠楀悇绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勮几鍏�銆佽几鍑�锛屽叾杓稿嚭灞ょ殑杓稿嚭鍗崇偤PID鎺у埗鍣ㄧ殑涓夊€�(g猫)鎺у埗鍙冩暩(sh霉)Kp銆並i銆並d锛�
(4).  瑷�(j矛)绠� PID鎺у埗鍣ㄧ殑杓稿嚭锛�
(5).  閫�(j矛n)琛岀缍�(j墨ng)缍�(w菐ng)绲�(lu貌)瀛�(xu茅)缈�(x铆)锛屽湪绶氳(di脿o)鏁村姞娆�(qu谩n)绯绘暩(sh霉)锛屽(sh铆)鐝�(xi脿n) PID鎺у埗鍙冩暩(sh霉)鐨勮嚜閬╂噳(y墨ng)瑾�(di脿o)鏁�锛�
(6).  浠=k+1锛岃繑鍥炵(1)姝ャ€�
4. 浠跨湡瀵�(sh铆)渚�
4.1 琚帶灏�(du矛)璞�
瑷�(sh猫)琚帶灏�(du矛)璞＄殑杩戜技鏁�(sh霉)瀛�(xu茅)妯″瀷鐐猴細锛屾墍閬哥殑杓稿叆淇¤櫉(h脿o)鐐轰竴鏅�(sh铆)璁婁俊铏�(h脿o)锛�
绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勭祼(ji茅)妲�(g貌u)閬告搰4-5-3锛屽(xu茅)缈�(x铆)閫熺巼鐐�0.55锛屾叄鎬х郴鏁�(sh霉)鐐�0.04锛屽姞娆�(qu谩n)绯绘暩(sh霉)鍒濆鍊肩偤鍗€(q奴)闁揫-0.5锛�0.5]涓婄殑闅ㄦ(j墨)鏁�(sh霉)锛岄噰妯ｉ牷鐜囩偤1000Hz銆�
Matlab浠跨湡绲�(ji茅)鏋滃鍦栦笁鎵€绀猴細

鍦�3-1  杓稿叆杓稿嚭鏇茬窔

鍦�3-2  瑾ゅ樊鏇茬窔

4.2 浠跨湡绲�(ji茅)鏋滃垎鏋�
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鍙冭€冩枃鐛�(xi脿n)
[1]  婧壇, 浠樿垐姝�. 绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌) PID 鍦ㄦ韩搴︽帶鍒剁郴绲�(t菕ng)涓殑鐮旂┒鑸囦豢鐪焄J].寰▓(j矛)绠楁(j墨)淇℃伅,2004(7):3-4.
[2]  鏄撶辜閸�.鏅鸿兘鎺у埗鎶€琛�(sh霉)[M].鍖椾含:鍖椾含宸ユキ(y猫)澶у(xu茅)鍑虹増绀�,1999:95- 138
[3]  绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐞嗚珫鑸嘙ATLAB 7瀵�(sh铆)鐝�(xi脿n)[M].鍖椾含:闆诲瓙宸ユキ(y猫)鍑虹増绀�.2005
[4]  鍚冲亯锛� 鏅忓あ(m猫ng)浜�锛� 榄忚埅淇�. 鍩轰簬绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨凱ID鎺у埗鍙婂叾浠跨湡锛岀従(xi脿n)浠ｉ浕瀛愭妧琛�(sh霉), 2009
[5]  鍔夐噾鐞�. 鍏堥€�(j矛n)PID 鎺у埗鍙婂叾MATLAB 浠跨湡[M ]. 鍖椾含: 闆诲瓙宸ユキ(y猫)鍑虹増绀�, 2003.