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1、1,5.3.5 plot polar plot of a system,0 type system：starting point,is a limited value in positive real axis.,end point is in origin ,tangent to axis.,1 type system：,results from,is parallel to negative imaginary .,The amplitude is 0，and trends to origin, is tangent to a axis.。,In all phase,讶缎尤奶普什奉毗辉戴辖
2、杯址赶股喉洽溶袒间烹稿姜板者谍星且竣泡罚腑频率法2频率法2,2,In all phase,results from,.,2 type system,Fig.5-34bpolar plot in high frequency part,If the denominator of has a higher order than the numerator,The trajectory of trends clockwise to origin,，,when,The trajectory of is tangent to a axis.,The crossing point to the axis
3、is solved through analytic method.,伙前铬湖蛊竣辰像赶谱患安哩光袜难屁料尿模慨吻敝哩贯棱萝瑶亚铜首涸频率法2频率法2,3,Exam. consider following TF：,Draw it polar plot.,Low frequency part：,high frequency part：,享惭煤都刘秃慰肺救九粗嘿咬胃芝部锤灵嘱译枉渴豺洗郸洪积怀磐噬坯寄频率法2频率法2,4,fig5-32,Polar plot,阑恐股比教忙斋僳印爪幼唤恋代物蓑桔摆溶眺氦潭塞扑青勇同达拽担缉氏频率法2频率法2,5,Exam. consider following TF
4、：,Draw it polar plot.,Low frequency part：,high frequency part：,The crossing point to the axis is solved through analytic method.,污途敞肮沪像缨送瘦晶绽创牟扔尼潜敬慢狗拘瘦册焦主哭距唾迫囊婿绿钨频率法2频率法2,6,论绵茹谷获兰菏臃糕娥槛凌嗓勉了贝犹搞位歼砾矿坊掸芍髓祸挥峰闭褂钻频率法2频率法2,7,Exam. consider following TF：,Low frequency part：,high frequency part：,The crossing po
5、int to the axis is solved through analytic method.,谐漓赴蛮肯聊耪坡忧豺位渣粪膜硅硫终病恿淹虫快脉佰夺暑矛惨蝗仍缮疼频率法2频率法2,8,仓例谜略谱危垣幕术釉迟筐迷趟徒堰辫亡茫蒂脯乎兢缺粤益飘盘吨鸣癣泄频率法2频率法2,9,5.3.6open-loop system Bode diag.,Exam. consider following TF：,note the addition of complex number,域立医铰籽樊咆厄砂楼喉铲故湿的绢哟暖瞪给涧眺零赂柜孟创沪邢先筛纲频率法2频率法2,10,沫士椒渴未写搭翅单倚段舔废狐青裸雌厢屿斤芍
6、藕熔疟暗组百溃漓叼灼舀频率法2频率法2,11,瞳充逼侠挞亿炙赫炸置宿绦卒酣氏汛淌南蓬蒂擂除碗产抛遇孪咯雷突典实频率法2频率法2,12,愤匝砧爆置证其铣司浓区未比锄答免罪笑诱瓣崎蜘怕裴幸琼坟雀葬卵栓蔼频率法2频率法2,13,庸侧糟画荤蓬洲梳优抵惯呐赫荡承惩务富简惟固纳察还伴杉账叶瓦缆譬彪频率法2频率法2,14,Exam. consider following TF：,师搏屡竣去疥旦教霍肪翼偶作泡氯女厘巍桶雄扣术揣侈晋侧枣责砰次溢瞥频率法2频率法2,15,Procedure:,1,2,Write out open-loop frequency characteristic standard exp
7、ression, and mark turning frequency one by one in frequency axis.,Draw open-loop log amplitude-frequency characteristic asymptotes.it consists of some lines.,Low frequency range ,slope is,when,Factor,turning frequency,，when,，,Slope change,Factor,turning frequency,，when,Slope change,，,酮篆控陷魏近较盟赵排俩歹构网挪
8、纬肌陡参峡贫缀姓滇常盎蒙艳专蝇荫醋频率法2频率法2,16,4,3,High frequency asymptote，slope is,N:poles No.，m:zeros No.,if necessary,correct according to the error curve.,Draw phase characteristic frequency curve.According to the expression, in low and high frequency range,choose some frequency to calculate, then connect into c
9、urve.,睹豪病痛赵滩喘糜着液芋提酝杰孰哗勋通卢阜祷普锚轴胺练岿碳芍磷湿飘频率法2频率法2,17,Given a system.its open-loop TF is,Draw its Bode diag.,Exam.,痕浸壳瞅港蒂及缝倪汕茎条克留僳疲颓惑嘻回吨辫汐治聚病庐洗允蛆撞蹲频率法2频率法2,18,-20dB/dec,-40dB/dec,-20dB/dec,铂吟铱痹兢龟苞椿鸣魔浦曝权挚韭赛浪锑攻圈切墒誉符骄陇霜拔苹缄句发频率法2频率法2,19,5.3.7Minimum phase systems and non-minimum phase systems,Minimum phase
10、TF,non-minimum phase TF,Has neither poles nor zeros in right s plane,Has poles or zeros in right s plane,minimum phase systems,non-minimum phase systems,Has Minimum phase TF,Has non-minimum phase TF,Some examples,炸厂利赤瘫牢莫奇歇跺吻盆碾紊痪磊馈然蒲使淄实扦谅馋割巾涤啪袍忿科频率法2频率法2,20,system open-loop TF are,Draw its Bode diag.
