This document summarizes Deepak Agarwal's master's dissertation on time-optimal control of the Z-axis motion in a wire bonding machine. Agarwal developed models of the wire bonder's rigid body and flexible dynamics. He then generated time-optimized motion commands using these models and implemented a two-degree-of-freedom controller with shaped commands, feedforward control, and feedback control to achieve precise motion with minimal residual vibrations in under 285.6 milliseconds. Simulation results showed the controller was able to successfully drive the system using the optimized commands.

1. 1
Ruth and Joel Spira Laboratories of
Electromechanical System
Time-optimal Control of Z-Axis of Wire Bonder
Master Dissertation Defense
Deepak Agarwal
February, 2004

2. 2
Ruth and Joel Spira Laboratories of
Electromechanical System
Advisor
Dr. Meckl
Committee
Dr. Yao
Dr. Chiu
Lab Mates
Acknowledgements

3. 3
Ruth and Joel Spira Laboratories of
Electromechanical System
CONTENTS
Introduction
System Modeling and Analysis
Command Generation
Control Strategies
Results
Conclusion and future work

4. 4
Ruth and Joel Spira Laboratories of
Electromechanical System
INTRODUCTIONINTRODUCTION

5. 5
Ruth and Joel Spira Laboratories of
Electromechanical System
OBJECTIVES
Research Motivation
Improve bond-cycle time to improve productivity.
Develop methodology to control residual vibrations of bond head.
Develop time-optimal motion commands.
Develop controller design framework.
Introduction

6. 6
Ruth and Joel Spira Laboratories of
Electromechanical System
Introduction
Input Force Output Acceleration
Rigid body
displacement
TIME OPTIMAL COMMAND METHODLOGY

7. 7
Ruth and Joel Spira Laboratories of
Electromechanical System
Wire Bonder: Kulicke and Soffa Model 1418/19
Main Components
Computer
Work area
Horizontal Movement: X-Y Table Vertical Movement: Z-axis
SYSTEM SETUP
Introduction

8. 8
Ruth and Joel Spira Laboratories of
Electromechanical System
SYSTEM MODELING ANDSYSTEM MODELING AND
ANALYSISANALYSIS

9. 9
Ruth and Joel Spira Laboratories of
Electromechanical System
SYSTEM MODELING
System Modeling

10. 10
Ruth and Joel Spira Laboratories of
Electromechanical System
EQUATIONS OF MOTION
Equation of motion are formulated from Lagrange’s method.
Lagrange formulation
Equation of motion
i
i i i i
d T T U R
Q
dt q q q q
 ∂ ∂ ∂ ∂
− + + = ÷
∂ ∂ ∂ ∂ & &
System Modeling
1,2,...,i N=
( )( ) ( ) ( )1 1( ) ,
.
C C T AJ J J b L K G V Tθ θ θ θ θ θ θ 
+ + + − = − ÷
 
&& &&
Nonlinear
inertial
effects
Nonlinear
damping
effects
Nonlinear
coriolis
effects
Net available
torque
Load torque

11. 11
Ruth and Joel Spira Laboratories of
Electromechanical System
EFFECTIVE INERTIA AND DAMPING
System Modeling
-150 -100 -50 0 50 100 150
0
1
2
3
4
5
x 10
-5
Crank angle (deg)
Nonlinearinertia(Kgm2
)
-150 -100 -50 0 50 100 150
1.45
1.5
1.55
x 10
-3
Crank angle (deg)
Nonlineardamping(Nmsec/rad)
( )J θ
CJ
Cb
( )
.
J θ
Operating Range
Operating Range
Operating range of crank rotation from -500
to 1000
.
Effective inertia is chosen as maximum value.
Effective damping is same as estimated damping from linear model.

