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6.5.3 YawDamper
The purpose of the yaw damper is to generate a yawing moment that opposes
any yaw rate that builds up from an unstable Dutch-roll mode. However, this type
of control augmentation has one drawback.lt will oppose any steady-state yaw rate
the pilot wants to intentionally generate, for example, during a steady coordinated
levevi'turn. In this case the pilot will have to fight the yaw damper system. One
way of avoiding this problem is to use a wash-out circuit in the feedback loop.
The wash-out circuit will filter out all the steady-state components so that the yaw
damper system will not respond to steady-state yaw rates.
AFs7crr:pIe yaw damper with yaw rate feedbackis shown in Fig. 6.36. To illustrate
the des;gPn procedure, consider the general aviation airplane and use the Dutch-roll
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 605
Refer
input
Referen
input
a) Schematic diagram
b) Block diagram
Fig.6.36 Yawdamper.
transfer function to rudder input. From Eq. (6.285),
AVt(s) -(0.1582 s + 0.0294)
A8r(S) = s~0 0340 S2+0 034~s+0~6~3~ (6.333)
so that
rls) sAp(s) .
A8r~S~ = ~8~s)
~(0.1582 s + 0.0294)
0.0340 S2 + 0.0347 s + 0~6~3
(6.334)
(6.335)
We assume that the rudder servo is a first-order system with a -10 so that
the time constant r = l/ti -. 0.10. As said before, we use the negative sign in
the numerator of the rudder servo transfer function because we have a negative
sign in the numerator of the yaw-rate-to-rudder-input transfer function as given by
Eq. (6.335). With this sign adjustment, we can use the negative feedback as shown
in Fig. 6.36b.
We assume that the transfer function of the wash-out circuit is given by
Gc=- s
: s +0 3333 (6.336)
Now we draw the root-locus as shown in Figs. 6.37 and 6.38. The root-locus of
Fig. 6.38 is a close-up of the root-locus around the origin. We select a point on
root-locus to have < - 0.8 for the Dutch-roll mode. We get krg -- 0.4228 and the
location of the closed-loop poles at ~6.9705, -2.0108 -1: j1.5140, -0.3619. This
gives us a damping ratio of 0.8 and a natural frequency of 2.5170 rad/s, giving us
level I Dutch-roll flying qualities for the general aviation airplane, which is a class
I airplane.
m 0.1
xo
o -0.1
o 0.05
a0
< -0.05
606
u,
x
<
o
d
E
PERFORMANCE, STABILI-fY, DYNAMICS, AND CONTROL
Fig. 637 Root-Iocus of the yaw damper system for the general aviation airplane.
Fig. 638 Root-Iocus of the yaw damper system for the general aviation airplane
(close-up around the origin).
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 607
Yaw Damper On
- YawDampcrOff(BasicSystem)
a}
7a
o:
3
d
>-
a) Dutch-roll approximation
b) Complete fifth-order system
Fig. 639 Unit-step response of the yaw damper for the general aviation airplane.
We can now verify the design by simulating the response to a unit-step function
as shown in Fig. 6.39a. We observe that the closed-loop system with yaw damperis
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