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3.3
Con
trolI
mplemen
tation
69
0 20 40 60 80
40
60
80
100
120
140
Time (s)
β [deg]
0 20 40 60 80
−200
−100
0
100
200
Time (s)
0 20 40 60 80
−40
−20
0
20
40
Time (s)
0 20 40 60 80
−1
−0.5
0
0.5
1
Time (s)
˙
β [deg/sec ]
˙α [deg/sec]
˙γ [deg/sec]
Fig. 3.37. Sensor data in balance control.
We mountahighresolution 2 / 3” ccd, formatCANON COMMUNICATION
CAM
ERA
VC
-C1
on atri
po
d.
Th
ecame
ra ha
sb
een
c al
ib
ra
ted
an
dw
eh
av
e
mapped the field of visiontothe Cartesian space coordinate which is anchored
on theground. The camerahas apixel arrayof768(H ) × 576(V ). In order to
communicate the data, an interface board(
digital I/O) is
installed in
aP
C
andthere arewireless modems to connect the PC andGyrover.
The firstp
roblemexperienced is that the system states exhibited highly
oscillatorybehavior and the second is that control inputs sometimes needed to
switchtoo sharply andfast.Both will cause difficulties forreal time control
andresult in worse performance.Tosolvetheseproblems,wepropose to
replace thesign functions in the controllers with tanh functions.
Let Tanh( . )beabipolar function described as follows:
Tanh( x )=
1 − e
− k
6
x
1+e
− k
6
x
(3.61)
where k
6
is apositive scalarconstant, whichcan be designed.
Let Uanh( . )beaunipolar function described as follows:
Uanh( x )=
1
1+e
− k
7
x
(3.62)
where k
7
is apositive scalarconstant, whichcan be designed.