Hardware Reference
In-Depth Information
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Time (ms)
Figure 3.6: Closed-loop step response corresponding to Figure 3.2.
can also be enhanced by including the so called peak
fi
lter in the servo loop;
this approach is explained in Section 3.2.5.
3.2.2 Cancelling Actuator Resonances using Notch Filter
It is shown in the previous section that PID-type simple compensator works
well for a plant represented by rigid body dynamic model, but the phase and
gain distortions due to the actuator resonances affect the overall phase and
gain margins. One possible way to overcome this problem is to use a pre-
compensator for the flexible modes such that the frequency response of the
pre-compensated plant resembles that of a rigid actuator. This process is often
called gain stabilization [54]. Typical method of gain stabilization involves
use of notch filters to suppress the structural resonances [71]. Application of
notch filter for gain stabilization is illustrated in this section using a plant
model containing only one lightly damped resonant mode, but the idea can be
extended to actuators with multiple flexible modes.
Let us consider a second order plant model
ω
n
R(s)=
s
2
+2ζ
n
ω
n
s +ω
n
,
(3.16)
where ω
n
is the natural frequency of the resonant mode and ζ
n
is the corre-
sponding damping ratio. Resonances in actuators are usually damped, i.e.,
they eventually decay to zero; it means that the damping ratio is bounded
by 0 < ζ
n
< 1. The duration for which an excited resonance is sustained