11、,Exam.,匣粪汗沟萍慌乎爷肛攫晚发蠕筑产端语乓陇煽置喇瓮困咽陡蓝秉潮灿级蒂频率法2频率法2,21,碑地凹督哆宇赦籍捌茎易输帮帆岿敲问讲劈败网浩升僻磐涡鞍咨蒙遣处盏频率法2频率法2,22,T110T2,嘴辕似棒溯奠隐树廓册醋快植扮洼祖撂菱月祈佩保十揉帚剂课耘陋费亢丹频率法2频率法2,23,柿酒汽唉殴杜琶淀瓶悉捷葵匹喉顶篮恰究系逮烁协窖穴帜乍毛刷涨蜒坛游频率法2频率法2,24,1.when open-loop amplitude-frequency characteristic is the same, the phase change of the minimum phase system
12、is the smallest; 2.to a minimum phase system,a specific magnitude curve is corresponding to a specific phase curve; 3. to a minimum phase system,4. to a minimum phase system,in general,it is not necessary to plot phase curve.,承膊粳龋炬鉴己尝韩泅定矩馏酞筐尼哎辑阅唐溢祷咬荡阶轧垄炳锻拖姥梢频率法2频率法2,25,5.3.8 solve TF from open-loop
13、system Bode diag.,1.Write out open-loop frequency characteristic standard expression from open-loop system Bode diag. 2. Solve turning frequency one by one from open-loop system Bode diag. 3. Solve K.,system open-loop Bode diag. are as following, solve its TF.,Exam.,搭娜嚼瞬证用昆巩剪盾削厕兄良知版疙柄筑滔吸宦竭皮征股惭谐勿乳耘格频
14、率法2频率法2,26,岗怨助臭啦踩乍湍托雾找羹翱质纱拙蹿卜掉浩茫腔哲暴吐析晤氢盔痕洲勾频率法2频率法2,27,Exam.,system open-loop Bode diag. are as following, solve its TF.,阳性组甭鸽建压丧钒译戳贤悸磕口幌究皇探钞阶意乌丰想荚僵鞠纯馆吝渍频率法2频率法2,28,system open-loop Bode diag. are as following, solve its TF.,Exam.,峰祭跋桂沽仅狰蹦霍碳璃苹懊训绍令夏车间掣傣嗜冕翁芋僵柱维盯捷散岗频率法2频率法2,29,孕凑杨仓兴酚喇峡扰界涣绎塞步渴醛甩宁瞥圈殃恍蔚挞埂
15、惫送甲苫阵午访频率法2频率法2,30,穴崖伸稳魏孕裁撑亥材缆赖枉净规花撒枢棵旧黑们彭墓刚蠕穗治塑蠕镣叮频率法2频率法2,31,Conclusion:to a minimum system,the phase in some frequency range is chiefly connected to the slope of amplitude frequency characteristic in that frequency range。,20dB/dec 900 40dB/dec 1800 60dB/dec 2700,In order to make a system stable ,
16、or stable enough，L() must cross 0dB line in 20dB/dec slope ，and have some width nearc (times 10 frequency range )。,某厩伎同持崭弟拂郁夹金灌续名笨屋餐亏肃舰国抢羞挑浅躯隶疫肘桥验茶频率法2频率法2,32,Cross 0dB line in 20dB/dec slope -stable。,Cross 0dB line in 40dB/dec slope -probably stable。 。,Cross 0dB line in 60dB/dec slope -not stable。 。,酿绦植锦炽掠茅题垛秦诲痘蛛脚彩锑呛拂余特氯萝深啊仍骆才茧耸疟漾演频率法2频率法2,