2002 Prentice Hall, Inc. Gene F. Franklin, J. David Powell, Abbas Emami-Naeini Feedback Control of Dynamic Systems, 4e

Transcription

1 u Figure 2.1 Cruise-control model

2 x Friction force bx m x u Figure 2.2 Free-body diagram for cruise control

3 S P 278 Figure 2.3 Automobile suspension

4 y m 2 k s b v car x m 1 k w Road surface r Inertial reference Figure 2.4 The quarter-car model

5 k s (y x) b(y x) m 1 x m 2 y k w (x r) k s (y x) b(y x) Figure 2.5 Free-body diagrams for suspension system

6 Figure 2.6 Communications satellite (Courtesy Space Systems/Loral)

7 u u M D d Gas jet F c Inertial reference Figure 2.7 Satellite control schematic

8 Figure 2.8 Disk read/write mechanism (Photo courtesy of Hewlett-Packard Company)

9 Disk Read head and track sensor u 2 Head inertia I 2 Flexible shaft k, b u 1 M c M D Motor inertia I 1 Figure 2.9 Disk read/write head schematic for modeling

10 u 1 u 1 u 2 u 2 k(u 1 u 2 ) k(u 1 u 2 ) M c M D b(u 1 u 2 ) b(u 1 u 2 ) I 1 I 2 Figure 2.10 Free-body diagrams of the disk read/write head

11 T c u l mg Figure 2.11 Pendulum

12 25 Pendulum angle (degrees) Time (sec) Figure 2.12 Response of the pendulum to a step input in the applied torque

13 Figure 2.13 Crane with a hanging load (Photo courtesy of Harnischfeger Corporation, Milwaukee, Wisconsin)

14 x u m t u I, m p Figure 2.14 Schematic of the crane with hanging load

15 u I, m p u m t x Figure 2.15 Inverted pendulum

16 x P N ˆ j ˆ i x l lu 2 lu x r u bx, friction I, m p x N Reaction force from pendulum P m p g u u (a) (b) (c) Figure 2.16 Hanging crane: (a) free-body diagram of the trolley; (b) free-body diagram of the pendulum; (c) position vector of the pendulum

17 Figure 2.17 (a) Flexible robot arm used for research at Stanford University; (b) model for a continuous flexible beam; (c) simplified model for the first bending mode; (d) model for the first and second bending modes (Photo courtesy of E. Schmitz)

18 10 8 Amplitude Time (sec) Figure 2.18 Response of the car velocity to a step in u

19 Symbol Equation Resistor v i v Ri Capacitor v i i C dv dt Inductor v i v L di dt Voltage source v v s v v s Current source i i i s i s Figure 2.19 Elements of electric circuits

20 C 2 R 2 1 R v i v 2 v1 C 1 v 3 v o 4 Figure 2.20 Bridged tee circuit

21 v i R 0 i 0 v i R 1 v 0 A(v v ) (a) i v v i v0 v v 0 (b) (c) Figure 2.21 (a) Op-amp simplified circuit, (b) op-amp schematic symbol, (c) Reduced symbol for v + = v = 0

22 R f i out v 1 i 1 R 1 v out v 2 i 2 R 2 Figure 2.22 The op-amp summer

23 C i out v in R in Figure 2.23 The op-amp integrator v out

24 Cone Electromagnet S N Cone Bobbin Low force suspension Coil S (a) Figure 2.24 Permanent magnet (b) Geometry of a loudspeaker: (a) overall configuration, (b) the electromagnet and voice coil

25 R i v a L x e coil Figure 2.25 A loudspeaker showing the electric circuit

26 i a Brush N Stator magnet Rotor windings Shaft angle u m Shaft Bearings Figure 2.26 S Brush Commutator Sketch of a DC motor Stator magnet

27 R a L a T u m v a i a e K e u m J m bu m (a) (b) Figure 2.27 DC motor: (a) electric circuit of the armature, (b) free-body diagram of the rotor

