(a) Torsional spring-mass system. (b) Spring element.

Transcription

1 m v s T s v a (a) T a (b) T a FIGURE 2.1 (a) Torsional spring-mass system. (b) Spring element.

2 by ky Wall friction, b Mass M k y M y r(t) Force r(t) (a) (b) FIGURE 2.2 (a) Spring-mass-damper system. (b) Free-body diagram.

3 Voltage v(t) e a 2t 0 Time 2(p/b 2 ) FIGURE 2.4 Typical voltage response for underdamped RLC circuit.

4 T u Length L p p 2 p 2 p u Mass M (a) (b) FIGURE 2.6 Pendulum oscillator.

5 s 1 jv jv n 1 z 2 u cos 1 z v n 2zv n zv n 0 s s 2 jv n 1 z 2 FIGURE 2.9 An s-plane plot of the poles and zeros of Y(s).

6 z 1 z increasing z 0 v n jv jv n z 1 z 1 z 1 0 s FIGURE 2.10 The locus of roots as z varies with vn constant.

7 Armature R a L a Rotor windings Brush Stator winding N Shaft i a V f R f i f (t) Field L f i a v, u Load Inertia J Friction b Inertia load Angle u S Bearings Brush Commutator (a) (b) FIGURE 2.17 A dc motor (a) wiring diagram and (b) sketch.

8 FIGURE 2.18 A pancake dc motor with a flat-wound armature and a permanent magnet rotor. These motors are capable of providing high torque with a low rotor inertia. A typical mechanical time constant is in the range of 15 ms. (Courtesy of Mavilor Motors.)

9 Disturbance T d (s) Field Load Speed I T 1 f (s) m (s) T L (s) 1 v(s) V f (s) K 1 m R f L f s Js b s Position u(s) Output FIGURE 2.19 Block diagram model of field-controlled dc motor.

10 Dorf/Bishop Disturbance T d (s) V a (s) Armature K m R a L a s T m (s) T L (s) 1 Js b Speed v(s) 1 s Position u(s) Back emf K b FIGURE 2.20 Armature-controlled dc motor.

11 V a (s) R a I a L a V b I f u, v J, b Table 2.5 Transfer Functions of Dynamic Elements and Networks 6. dc motor, armature-controlled, rotational actuator

12 Shaft u(s), v(s) V 2 (s) Table 2.5 Transfer Functions of Dynamic Elements and Networks 13. Tachometer, velocity sensor

13 V f (s) K G(s) m s(js b)(l f s R f ) Output u(s) FIGURE 2.22 Block diagram of dc motor.

14 R 1 (s) R 2 (s) Inputs System Outputs Y 1 (s) Y 2 (s) FIGURE 2.23 General block representation of two-input, two-output system.

15 R 1 (s) G 11 (s) Y 1 (s) R 2 (s) G 12 (s) G 21 (s) G 22 (s) Y 2 (s) FIGURE 2.24 Block diagram of interconnected system.

16 m v s T s v a (a) T a (b) T a FIGURE 2.1 (a) Torsional spring-mass system. (b) Spring element.

17 by ky Wall friction, b Mass M k y M y r(t) Force r(t) (a) (b) FIGURE 2.2 (a) Spring-mass-damper system. (b) Free-body diagram.

18 Voltage v(t) e a 2t 0 Time 2(p/b 2 ) FIGURE 2.4 Typical voltage response for underdamped RLC circuit.

19 f Mass M f y 2 Nonlinear spring y Spring force f 0 df dy y y 0 Equilibrium (operating point) y 0 y (a) (b) FIGURE 2.5 (a) A mass sitting on a nonlinear spring. (b) The spring force versus y.

20 T u Length L p p 2 p 2 p u Mass M (a) (b) FIGURE 2.6 Pendulum oscillator.

21 jv s pole zero FIGURE 2.7 An s-plane pole and zero plot.

22 s 1 jv jv n 1 z 2 u cos 1 z v n 2zv n zv n 0 s s 2 jv n 1 z 2 FIGURE 2.9 An s-plane plot of the poles and zeros of Y(s).

23 z 1 z increasing z 0 v n jv jv n z 1 z 1 z 1 0 s FIGURE 2.10 The locus of roots as z varies with vn constant.

24 y(t) y 0 Overdamped case 0 Time Underdamped case e zv nt envelope FIGURE 2.12 Response of the spring-mass-damper system.

25 Friction b 2 Friction b 1 M 2 k Velocity v 2 (t) Current r(t) v 1 (t) R 1 v 2 (t) C 1 R 2 C 2 L M 1 Velocity v 1 (t) Force r(t) (a) (b) FIGURE 2.16 (a) Two-mass mechanical system. (b) Two-node electric circuit analog C1 = M1, C2 = M2, L = 1/k, R1 = 1/b1, R2 = 1/b2.

26 Armature R a L a Rotor windings Brush Stator winding N Shaft i a V f R f i f (t) Field L f i a v, u Load Inertia J Friction b Inertia load Angle u S Bearings Brush Commutator (a) (b) FIGURE 2.17 A dc motor (a) wiring diagram and (b) sketch.

27 FIGURE 2.18 A pancake dc motor with a flat-wound armature and a permanent magnet rotor. These motors are capable of providing high torque with a low rotor inertia. A typical mechanical time constant is in the range of 15 ms. (Courtesy of Mavilor Motors.)

28 Disturbance T d (s) Field Load Speed I T 1 f (s) m (s) T L (s) 1 v(s) V f (s) K 1 m R f L f s Js b s Position u(s) Output FIGURE 2.19 Block diagram model of field-controlled dc motor.

29 Dorf/Bishop Disturbance T d (s) V a (s) Armature K m R a L a s T m (s) T L (s) 1 Js b Speed v(s) 1 s Position u(s) Back emf K b FIGURE 2.20 Armature-controlled dc motor.

30 V f (s) R f L f I a J, b I f u, v Table 2.5 Transfer Functions of Dynamic Elements and Networks 5. dc motor, field-controlled, rotational actuator

31 V a (s) R a I a L a V b I f u, v J, b Table 2.5 Transfer Functions of Dynamic Elements and Networks 6. dc motor, armature-controlled, rotational actuator

32 Shaft u(s), v(s) V 2 (s) Table 2.5 Transfer Functions of Dynamic Elements and Networks 13. Tachometer, velocity sensor

33 V f (s) K G(s) m s(js b)(l f s R f ) Output u(s) FIGURE 2.22 Block diagram of dc motor.