鎽� 瑕侊細鍦ㄥ€掔珛鎿虹郴绲�(t菕ng)鐨勬暩(sh霉)瀛�(xu茅)妯″瀷鍩虹(ch菙)涓婏紝灏嶇郴绲�(t菕ng)閫�(j矛n)琛屼簡鎬ц兘鍒嗘瀽銆傞噰鐢↙QR灏嶄竴绱氬€掔珛鎿洪€�(j矛n)琛屼簡鏈€鍎�(y艒u)鎺у埗鍣ㄧ殑瑷�(sh猫)瑷�锛屽苟灏囧叾鎳�(y墨ng)鐢ㄤ簬鍊掔珛鎿哄(sh铆)闅涙帶鍒朵腑锛屽(sh铆)鏅傛帶鍒舵晥鏋滆壇濂�銆� 闂�(gu膩n)閸佃锛�LQR锛屽€掔珛鎿�锛屽(sh铆)鏅傛帶鍒� [b][align=center]An Linear Inverted Pendulum Control Based on LQR Xie Lirong锛學ang Zhiyong锛學ang Li[/align][/b] Abstract锛�In this paper ,on the base of the model of the single inverted pendulum, analysy the capability of the system. An LQR - based on optimal control system is designed used to the actual control of an inverted pendulum and acquire a good effect. Keywords锛�LQR锛孖nverted Pendulum锛孯eal Control 0 寮曡█ 銆€銆€鍊掔珛鎿虹郴绲�(t菕ng)鏄潪绶氭€�銆佸挤(qi谩ng)钘曞悎銆佸璁婇噺鍜岃嚜鐒朵笉绌�(w臎n)瀹氱殑绯荤当(t菕ng)銆傜窔鎬т簩娆″瀷鏈€鍎�(y艒u)鎺у埗锛圠inear Quadratic Regulator鈥擫QR锛夊晱椤屽湪鐝�(xi脿n)浠ｆ帶鍒剁悊璜栦腑鍗犳湁闈炲父閲嶈鐨勪綅缃�銆傜敱浜庣窔鎬т簩娆″瀷锛圠Q锛夋€ц兘鎸囨(bi膩o)鏄撲簬鍒嗘瀽銆佽檿鐞嗗拰瑷堢畻锛岃€屼笖閫氶亷绶氭€т簩娆″瀷鏈€鍎�(y艒u)瑷�(sh猫)瑷堟柟娉曞緱鍒扮殑鎺у埗绯荤当(t菕ng)鍏锋湁杓冨ソ鐨勯妫掓€ц垏鍕曟厠(t脿i)鐗规€х瓑鍎�(y艒u)榛�(di菐n)锛岀窔鎬т簩娆″瀷鍦ㄦ帶鍒剁晫寰楀埌鏅亶閲嶈銆傞亱(y霉n)鐢↙QR灏嶅€掔珛鎿洪€�(j矛n)琛屾渶鍎�(y艒u)鎺у埗绯荤当(t菕ng),骞跺緸瀵�(sh铆)鏅傛帶鍒舵晥鏋滃嚭鐧�(f膩), 1 鍊掔珛鎿虹郴绲�(t菕ng)鍒嗘瀽 銆€銆€娣卞湷鍥洪珮鍏徃鐮斿埗闁嬬櫦(f膩)鐨勪竴绱氱洿绶氬€掔珛鎿篏IP-100-L ,瀹冩槸涓€鍊嬪柈杓稿叆澶氳几鍑虹殑鍥涢殠鎺у埗绯荤当(t菕ng),绲�(ji茅)妲�(g貌u)绲勬垚濡傚湒1鎵€绀恒€� [align=center] 鍦�1 銆€鍊掔珛鎿虹郴绲�(t菕ng)妲�(g貌u)鎴怺/align] 銆€銆€1.1 鍊掔珛鎿虹郴绲�(t菕ng)妯″瀷 銆€銆€灏嶅€掔珛鎿虹郴绲�(t菕ng)閫�(j矛n)琛屽彈鍔涘垎鏋怺1]鍙互寰楀埌绯荤当(t菕ng)鐨勭媭鎱�(t脿i)绌洪枔琛ㄩ仈(d谩)寮忕偤锛� 