2022年自动控制理论 .pdf
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1、E7.1 Let us consider a device that consists of a ball rolling on the inside rim of a hoop 11. This model is similar to the problem of liquid fuel sloshing in a rocket. The hoop is free to rotate about its horizontal principle axis as shown in Figure E7.1. The angular position of the hoop may be cont
2、rolled via the torque T applied to the hoop from a torque motor attached to the hoop drive shaft. If negative feedback is used, the system characteristic equation is 2(4)122Ks sss+=0. (a) Sketch the root locus. (b) Find the gain when the roots are both equal. (c) Find these equal roots. (d) Find the
3、 settling time of the system when the roots are equal. E7.2 A tape recorder has a speed control system so that H(s)=1 with negative feedback an 2( )(2)(45)KG ss sss=+. (a) Sketch a root locus for K, and show that the dominant toots ate s=-0.35j0.08 when K=6.5. (b) For the dominant roots of part (a),
4、 calculate the settling time and overshoot for a step input. E7.3 A control system for an automobile suspension tester has negative unity feedback and a process 1222(48)( )(4)KssG sss+=+. We desire the dominant roots to have a equal to 0.5. Using the root locus, show that K=7.35 is required and the
5、dominant roots are s=-1.3j2.2. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页,共 13 页 - - - - - - - - - E7.4 Consider a unity feedback system with2(1)( )45KsG sss+=+. (a) Find the angle of departure of the root locus from the complex poles. (b) Find the entry poin
6、t for the root locus as it enters the real axis. Answers: 225o;-2.4 E7.6 One version of a space station is shown in Figure E6.3 30.It is critical to keep this station in the proper orientation toward the sun and the Earth for generating power and communications. The orientation controlling may be re
7、presented by a unity feedback system with an actuator and controller, such as 225( )(24100)KG ss ss=+. Sketch the root locus of the system asK increases. Find the value of K that results in an unstable system. Answers: K=96 E7.9 The world s largest telescope is located in Hawaii. The primary mirror
8、has a diameter of 10 m and consists of a mosaic of 36 hexagonal segments with the orientation of each segment actively controlled. This unity feedback system for the mirror segments has 2( )(25)KG ss ss=+. (a) Find the asymptotes and draw them in the s-plane. (b) Find the angle of departure from the
9、 complex poles. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页,共 13 页 - - - - - - - - - (c) Determine the gain when two roots lie on the imaginary axis. (d) Sketch the root locus. E7.25 A closed-loop feedback system is show in Figure E7.25. For what range of valu
10、es of the parameters K is the system stable? Sketch the root locus as 0k . P7.5 Automatic control of helicopters is necessary because, unlike fixed-wing aircraft which possess a fair degree of inherent stability, the helicopter control system that utilizes an automatic control loop plus a pilot is s
11、hown in FIGURE P7.5. When the pilot is not using the control stick, the switch may be considered to be open. The dynamics of the helicopter are represented by the transfer function 225(0.03)( )(0.4)(0.360.16)sG ssss+=+-=. (a) With the pilot control loop open (hands-off control), sketch the root locu
12、s for the automatic stabilization loop. Determine the gain 2K that results in a dumping for the complex roots equal to =0.707. (b) For the gain 2K obtained in part (a), determine the steady-state error due to a wind gust dT(s)=1/s. (c) With the pilot loop added, draw the root locus as 1K varies from
13、 zero to when 2K is set at the value calculated in part (a). (d) Recalculate the steady-state error of part (b) when 1K is equal to a suitable value based on the root locus. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页,共 13 页 - - - - - - - - - P7.6 An attitude
14、control system for a satellite vehicle within the earths atmosphere is shown in Figure P7.6. The transfer functions of the system are (0.20)( )(0.90)(0.60)(0.10)K sG ssss+=+- and (21.5)(21.5)( )(4.0)csjsjGss+-=+. (a) Draw the root locus of the system as K varies from 0 to . (b) Determine the gain K
15、that results in a system with a settling time (with a 2% criterion) less than 12 seconds and a damping ratio for the complex roots greater than 0.50. P7.9 The achievement of safe, efficient control of the spacing of automatically controlled guided vehicles is an important part of the future use of t
16、he vehicle =s in a manufacturing pant 14, 15. It is important that the system eliminate the effects of disturbances (such as oil on the floor) as well as maintain accurate spacing between vehicles on a guideway. The system can be represented by the block diagram of Figure P7.9. The vehicle dynamics
17、can be represented by 22(0.1)(2289)( )(0.4)(0.8)(1.45361)sssG ss ssss+=-+. (a) Sketch the root locus of the system. (b) Determine all the roots when the loop gain K=1K2K is equal to 4000.名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页,共 13 页 - - - - - - - - - P7.1
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