1、第五章習題The engine,body,and tires of a racing vehicle affect acceleration and speed attainable.The speed control of the carrepresented by the 第五章習題The engine,body,and tires of a racing vehicle affect acceleration and speed attainable.The speed control of the carrepresented by the shown in FigureE5.2.(a

2、)Calculate easpeed.(b)CalculateovershootofthespeedtoaE5.3Foryears,Amtrakhasstruggledtoattractpassengersonago.During the same time,foreign railroads were ssenger rail t profitably compete with -06,a U.S. Experimental magnetic ion showninFigureto provide contactless vehicle movement makes -06 technolo

3、g radically different from theto provide contactless vehicle movement makes -06 technolog radically different from the Metroliner.TheundersideoftheTR-06carriage(wheretheaaelectromagnets wraparound,pulling it up toward abovetheTheioncontrolisrepresentedbyFigureTable 5.6 for a nput,select K t the syst

4、em provide Table 5.6 for a nput,select K t the system provide expectedovershoottoanputofE5.5 A low-inertia plotter is shown in Figure system by (a)Calculatethesteadyerrorfora(b)Selectavalueofinput.Providethemosttwillresultinzeroovershoottoat(b)Selectavalueofinput.Providethemosttwillresultinzeroovers

5、hoottoatisPlot the poles and zeros of the system and discuss dominanceofthecomplexpoles.WhatovershootforadoyouEffective control of insulin injection can result in jection by means of a pump and a t measures sugar can be very effective.A pump and injection system has feedback control as shown in Figu

6、re E5.6.Calculate the gaint theovershoot ofthe step responsedue to the injection is y 7%.R(s) is the desired blood-levelandY(s),istheactualblood-sugarFigureE5.8 A unity negative feedback control system has the transferKs(s 2K G(s) (a)Determinethepercentovershootandsettingtime(usingasettingtransferKs

7、(s 2K G(s) (a)Determinethepercentovershootandsettingtime(usingasettingcriterion)duetoaunit (b)ForwhatrangeofKisthe settingtimen1A system ity feedback is shown E5.10.Determinethesteady-e error for a step and 6(s 5G(s) s(s 1)(s 3)(s 10We are all familiar with the Ferris wheel featured seGalesbueg,Illi

8、nois,in 1859;he later moved to Nevada and graduated from aer Polytechnic Institute in 1881. bridge construction.He conceived and constructed his wheel for the 1893 Columbian ition in Chicago. To upsetting passegers,set a t thewheel for the 1893 Columbian ition in Chicago. To upsetting passegers,set

9、a t the steady-e must be controlled to within 5% of the desired speed for systemshowninFigure(a) Determine the required gain K to achieve the steady-e(b) For the gain of the part(a),determine and plot the error for a distrbance D(s)=1/s.Does the speed change n5%?(setR(s)=0foreaseofAfeedbacksystemiss

10、howninFigure(a)Determine the steady-e error for a unit step when and(b)Select an appropriate value f errorisequaltozerofortheunitstp(s)tthesteady-and(b)Select an appropriate value f errorisequaltozerofortheunitstp(s)tthesteady-eAclosed-loop control system transfer function T(s) two dominant complex

11、conjugate poles.Sketch the nds-planewherethecomplexpolesshouldbelocatedmeetthegiven (a)0.6 0.8,n 10(b)0.5 0.707,n 10(c(d 0.5,5 n 10 0.707,5 n 0.6,n AsystemisshowninFigure E5.17(a).The responseto unit step,when K=1,is shown in Figure E5.17(b).Determine valueofKtthesteady-eerrorisequaltoP5.1 A importa

12、nt problem systems is the P5.1 A important problem systems is the camera.This effect occurs when the camera is mounted in moving designed to reduce the effect of scanning Aexpected.LetKg=Kf=1andtgis(a)Determinetheerrorofthesystem(a)Determinetheerrorofthesystemeerroris(c)The motor time constant is 0.

