hesam zomorodi moghadam advisor: dr. robert g. landers, dr. s. n. balakrishnan
DESCRIPTION
Application of Hierarchical Optimal Control in Force-Position control of Complex Manufacturing Processes. Hesam Zomorodi Moghadam Advisor: Dr. Robert G. Landers, Dr. S. N. Balakrishnan Mechanical and Aerospace Engineering. - PowerPoint PPT PresentationTRANSCRIPT
Application of Hierarchical Optimal Control in Force-Position control of Complex Manufacturing Processes
Hesam Zomorodi Moghadam
Advisor: Dr. Robert G. Landers, Dr. S. N. Balakrishnan
Mechanical and Aerospace Engineering
AGGREGATING TOP LEVEL ERROR
Application of Hierarchical Optimal Control in Force–Position Control of Complex Manufacturing Processes
OBJECTIVES Developing a hierarchical optimal controller to regulate the cutting force
and tool position, simultaneously, in a micro end milling process.
Analyze the performance of the proposed methodology for a sharp corner and compare to normal methods.
Hesam Zomorodi MoghadamMechanical and Aerospace Engineering
Dr. Robert G. LandersDr. S.N. BalakrishnanMechanical and Aerospace Engineering
FUTURE WORK Apply this methodology on a parallel CNC machine with six axes to
perform a complex end milling tasks.
Improve robustness properties of the controller for process uncertainties.
AcknowledgementsThis research was supported by the
Missouri S&T Intelligent Systems Center
BACKGROUND
Micro machining: Position tracking versus forces
Axes can be treated as subsystems
Decentralized controlSimple structureNot proper for coupled systems
Unsynchronized motion
Distributed controlInteraction among local controllersCommunication delays Approximations apply
Hierarchical controlHigher level coordinators Lower communication delays Simpler structure
An intelligent method is needed to simultaneously regulate axial and machining force errors.
http://www.alibaba.comhttp://cuttingtoolschicago.com
M.W. Cho,2007, Journal of ECERS
http://karnataka.inetgiant.in
APPROACH Hierarchical optimal control method with modified cost function.
Higher level goal (zero cutting force tracking error) is expressed by bottom level states.
Relationship between cutting force and axial errors.Machining force in an end milling process is a function of depth of cut, spindle speed and the feed.
general tracking with Internal Model Principle
aggregation relationship
modified cost function 1
1
2
bot bot
T Tbot bot bot bot bot bot
C x C x
u R u x Q x
T
botk
r rF Fk k k q k k k
Jk
e
k k
e
k
control axes
top level goal
depth of cut
End Mill
θi,j
Part
feed direction
Ns
TF CF
i,jLF
z
CF i,j
i,ji,j
jth division of ith flute
fi,j is the instantaneous feed (mm) d is the depth of cut (mm) V is the cutting velocity (mm/min) ai,j is the chip area (mm2)
T T T
C C C
L L L
α β γi,j i, jT T
α β γi,j i, jC C
α β γi,
i,j
i,j
j ii,L j
, jL
F k K f k d k V k a k
F k K f k d k V k a k
F k K f k d k V k a k
- part clamped on dynamometer- different depths of cut and feedsNI SCXI-
1143 DAQ card
Amplifier
New10 slots 5 slots15 slots
Simulation results vs. experimental data Ns = 7000 rpm, feed rate = 0.5 in/min
and d = 0.02, 0.03. 0.04 and 0.05 in
Higher Level Goal: Keep maximum valueof normal cutting force per each spindle revolution at a specified value
21
21
21
2121
21
2 2 211 12max max
112
11 12
2 211 12
11
2
2
211 2
2
1
( )ref
crx s s s
n nd
cx s s s
d
b
ry
b
y
V N N c N cF F F K
d d d d d
V N N c N cK
d d d d d
V
V
Top level error
RESULTSTracking diamond profile while keeping the maximum cutting
force at a desired value
Two control structures were compared;Hierarchical controllerDecentralized controller (q = 0, i.e., no coupling between axes)
6.1 6.15 6.2 6.25
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
time (s)
ex (
mm
)
6.12 6.13 6.14-15
-10
-5
0
x 10-4
time (s)
ey (
mm
)
6.126.14 6.16 6.18 6.2
0
50
100
time (s)
F
(N
)
18.76 18.78 18.8
-20
-15
-10
-5
0
5
x 10-3
x (mm)
y (
mm
)
qbot
=0.0001
qbot
=0.001
qbot
=1
qbot
=10
Results for decentralized controller
6 6.5 7 7.5-15
-10
-5
0
x 10-4
time (s)
ey (
mm
)
6.12 6.13 6.14 6.15
0
50
100
time (s)
eF (
N)
18.76 18.78 18.8
-20
-15
-10
-5
0
5
x 10-3
x (mm)
y (
mm
)
6.1 6.15 6.2 6.25
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
time (s)
ex (
mm
)
q/qbot
=5
q/qbot
=2
q/qbot
=1
q/qbot
=0.1
q/qbot
=0.0002
Results for hierarchical controller
Emphasis on ex decreases
0 5 10 15 20 25
-10
-5
0
5
10
15
X [mm]
Y [
mm
]
Start point
20o
DISCUSSION AND CONCLUDING REMARKS
A Hierarchical Optimal controller combined with Internal Model Principle was proposed.
A decentralized controller was tested with the same conditions.
Decrease in emphasis on axial error resulted in an increase in transient axial error as well as the settling time; however, it caused a decrease in transient cutting force error.
When decentralized controller was implemented, cutting force error generally had larger overshoot values and, even when the error was comparable to the error from the hierarchical controller, axial errors were larger (i.e., almost two times).
Fitting simulated forces to measured forces using particle swarm optimization
Data acquisition (Labview)
21 21
21
max 211 11 12
211 12
cn s
bt s s
d
F K N N c N c
d d d d
V
d
A curve was fit to maximum value of normal cutting force per spindle revolution
Linearizing around the operating point bF k C k k x
Modeling forces in end milling processes
Tool wear monitor
Finding Unknown Model Parameters
500 1000 1500 2000 2500 3000
103
104
iteration
pe
rfo
rma
nc
e in
de
x (
N2)
Optimization index history for the second goal function
32.145 32.15 32.155 32.16 32.165 32.17-10
-5
0
Fx
[N
]
32.145 32.15 32.155 32.16 32.165 32.17
-10-5
05
Fy
[N
]
32.145 32.15 32.155 32.16 32.165 32.17
-2
-1
0
1
Fz
[N]
time [s]