自动控制理论第五章习题

1、第五章习题E5.2 The engine,body,and tires of a racing vehicle affect the acceleration and speed attainable.The speed control of the car is represented by the model shown in FigureE5.2.(a)Calculate the steady-state error of the car to a step command in speed.(b)Calculate overshoot of the speed to a step co

2、mmand.E5.3 For years,Amtrak has struggled to attract passengers on its routes in the Midwest,using technology developed decades ago.During the same time,foreign railroads were developing new passenger rail systems that could profitably compete with air travel.Two of these systems,the French TGV and

3、the Japanese Shinkansen,reach speed of 160 mph.The Transrapid-06,a U.S. Experimental magnetic levitation train,is shown in Figure E5.3(a). The use of magnetic levitation and electromagnetic propusion to provide contactless vehicle movement makes the Transrapid-06 technolog radically different from t

4、he existing Metroliner.The underside of the TR-06 carriage(where the wheel trucks would be on a conventional car)wraps around a guideway.Magnets on the bottom of the guideway attract electromagnets on the wraparound,pulling it up toward the guideway.This suspends the vehicles about one centimeter ab

5、ove the guideway. The levitation control is represented by Figure E5.3(b).(a)using Table 5.6 for a step input,select K so that the system provide an optimum ITAE response.(b)Using Figure5.3 determine the expected overshoot to a step input of I(s).E5.5 A low-inertia plotter is shown in Figure E5.5(a)

6、.This system may be represented by block diagram shown in Figure E5.5(b).(a)Calculate the steady error for a ramp input.(b)Select a value of K that will result in zero overshoot to a step input.Provide the most rapid response that is attainable. Plot the poles and zeros of the system and discuss the

7、 dominance of the complex poles.What overshoot for a step input do you expect?E5.6 Effective control of insulin injection can result in better lives for diabetic persons.Automatically controlled insulin jection by means of a pump and a sensor that measures blood sugar can be very effective.A pump an

8、d injection system has a feedback control as shown in Figure E5.6.Calculate the suitable gain K,so that the overshoot of the step response due to the drug injection is approximately 7%.R(s) is the desired blood-sugar level and Y(s),is the actual blood-sugar level.Figure E5.6E5.8 A unity negative fee

9、dback control system has the plant transfer function(a) Determine the percent overshoot and setting time (using a 2% setting criterion) due to a unit step input.(b) For what range of K is the setting time less than 1 second?E5.10 A system with unity feedback is shown in Figure E5.10.Determine the st

10、eady-state error for a step and ramp input whenE5.11 We are all familiar with the Ferris wheel featured at state fairs and carnivals,George Ferris was born in Galesbueg,Illinois,in 1859;he later moved to Nevada and then graduated from Rensselaer Polytechnic Institute in 1881. By 1891,Ferris had cons

11、iderable experience with iron,steel,and bridge construction.He conceived and constructed his famous wheel for the 1893 Columbian Exposition in Chicago. To avoid upsetting passegers,set a requirement that the steady-state speed must be controlled to within 5% of the desired speed for the system shown

12、 in Figure E5.11.(a) Determine the required gain K to achieve the steady-state requirement.(b) For the gain of the part(a),determine and plot the error e(t) for a distrbance D(s)=1/s.Does the speed change more than 5%?(set R(s)=0 for ease of computation.)E5.13 A feedback system is shown in Figure E5

13、.13.(a) Determine the steady-state error for a unit step when K=0.4 and Gp(s)=1.(b) Select an appropriate value for Gp(s) so that the steady-state error is equal to zero for the unit step input.E5.16 A closed-loop control system transfer function T(s) has two dominant complex conjugate poles.Sketch

14、the region in the left-hand s-plane where the complex poles should be located to meet the given specifications.E5.17 A system is shown in Figure E5.17(a).The response to a unit step,when K=1,is shown in Figure E5.17(b).Determine the value of K so that the steady-state error is equal to zero.P5.1 A i

15、mportant problem for television systems is the jumping or wobbling of the picture due to the movement of the camera.This effect occurs when the camera is mounted in a moving truck or airplane. The Dynalens system has been designed to reduce the effect of rapid scanning motion;see Figure P5.1. A maxi

16、mum scanning motion of 25% is expected.Let Kg=Kf=1 and assume that g is negligible.(a) Determine the error of the system E(s).(b) Determine the necessary loop gain,KaKmKt,when a 10/s steady-state error is allowable.(c) The motor time constant is 0.40s.Determine the necessary loop gain so that the setting time(to within 2% of the final value of vb) is less than or equal to 0.03s.P5.2 A specific closed-loop control system is to be designed for an underramped response to a step input.The specification for the system ar