銆€銆€ 銆€銆€1.2 鍊掔珛鎿虹郴绲�(t菕ng)绌�(w臎n)瀹氭€у垎鏋� 銆€銆€灏嶅紡锛�1锛夋墍鎻忚堪鐨勫€掔珛鎿虹郴绲�(t菕ng)閫�(j矛n)琛岄殠韬嶉熆鎳�(y墨ng)鍒嗘瀽[2]銆傚皬杌婁綅绉诲拰鎿烘】瑙掑害闅庤簫闊挎噳(y墨ng)鏇茬窔濡傚湒2鍜屽湒3鎵€绀�銆� [align=center] 鍦�2 灏忚粖浣嶇Щ闅庤簫闊挎噳(y墨ng)鏇茬窔 鍦�3 灏忚粖瑙掑害闅庤簫闊挎噳(y墨ng)鏇茬窔[/align] 銆€銆€灏忚粖浣嶇Щ鍜屾摵妗胯搴﹂兘鏄櫦(f膩)鏁ｇ殑锛屽€掔珛鎿虹郴绲�(t菕ng)涓嶇┅(w臎n)瀹氥€� 銆€銆€1.3 鍊掔珛鎿虹郴绲�(t菕ng)鑳芥帶鎬у垎鏋� 銆€銆€绯荤当(t菕ng)鑳芥帶鎬ф槸鎺у埗鍣ㄨō(sh猫)瑷堢殑鍓嶆彁銆傜敱鑳芥帶鎬х煩闄=[B AB 鈥[sup]n-1[/sup]B ]锛屽湪MATLAB涓埄鐢ㄥ彲鎺ф€х煩闄ｇ殑ctrb鍛戒护渚嗚▓绠�锛屽彲浠ュ緱鍑篟ank锛圡锛�=4,鍙煡绯荤当(t菕ng)鍙帶銆� 2 LQR鎺у埗鍣ㄨō(sh猫)瑷� 銆€銆€2.1 浜屾鍨嬫渶鍎�(y艒u)鎺у埗鍘熺悊 銆€銆€瑷�(sh猫)绲﹀畾绶氭€у畾甯哥郴绲�(t菕ng)鐨勭媭鎱�(t脿i)鏂圭▼鐐� 銆€銆€ 銆€銆€浜屾鍨嬫€ц兘鎸囨(bi膩o)鍑芥暩(sh霉)[3]: 銆€銆€ 銆€銆€鍏朵腑:鍔犳瑠(qu谩n)闄鍜孯鏄敤渚嗗钩琛＄媭鎱�(t脿i)鍚戦噺鍜岃几鍏ュ悜閲忕殑娆�(qu谩n)閲�,Q鏄崐姝ｅ畾闄�,R闄ｆ槸姝ｅ畾闄�銆� 銆€銆€鏈€鍎�(y艒u)鎺у埗瑕�(gu墨)寰嬶細 銆€銆€ 銆€銆€ 銆€銆€鍏朵腑锛欿鐐烘渶鍎�(y艒u)鍙嶉澧炵泭锛孭鐐洪粠鍗℃彁鐭╅櫍鏂圭▼鐨勮В銆� 銆€銆€榛庡崱鎻愮煩闄ｆ柟绋嬶細 銆€銆€ 銆€銆€ 銆€銆€鍓�锛屾渶鍎�(y艒u)鍙嶉澧炵泭K鐐猴細 銆€銆€ 銆€銆€2.2 LQR鍙冩暩(sh霉) 銆€銆€鐢盡ATLAB瑾炲彞K=lqr锛圓,B,Q,R锛�,鍙朡=diag锛�1000,0,70,0锛夛紝姹傚緱K=[-31.623 ,-20.151,72.718,13.155]锛屽嵆鐐篖QR鎺у埗鍣ㄦ帶鍒跺櫒鍙冩暩(sh霉)[5]銆� 3 绯荤当(t菕ng)浠跨湡鑸囧(sh铆)鎺� 銆€銆€3.1绯荤当(t菕ng)浠跨湡 銆€銆€鍦∕ATLAB/Simulink鐠�(hu谩n)澧冩惌寤哄鍦�4鎵€绀轰豢鐪熸ā鍨媅4]銆� [align=center] 鍦�4 浠跨湡妯″瀷鍦朳/align] 銆€銆€閬�(y霉n)琛岀祼(ji茅)鏋滃鍦�5鎵€绀猴細 [align=center] 鍦�5 浠跨湡绲�(ji茅)鏋滃湒[/align] 銆€銆€鐢卞湒5鍙互鐪嬪嚭锛岀郴绲�(t菕ng)鑳借純濂界殑璺熻工闅庤簫淇¤櫉锛屾摵妗跨殑瓒呰(di脿o)閲忚冻澶犲皬,绌�(w臎n)鎱�(t脿i)瑾ゅ樊銆佷笂鍗囨檪闁撹垏瑾�(di脿o)鏁存檪闁撲篃绗﹀悎瑷�(sh猫)瑷堟寚妯�(bi膩o)瑕佹眰銆傞€欐檪濡傛灉鍐嶅澶 ,绯荤当(t菕ng)鐨勯熆鎳�(y墨ng)閭勬渻鏈夋墍鏀瑰杽,浣嗘槸鍦ㄤ繚璀塓瓒冲灏忓苟鍏奸¨鍏跺畠闊挎噳(y墨ng)鎸囨(bi膩o)鏅�,绯荤当(t菕ng)闊挎噳(y墨ng)宸茬稉(j墨ng)鑳藉婊胯冻瑕佹眰浜�銆� 銆€銆€3.2 绯荤当(t菕ng)瀵�(sh铆)鎺� 銆€銆€鍒╃敤鍥洪珮鍊掔珛鎿虹郴绲�(t菕ng)MATLAB瀵�(sh铆)鏅傛帶鍒跺钩鑷猴紝寤虹珛绯荤当(t菕ng)鏅傛帶妯″瀷濡傚湒6鎵€绀猴細 [align=center] 鍦�6 鏅傛帶妯″瀷鍦朳/align] 銆€銆€鍒╃敤LQR瑷�(sh猫)瑷堢殑鎺у埗鍣ㄥ皪鍊掔珛鎿洪€�(j矛n)琛屽(sh铆)鏅傛帶鍒�,鍙互浣垮€掔珛鎿洪仈(d谩)鍒扮┅(w臎n)瀹�,璧锋摵鏅傚皬杌婁綅缃拰鎿烘】瑙掑害闊挎噳(y墨ng)鏇茬窔濡傚湒7銆佸湒8鎵€绀�銆� [align=center] 鍦�7 璧锋摵閬庣▼灏忚粖浣嶇Щ瀵�(sh铆)鎺ф洸绶� 鍦�8 璧锋摵閬庣▼鎿烘】瑙掑害瀵�(sh铆)鎺ф洸绶歔/align] 銆€銆€鍦ㄥ€掔珛鎿虹郴绲�(t菕ng)绌�(w臎n)瀹氱殑鎯呮硜涓�,灏嶇郴绲�(t菕ng)鏂藉姞骞叉摼 , 灏忚粖浣嶇疆鍜屾摵妗胯搴﹂熆鎳�(y墨ng)鏇茬窔濡傚湒9銆佸湒10鎵€绀�銆� [align=center] 鍦�9 灏忚粖浣嶇Щ鍙楁摼鍕曞(sh铆)鎺ф洸绶� 鍦�10 鎿烘】瑙掑害鍙楁摼鍕曞(sh铆)鎺ф洸绶歔/align] 銆€銆€灏忚粖鑳借繀閫熻(di脿o)鏁�,浣挎暣鍊嬬郴绲�(t菕ng)鍦ㄥ緢鐭殑鏅傞枔鍏�(n猫i)鎭㈠京(f霉)骞宠　銆� 4 绲�(ji茅)鏉熻獮 銆€銆€閬�(y霉n)鐢↙QR瀵�(sh铆)鐝�(xi脿n)浜嗕竴绱氬€掔珛鎿虹殑鎺у埗锛屼豢鐪熷拰瀵�(sh铆)鎺ц瓑鏄庤ō(sh猫)瑷堟帶鍒跺櫒鐨勬湁鏁堟€�锛岀郴绲�(t菕ng)鍏锋湁鑹ソ鐨勭┅(w臎n)瀹氭€у拰榄鎬с€� 鍙冭€冩枃鐛�(xi脿n)锛� 銆€銆€[1]鍥洪珮绉戞妧鏈夐檺鍏徃.鍥洪珮鍊掔珛鎿鸿垏鑷嫊鎺у埗鍘熺悊瀵�(sh铆)椹�(y脿n)鎸囧皫(d菐o)鏇竅M].娣卞湷:鍥洪珮绉戞妧鏈夐檺鍏徃,2005骞�9鏈�銆� 銆€銆€[2]閯掍集鏁�.鑷嫊鎺у埗鐞嗚珫[M].鍖椾含:姗�(j墨)姊板伐妤�(y猫)鍑虹増绀撅紝2003骞�銆� 銆€銆€[3]鍔夎惫.鐝�(xi脿n)浠ｆ帶鍒剁悊璜朳M].鍖椾含:姗�(j墨)姊板伐妤�(y猫)鍑虹増绀�锛�2007骞�銆� 銆€銆€[4]鍚虫泬鐕�,寮甸洐閬�.MATLAB鍦ㄨ嚜鍕曟帶鍒朵腑鐨勬噳(y墨ng)鐢╗M] .瑗垮畨锛氳タ瀹夐浕瀛愮鎶€澶у(xu茅)鍑虹増绀�,2006骞�銆俒5]鐜嬪＋鐟�,寮靛嘲,闄冲織鍕�,瓒欏崝(xi茅)寤�.鐩寸窔涓€绱氬€掔珛鎿虹殑LQR鎺у埗鍣ㄨō(sh猫)瑷圼J].淇℃伅鎶€琛�(sh霉).2006骞�, 35锛�6锛�:98锝�99銆� 銆€銆€[6]鐜嬩徊姘�,瀛缓杌�,宀冲畯.鍩轰簬LQR鐨勫€掔珛鎿烘渶鍎�(y艒u)鎺у埗绯荤当(t菕ng)鐮旂┒[J].宸ユキ(y猫)鍎€琛ㄨ垏鑷嫊鍖栬缃�.2005骞�,3锛�6锛�:28锝�32銆