... equations in (26) into
(25) and after operating and simplifying we have:
( ) ( ) 0 0
1 1 1
1 1
2 1 3 1
0 ( ) ( ) 0
2 2 2 22 3 2 1 2
0 0 ( ) ( )
2 3 3 3
1 3
3 3 3
m m m
P
s s
x y z
x
m m m P ... equations in (26) into
(25) and after operating and simplifying we have:
( ) ( ) 0 0
1 1 1
1 1
2 1 3 1
0 ( ) ( ) 0
2 2 2 22 3 2 1 2
0 0 ( ) ( )
2 3 3 3
1 3
3 3 3
m m...
...
2 2
2
3 3 3 3 3 3 3 3
m a I m a m m g a c a P c P s h H s P c
c a b a b x y z
(51)
Fig. 7. Basic architecture of the control system ...
2 2
2
3 3 3 3 3 3 3 3
m a I m a m m g a c a P c P s h H s P c
c a b a b x y z
(51)
Fig. 7. Basic architecture o...
... x
p3
x
p4
+
p
10
p
4
cos x
p3
(
¨
e
1
− r
1
(x)
)
p
5
cos x
p3
+ p
6
sin x
p3
+ p
7
x
p4
+
p
10
p
4
cos x
p3
x
p4
−
p
10
p
4
(
p
3
− p
9
)
tan x
p3
e
(3)
1
+
p
10
p
4
tan x
p3
{
(
p
3
− ... x
p1
x
p2
+
p
3
p
10
p
4
cos x
p3
x
p4
+
p
10
p
4
tan x
p3
p
3
p
9
− p
1
sin x
p1
+ p
2
cos x
p1
(
x
M3
− r
1
(x)
)
+
p
3
(
x
M3
− r
1
(x)
)
+ (2x
p4
tan x
p3
− p
3
+ p...
... & Romano 2007b).
Mechatronic Systems, Simulation, Modelling and Control1 86
Mechatronic Systems, Simulation, Modelling and Control1 82
where
1
,
K
diag k k
and assume that
1
0
K
B
... which makes
controller’s tuning simpler.
The dynamic part of the control law from (26) has the following form:
3 2 1
3 2
,2 ,1 ,0
3 2...
... using Eq. (54) and the state feedback control law
1
,
B B
T EF x v b (55)
into a linear system
3 3 3 3 3 3
3 3 3 3 3 3
x x x
x x x
0 ... test was .32 7 m/s which correspond to a total
impulse of 8.55 Ns.
Mechatronic Systems, Simulation, Modelling and Control2 06
t 10
-2
s
g
3. 76 x 10
-3
rad-s
-3/ 2
...
...
2008 IEEE International Conference on Systems, Man, and Cybernetics, pp. 36 06 -36 11,
Suntec, Singapore
Mechatronic Systems, Simulation, Modelling and Control2 44
Ε S t
( )
[ ]
= v ⋅ exp
λ
s
( ... rate, and the cumulative MTBF as software reliability assessment measures,
and the predicted relative error.
Mechatronic Systems, Simulation, Modelling and Control2 36
outp...
... Mechatronic Systems, Simulation, Modelling and Control2 86
Fig. 2. General approach for modelling and testing active flexible micromechanisms
2.2 Design optimization
Modeling, ... the system must be controlled
using proper actuators and sensors positions ( Control authorithy’): actuator and sensor
positions are sought for influencing (controllability) and sensing (observab...
...
max1
max1
1
f
f
N
f
kf
N
k
kfM
s
s
(33 )
Also, we have:
.
1
1|
max1
1
max11
f
kkfM
ff
(34 )
Considering Equations (33 ) and (34 ), the following equation is resulted:
max1
NM
f
f
s
(35 )
The value ... Vibration, US Patent No.5241 236 .
Mechatronic Systems, Simulation, Modelling and Control2 2
cos
,
sin
S md F
d d
l i
d d
...