12. 12
Ruth and Joel Spira Laboratories of
Electromechanical System
RIGID BODY DYNAMICS (PARAMETER ESTIMATION)
System Modeling
Z Motor Dynamics
c c m T AJ b K G Vθ θ τ+ = =&& &
Motor Frequency Response
Input: Voltage input to servo
amp
Output: Tachometer velocity
(volts)
Jc =3.32x10-5
kgm2
bc=1.494x10-3
Nm sec/rad
(estimated value)

13. 13
Ruth and Joel Spira Laboratories of
Electromechanical System
FLEXIBLE DYNAMICS (PARAMETER ESTIMATION)
System Modeling
Overall Frequency Response
Input: Servo amplifier
Voltage
Output: Tip Acceleration
(Volts)
ωn =4158 rad/sec
ς=0.032 (estimated value)
Overall linear transfer function
( )
( ) ( ) ( )
2
2 2
2.5
1 2
n
c c n n
K s
G s
J s b s s s
ω
τ ςω ω
=
+ + + +

14. 14
Ruth and Joel Spira Laboratories of
Electromechanical System
LINEARIZED AND NONLINEAR MODEL COMPARISON
L L
s
J s b+
Control Strategy

15. 15
Ruth and Joel Spira Laboratories of
Electromechanical System
MODEL VALIDATION (SERVO SYSTEM)
OPEN LOOP
Input: Voltage to amplifier
Output: Servo angular
displacement
Discrepancy
Uncertainties and
nonlinearities not modeled.
System Analysis

16. 16
Ruth and Joel Spira Laboratories of
Electromechanical System
MODEL VALIDATION (OVERALL SYSTEM)
System Analysis
0.88 0.9 0.92 0.94 0.96 0.98 1
-20
-10
0
10
20
Actual Response 15 deg
Simulated Response 15 deg
0.88 0.9 0.92 0.94 0.96 0.98 1
-10
0
10
TimeResponse(Volts)
Actual Response 0 deg
Simulated Response 0 deg
0.88 0.9 0.92 0.94 0.96 0.98 1
-10
-5
0
5
10
Time (sec)
Actual Response -65 deg
Simulated Response -65 deg
OPEN LOOP
Input: Square wave voltage
to amplifier
Output: Accelerometer
output (volts)
0.87 0.875 0.88 0.885 0.89 0.895 0.9
-20
-15
-10
-5
0
5
10
15
20
Actual Response 15 deg
Simulated Response 15 deg

17. 17
Ruth and Joel Spira Laboratories of
Electromechanical System
COMMAND GENERATIONCOMMAND GENERATION

18. 18
Ruth and Joel Spira Laboratories of
Electromechanical System
OBJECTIVES
Develop methods for generating exact zero-vibration commands.
Develop methods for generating commands that are robust to
modeling errors.

19. 19
Ruth and Joel Spira Laboratories of
Electromechanical System
WIRE BONDING CYCLE (Z WAVEFORMS)
Command Generation
Prime Focus: 5 High Acceleration Moves in the Cycle

20. 20
Ruth and Joel Spira Laboratories of
Electromechanical System
0 0.05 0.1 0.15 0.2 0.25
-40
-20
0
20
40Velcoity(rad/s)
0 0.05 0.1 0.15 0.2 0.25
-5000
0
5000
Time (sec)
Acceleration(rad/s2
)
Obtain Z-velocity waveforms experimentally
Differentiate to get acceleration profile
Command Generation

21. 21
Ruth and Joel Spira Laboratories of
Electromechanical System
DEVELOPMENT OF TIME OPTIMIZED WAVEFORMS
Utilize maximum available torque supplied by the actuator
THE APPROACH
Divide actuator saturation limit by peak acceleration in the
bonding cycle.
Use this scale factor to increase the current waveform acceleration.
Numerically integrate acceleration profile to generate
displacement.
Find the time-value where the current waveform’s displacement
equals the new displacement.
The reduced time is optimized-time for each move.
Generate a complete waveform.
Command Generation

