Hardware Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time in sec. solid: y due to y(0), dash−dot: IVCed
Figure 3.41: Simulation result of the IVC.
The response of the system is shown in Figure 3.41.
Solution 2:
In view of equation (3.77), let
T (s)
= −
(s + 1000)7.143
×
10
−6
s
2
I
v
= −
S(s)
,
(3.79)
s +71.43
so that the effect of initial values is totally canceled out. However, this transfer
function is not causal. We can make I
v
(s) causal by including additional (fast)
poles. Then I
v
can be expressed as
I
v
(s)=−
S(s)
T (s)
1
additional (fast) poles
−6
s
3
+0.007143s
2
s +71.43
= −
10
1
additional (fast) poles
.
(3.80)
Tak ing I
v
into consideration, the transfer function from the initial position
value to plant output is,
y
y(0)
= S + I
v
T = S(1−
1
additional (fast) poles
).
(3.81)
By selecting the additional poles to be a few times faster than those of S(s)
with a damping ratio close to 1, the effect of y(0) on y is dominated by these
fast poles and diminishes quickly.
