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Basic Lateral Controllers (II) Lateral coordination
controllerPreliminaries about coordination of lateral motion
A coordinated lateral motion is a lateral motion with zero
sideslip, or 0= .
Coordination of lateral flights will reduce adverse sideslip,
thereby minimizing the couplingbetween the yaw and the roll
motions, and enhancing the yaw responsiveness.
It is much desirable to suppress sideslip in most lateral
maneuvers.
Dutch roll/yaw damper along will not achieve coordination.
Closed-loop response of an A/C controlled by a Dutch roll damper
with washout filter.
--- A pulse aileron input is used for this closed-loop response
simulation.
--- A pulse aileron input is a typical pilots input to initiate
a turn, a typical lateral maneuver. ==> Substantial sideslip
still remains.
==> Other means of control is needed to suppress the
sideslip.
==>We will seek only reduction in sideslip. In general, it is
not practical to expect 0 .
r(t)
(t)
0 5 10 15 20
-0.05
0
0.05
0.15
0.2
0.3
0 5 10 15 200
0.1
0.2
0.3
0.4
Aircrafte
r
rServoRudder
0.635
r
s+0.4
s
-11
Open-loop
r(t)
(t)
0 5 10 15 20
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 200
0.5
1
1.5
2
2.5
-0.1
0.1
0.25
Washed out
A pulse a
0
sec
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Lateral coordination controller A basic design conceptTypical
block diagram:
--- Feedback of is usedto suppress the sideslip.
--- The controlling input is
still the rudder, a most
effective input for .--- The Dutch roll damper
is included as the inner-
loop of this design.
A/C model -- for the example plant in Closed-loop system of the
Dutch roll damper:
--- Open-loop rudder to yaw transfer function:
)(10
10)(),(
]97.1335.0)[0019.0(
]305.00584.0[471.3)( se
sss
jss
jssr rrr
+=
++
++=
--- Dutch roll damper design: )(
/1
)( se
s
sKse zdr
+
=
--- Closed-loop system of the Dutch roll damper (with 5.2= : and
635.0=dK ):
)06.2)(01.2)[31.6)(692.0)(0017.0(
]305.00584.0[4.0(71.34
)(
)(
++++
+++=
sssss
js)s
se
sr
z
--- Note that the pole of the washout filter appears in the
closed-loop system as a zero. The same
will be true for any filter pole(s) placed in the feedback
loop.
AircraftOpen-loop
er
r
ServoRudder
Kd
r
s
s+1/
K
Servo
Aileron a
command
Pilot's aileron
Pilot's ruddercommand
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For the outer-loop design, we need to convert the plant output
from r to :
--- From the open-loop lateral dynamic:]97.1335.0)[0019.0(
)017.0(471.3
)(
)(
jss
s
s
s
r
++
=
The roll mode remains nearly cancelled by a zero in the
numerator.
--- As a result, the ratio between r to
becomes:]305.00584.0[
0017.0
)(
)(
jss
sr
s
++
=
--- The plant model for the outer-loop design thus will be
)06.2)(01.2)[31.6)(692.0)(0017.0(
)4.0)(0017.0(71.34
)(
)(
)(
)(
)(
)(
++++
+==
sssss
ss
sr
s
se
sr
se
s
zz
The spiral mode is also nearly cancelled, and will not be
affected by this design.Outer-loop design analysis:
1
2
-1
-1-2-3-4-5
j
-2
-6-7
Solution at = 2.5, Kd
= 0.635 and K= 0.42
ez
K
)06.2)(01.2)[31.6)(692.0(
)4.0(71.34
++++
+
ssss
s
Note that the dominant locus moves straight outward. If
we did not over damp the Dutch roll mode, we would not
have chance to obtain a satisfactory design here.
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Closed-loop response of the coordination controller to a pulse
aileron input:
--- feedback does not change and r very much.--- Reduction in is
also limited, especially as the steady state value is
concerned.
Inclusion of a lag filter, > Other method is needed to reduce
it.
0 5 10 15 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 5 10 15 20-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 200
0.5
1
1.5
2
2.5
3
(t)
r(t)(t)No feedback
With feedback
0 5 10 15 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 5 10 15 20-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 200
0.5
1
1.5
2
2.5
3
3.5
(t)
r(t)(t)
No feedback
-0.05
=0.05, =0.5 =0, =0.5
feedback through a filterDirect feedback
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Method for removing transient sideslip
Lateral coordination control with a matching aileron input
From open-loop lateral dynamics:)(
)()()()()(s
ssBssBs aarr
+=
--- )(),(),( sBsBs ar : Polynomials of s .
A tactic to remove )(s : Actuating the aileron so that )()(
)()( s
sB
sBs r
a
ra =
==> Then, 0
)(
)()(
)(
)()(
)(
)()()()()(
=
+=
s
ssB
s
ssB
s
ssBssBs rrrraarr
---In theory, we can completely eliminate )(s with this
control.In reality, complete elimination of )(s is not possible,
due to the following difficulties:
(a) Implementation of the method will be in trouble if )(sBa is
non-Hurwitz.--- When )(sBa do have RHP root(s), a Hurwitz
approximate of )(sBa will be used in place
of the real )(sBa . The approximation decreases the
effectiveness of the design.
(b)The proposed method is a feed forward control approach, and
therefore will be highly sensitiveto error in the parameters of
)(sBa and )(sBr .
-- In general, errors in the parameters of )(sBa and )(sBr are
inevitable and large.
Nevertheless, the use of this control, even with an erroneous
)(sBr and an approximated )(sBa ,
may help in reducing the peak value of during the transient.This
feed forward control can work in conjunction with the feedback
method discussed previously.
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Further discussions about the lateral coordination controlThe
spiral motion remains unstable.
The problem with the opposite-signed deflection prohibits the
stabilization of the spiral modethrough actuation of the rudder.
The spiral mode will be stabilized by actuation of the aileron.
--- See theYaw Orientation Autopilotdesign
Other approaches for lateral coordination control exist:
(1) Feedback lateral acceleration to achieve coordination:
Replace the feedback with v&& .--- Coordinated motion means
no lateral acceleration. Therefore, a feedback design to
suppress
lateral acceleration can be used to improve coordination.
--- True lateral acceleration is difficult to measure
