misc transfer functions_8
DESCRIPTION
feedback controlTRANSCRIPT
Miscellaneous Systems
Dr. Aaron Don M. Africa
Transfer Function for Systems with Gears
2
1
2
1
2
1
2211
N
N
r
r
rr
Transfer functions for
a. angular displacement in lossless gears and b. torque in lossless gears
2
1
2
1
2
2
1
1
2
1
2
2
1
2211
N
N
T
T
N
N
T
T
TT
a. Rotationalsystem drivenby gears;b. equivalent system at the output after reflection of input torque;c. equivalent system at the inputafter reflection ofimpedances
1
212
2 )()()(N
NsTsKDsJs
Writing Equations:
Example 1
Find the transfer function, θ2(s) / T1 (s) for the figure
System after reflection on torques and impedances to the output shaft
2
2
1
21
2
2
1
21
1
212
2 )()()(
DN
NDD
JN
NJJ
N
NsTsKsDsJ
e
e
eee
Ke=K2
Recitation find )(/)( 12 sTs
eee KsDsJ
NN
sT
ssG
212
1
2 /
)(
)()(
1642
5314
NNN
NNN
Example 2
Find the transfer function θ1(s) / T1(s) for the system in the figure
)()()( 112 sTssDsJ ee
sDsJsT
ssG
ee
21
1 1
)(
)()(
Electromechanical System Transfer Function
NASA flightsimulatorrobot arm withelectromechanicalcontrol systemcomponents
a
btm
m
mat
a
m
RKK
DJ
ss
JRK
sE
s
1
)/(
)(
)(
Electro Mechanical System
Given the system and torque-speed curve in the figure find the transfer function θL(s) / Ea(s) ώnoload = 50
2
2
2
1
2
2
2
1
10
18002
1210
17005
m
Lam
m
Lam
D
N
NDDD
J
N
NJJJ
)667.1(
417.0
)(
)(
)2*5(10121
12/5
)(
)(
250
100
5100
500
100
50
500
sssE
s
sssE
s
eK
e
T
R
K
e
T
a
m
a
m
loadno
ab
a
stall
a
t
a
loadno
stall
Electric Circuit Analogs
)()()( 2 sFsXKsfMs v
Series Analog
)()(1
sEsICs
RLs
)()(
)()(2
sVs
KfMssF
sXs
KsfMssF
v
v
X(s)=V(s) / s
)()()( 2 sFsXKsfMs v
Parallel Analog
Development ofparallel analog:a. mechanical system; b. desired electricalrepresentation; c. parallel analog;d. parameters forparallel analog
)()(11
sIsELsR
CS
Kirchoff’s nodal equation for simple RLC network in b
Draw a series and parallel analog for the rotational system
Example 5
Physical System
Schematic Block Diagram
a. Torques on J1
due only to themotion of J1
b. torques on J1
due only to themotion of J2
c. final free-bodydiagram for J1
a. Torques on J2due only to themotion of J2;b. torques on J2due only to themotion of J1c. final free-bodydiagram for J2
0)()()(
)()()()(
222
21
2112
1
sKsDsJsK
sTsKsksDsJ
