控制工程课件

1、ch4 the performance of feedback control systems4.6 steady-state error of feedback control systemsfor unity negative feedback system, the steady-state error is:)(1)(lim)(lim)(lim00sgssrsseteesstssclosed-loop control systemsteady-state error for the three standard test inputs (h(s)=1)step input (r(t)=

2、a)ramp input (r(t)=at)acceleration input (r(t)=at2/2)0(1)(1)/(lim0gasgsasesss)(lim)0(lim)(1)/(lim0020ssgasgsasgsasesssss)(lim)(1)/(lim2030sgsasgsasesssstype number of systemthe general form of open-loop transfer function is: *11()( )()miin vvjjkszg ssspthe number of integration v reflect the trackin

3、g ability of the system, which is called type numbernjjmiistsskshsg11) 1() 1()()()() 1() 1() 1() 1(11lim110srststsssksnms)() 1() 1() 1() 1() 1() 1(lim1110srsskststsststssmnnskssrss)(lim10)()(lim0srsesesssopen-loop transfer function:steady-state error:steady-state error is dependent on 3 factors:type

4、 numberdc gaininput (amplitude & form) definition of three error constantsposition error constantvelocity error constantacceleration error constant)(lim0sgksp)(lim0ssgksv)(lim20sgsksa)( 1)(trtrsrksssrshsgsessss100lim)()()(11lim)()(lim0shsgkspskksp0limpsskre1step input:steady-state error:trtr)(20

5、0)()(1lim)()()(11limsrshsgssrshsgsessss)()(1lim0shsgsrs)()(lim0shssgksv10limskksvvsskre ramp input:steady-state error:2)2/()(trtr300)()(1lim)()()(11limsrshsgssrshsgsessss)()(1lim20shsgsrs)()(lim20shsgsksa20limskksaasskre acceleration input:steady-state error:the relationship between error constant a

6、nd type number0 k p 0 01 infinite k v 02 infinite infinite k atype number position velocity acceleration refer to table 5.5 (p263)an example and illustrationmobile robot steering controlp controller and pi controller112( )/g skks the three error constants describe the ability of a control system to

7、reduce or eliminate the steady-state error.the designer try to increase the error constants while maintaining an acceptable transient response. a compromise is needed. steady-state error of non-unity feedback system conversion into unit feedback systemfrom the error definition refer to example 5.4re

8、fer to example 5.54.7 performance indicesise:iae:itae:itse:optimum performance indices jtdttej02)(tdttej0)(tdttetj0)(tdtttej02)(performance indices:tdttej02)(goal of controller designtdtttytrtefj0),(),(),(the general form of the performance integral isthe goal of control system design is to minimize

9、 the performance indices by selecting suitable controller parameters.refer to some examples (p269-276)4.8 examples and simulationhubble telescope pointing controlaircraft roll control using simulinksequential design example:disk drive read systemself-learning after classrefer to p286-291pay attention to design processsummarytransient and steady-state performanceperformance indices and evaluationsteady-state error evaluationconcept of compromise or trade-off domin