Page 46 - Servo Motors and Industrial Control Theory -

38 2 Feedback Control Theory Continued

Fig. 2.17 Block diagram rep-
resentation of linear system
F X
1/K

Fig. 2.18 A mechanical
device for proportional feed- b
back system a

x 2
X 1 y

Fig. 2.19 Block diagram x b +
representation of a propor- 1 y
tional control a+b +
–

x a
2 a+b

For x , x , y the same direction the relation between the output y and x , x
1
1
2
2
becomes
b a
y = x + x (2.22)
ab− 1 ab− 2
If the direction of x or x is changed the system becomes a negative feedback con-
2
1
trol.

y = b x − a x 2 (2.23)
−
1
−
ab ab
The above equations in block diagram form are shown in Fig. 2.19. The arrows
show the direction of signal flow.
Example 4 Mass–Spring–Damper system.
A simple mass–spring–damper system is shown in Fig. 2.20. The input is usually
force and the output is the displacement. Writing equation of motion the relation
between displacement and force becomes,