Page 51 - Servo Motors and Industrial Control Theory -

2.7 Bode Diagram 43

Fig. 2.26 A lead-lag network C 2 R 2
with OP-AMP
R 1
V 1 C 1
- V
OP-AMP 0
+

R

Fig. 2.27 A simple model for 1
position control system θ i K s s(0.5s + 1) θ o

In this case,
)
V ( R + C 1 V [C ·(R ·C · s+1) ]
2
o := 2 ·s o := 1 2 2 (2.34)
V i R + C 1 ·s V i C ·(R ·C · s+1)
1
1
2
1
1
Often it is desirable to increase the gain of a feedback control systems so to increase
the speed of response and to reduce steady state error. When the gain is increased,
the systems move towards instability. To overcome this problem, the Proportion-
al + Integral +derivative, (PID) control network may be used. The problem is to ad-
just the three parameters of the PID. The derivative action always amplifies the
noise present in the system. In this case, a lead-lag network is preferred.
Example 7 A servo position control.
The simplest model for a position control system with separately excited DC motor
is shown in Fig. 2.27. In the loop, there is a lag network because of the rotor inertia
and there are two integrators. One to convert velocity to position and one to achieve
zero steady state error. This will be discussed in detail in the proceeding chapters.
The closed loop transfer function can be obtained as

θ o = K (2.35)
θ 0.5s + s + K
2
3
i