13、40s.Determine the loopgain ofvb)istthe setting time(to within 2% of the final norequaltoA specific closed-loop system is to be nput.The for an ed response to a forthesystemareasSetting(a)Identifythedesiredareaforthedominantrootsofthe(b)Determine thesmallest valueofathird root,r3,iftheconjugaterootsa

14、retorepresentthedominant(b)Determine thesmallest valueofathird root,r3,iftheconjugaterootsaretorepresentthedominantthird-order,and the feedback has a unity gain, Determine the forword transfer function,G(s)=Y(s)/E(s).when the setting time to within 2% of the final value is 0.6s and the percent isast

15、ronamicalexperiments.Theingcontrolsystemisto achieve 0.01 minute of arc and track solar objects apparent motion up to 0.21 minute per second. illustrated in Figure P5.5(a).The control system system shown in At(a)DeterminethegainK=K1K2 requiredttheresponse tod is as as reasonable with an overshoot n(

16、b)Determine(a)DeterminethegainK=K1K2 requiredttheresponse tod is as as reasonable with an overshoot n(b)Determine the steady-e error of the system for a step r(c)DeterminethevalueofK1K2forITAEoptimal systemfora nputand(2)aP5.6 A robot is programmed to have a tool or welding follow a prescribed path.

17、 Consider a robot t is to asfunctionoftheplant75(s G(s) s(s 5)(s The transfer function of the plant is for the closed-loop showninFigureP5.6(b).Calculatethesteady-eP5.7 Astronaut Bruce McCandless II took P5.7 Astronaut Bruce McCandless II took walk in space on February 7,1984,using the gas-jet repre

18、sentedbyagainK2,showninFigureP5.7(b).Theinertia esis25Kg-theequipmentandmanwithhisarmsatFIGURE P5.7 (a)Astronaut Bruce McCandless II is shown a few meters away from the earth-orbiting space shuttle, Challenger. He used a nitrogenpropelled handcontrolled device called the manned maneuvering unit.(Cou

19、rtesy of National Aeronautic and space Administration) (b)Block diagram of controller(a)Determine the sary gain K3 to ain a steady-eerrorequalFIGURE P5.7 (a)Astronaut Bruce McCandless II is shown a few meters away from the earth-orbiting space shuttle, Challenger. He used a nitrogenpropelled handcon

20、trolled device called the manned maneuvering unit.(Courtesy of National Aeronautic and space Administration) (b)Block diagram of controller(a)Determine the sary gain K3 to ain a steady-eerrorequalto1cmwhentheinputisa With this gain K3,determine the nesarygainK1K2inorder to restrict the percent overs

21、hoot to 10%.Determine annalytically the gain K1K2 in order to theISEperformanceindexforaElectronic pacemakers speed of the heart pump.A human hearts regulate ed closed-loop tincludes a pacemaker and measurement of the heart rate shown in Figure P5.16.The transfer function of the heart pump and the p

22、acemake is found to be:KG(s) s(s /12DesignlifieroyieldasystemKG(s) s(s /12Designlifieroyieldasystemsettingtimea step disturbance of n 1 second.The overshoot to a indesiredheartrateshouldbenFIGUREP5.16HeartFindasuitablerangeofIfthenominalvalueofKisK=10,find thesensitivityofthe system to a small chang

23、e in K.(c)Evaluatethesensitivityofpart(b)et(d)Evaluatethemagnitudeofthesensitivityatnormalheartof60AsystemisshowninFigure(a)Determinethesteady-eerrorforaunitofKandK1,whereE(s)=R(s)-(b)Select K1tthesteady-(a)Determinethesteady-eerrorforaunitofKandK1,whereE(s)=R(s)-(b)Select K1tthesteady-eerrorisAclos

24、ed-looptransferfunctionT(s)Y(s)(s8)(s2 8s(a)Determinethesteady-eerrorforaunitnputtthecomplexpolesdominate,anddetermineovershootandsettingtimetowithin2%ofthefinal(c)Plot the actual system response,and compare it with the estimate of part(b).AP5.3 A closed-loop system is shown in Figure AP5.3.Plot response to a unit nput for system with p=0, 0.5, 2,and Record the percent overshoot,rise time,and settling p varies.Describep .Compare the loca