28 v a V 2 (V 1 ) v a V 4 V 3 Torque, T v a V 1 Torque, T V 2 Slope K 2 V 1 Speed, u m Speed, u m (a) (b) Figure 2.28 Torque-speed curves for a servo motor showing four amplitudes of armature voltage; (a) low-rotor-resistance machine; (b) high-rotor-resistance machine showing four values of armature voltage, v a

29 q 2 R 2 Temperature outside, T O R 1 q 1 Figure 2.29 Dynamic model for room temperature

30 A s T si w s K s A s Water w T wi T w T m T s Figure 2.30 Heat exchanger

31 in h Pressure p 1 out Figure 2.31 Water-tank example

32 x Piston F D Liquid at pressure p Figure 2.32 Hydraulic piston actuator

33 2 1 Valve x p e p s p e 2 1 u p 2 p 1 F y l d F a Low-pressure oil High-pressure oil Aerodynamic control surface Figure 2.33 Hydraulic actuator with valve

34 Figure 2.34 A magnetic bearing (Photo courtesy of Magnetic Bearings, Inc.)

35 Figure 2.35 Magnetic ball levitator used in the laboratory

36 i x Figure 2.36 Model for ball levitation

37 200 i ma Force, f m (10 3 N) Slope K x i ma i ma x Distance, x (mm) 6 Figure 2.37 Experimentally determined force curves

38 b 1 m 1 x 1 k 2 x 2 m 2 k 3 y k 1 No friction Friction, b 2 (a) k 1 m 1 k 2 m 2 k 3 Friction, b 1 No friction (b) b 1 k 1 m 1 m 2 F k 2 No friction No friction (c) Figure 2.38 Mechanical systems

39 k m Figure 2.39 m Double pendulum

40 m x k M y u b Figure 2.40 Schematic of a system with flexibility

41 R f V in R in v v V out Figure 2.41 Circuit for Problem 2.11

42 v V in v V out Figure 2.42 Circuit for Problem 2.12

43 v V in v V out Figure 2.43 Circuit for Problem 2.13

44 R f R in v V in R v I a dc motor V out R s Figure 2.44 Op-Amp circuit for Problem 2.14

45 R f R in v v V in r R Vout Figure 2.45 Op-Amp circuit for Problem 2.15

46 R f V in R 2 R 1 V out C (a) R 2 R 1 V in R in C V out (b) C C V in R R/2 2C R V out (c) Figure 2.46 Lead (a), lag (b), notch (c) circuits

47 C R R 2 C R R 1 R R V in V 1 V 2 V 3 R a R R b R c V out R d Figure 2.47 Op-amp

48 B x 1 x 2 No friction K v 2 r 2 J 1, B 1 r 1 v 1 Take-up capstan Head Idler wheel J 2, B 2 dc motor F Vacuum column i a u Figure 2.48 Tape drive schematic

49 L R K b i(t) A a v B f s (t) M x Figure 2.49 Simplified model for capacitor microphone

50 L a R a u 1 v a k, b u 2 J 1 J 2 Figure 2.50 Motor with a flexible load

51 d v i T act v i (a) (b) Figure 2.51 (a) Precision table kept level by actuators; (b) side view of one actuator

52 R o R i Fourth floor (b) (a) Figure 2.52 Building air conditioning: (a) high-rise building; (b) floor plan of the fourth floor

53 in out Figure 2.53 Two-tank fluid-flow system for Problem 2.26

54 h 1 h 3 Pump A h 2 B C Figure 2.54 Two-tank fluid-flow system for Problem 2.27

55 R u l Ru l Figure 2.55 Motion of cord wrapped around a fixed cylinder

56 k Rotor u m 1 m 2 y 1 b y 2 Figure 2.56 Schematic diagram of the GP-B satellite and probe

57 i G G L 1 u v G C 1 v i R 1 Figure 2.57 Nonlinear circuit for Problem 2.31

58 i 1 v 1 x 2 u 1 (1 V) R 1 1 F x 1 1 F u 2 (27 A) R 2 1 H v 2 i 2 x 3 Figure 2.58 A non-linear circuit

59 v 2 Slope Slope ½ 1 0 i 2 Figure 2.59 Non-linear resistance