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]