22. 22
Ruth and Joel Spira Laboratories of
Electromechanical System
RESULTS
Current waveform
Residual vibration : 2 m/s2
Torque-optimized waveform
Residual vibration : about 40 m/s2
Time saving: 17.8%
Command Generation

23. 23
Ruth and Joel Spira Laboratories of
Electromechanical System
APPROACH FOR GENERATING TORQUE-OPTIMIZED
COMMANDS
1ST
STEP
Rigid body optimal move time estimation.
Tr – rigid body move time (sec)
b – viscous damping (Nm sec/rad)
J – rigid body inertia (kgm2
)
- rigid body move (rad)
Command Generation
2 2
1 2 0
fr
r
MAX
bb T b
TJ F J
e e
θ × 
+ ÷
 
− + =
fθ

24. 24
Ruth and Joel Spira Laboratories of
Electromechanical System
APPROACH
2nd
STEP
Non-dimension form of transfer function
is non-dimensional rigid body pole,
ς is the damping ratio of the flexible mode.
is the natural frequency of flexible mode
Command Generation
( ) ( )( )
*
2 * 2
4 1
( )
2 1n r
G s
s s s sT τ ςω
=
+ + +
*
τ
nω
( ) ( )( )( )
*
2 * 2 2
4 1
( )
2 1 2 1n r
G s
s s s s s sT τ ς ςω
=
+ + + + +
Non-robust case
Robust case

25. 25
Ruth and Joel Spira Laboratories of
Electromechanical System
APPROACH
3rd
step
Discretizing the continuous state space form of the system.
where is discrete system matrix
discrete input matrix
4th
step
Least square optimization such that
subject to constraint
Command Generation
( ) k
ϕ = +0UΦ x CU
T
e= A
Φ
1
[ k−
=CΦ Γ 2k−
Φ Γ 3k−
Φ Γ ......... ]Γ
0
T
e dξ
ξ= ∫
A
Γ b
0[u=U 1u 2u 1......... ]ku −
1
2
min( )T
η ϕ ϕ=
min 1 maxku u u−< <

26. 26
Ruth and Joel Spira Laboratories of
Electromechanical System
SIMULATION RESULTS
0 0.05 0.1 0.15 0.2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time (sec)
Shapedtorque(Nm)
Command Generation
0 0.05 0.1 0.15 0.2
-1000
0
1000
Time (sec)
Tipacceleration(m/sec2
)
0.092 0.094 0.096 0.098 0.1 0.102 0.104 0.106 0.108
-2
0
2
Time (sec)
Tipacceleration(m/sec2
)
0 0.05 0.1 0.15 0.2
-0.01
-0.005
0
Time (sec)
Tipdisplacement(m)
Open loop linear
system
INPUT
OUTPUT

27. 27
Ruth and Joel Spira Laboratories of
Electromechanical System
COMMAND GENERATION FOR NONLINEAR SYSTEM
Command Generation
Rigid body moves Inertia value Damping value
Descent to first bond. 1.08Jc bc
Ascent to loop
height/Descent to second
bond
1.15Jc bc
Ascent to clamp height. 1.6Jc bc
Rise to reset height 1.5Jc bc
Effective values of inertia and damping used for different moves

28. 28
Ruth and Joel Spira Laboratories of
Electromechanical System
CONTROL STRATEGYCONTROL STRATEGY

29. 29
Ruth and Joel Spira Laboratories of
Electromechanical System
CONTROL DESIGN FRAMEWORK - 2 DOF CONTROLLER
DESIGN
Control Strategy
The most effective control strategy is one which combines:
•Shaped command
•Feedback controller
•Feedforward controller
Command
Generator
Feedforward
Controller
Feedback
Controller Plant
Output
Desired
Action
Reference

30. 30
Ruth and Joel Spira Laboratories of
Electromechanical System
TASK DELEGATION
Shaped commands
Serve as reference for the system.
Incorporates robustness into shaped commands to variations in natural
frequency and damping ratio.
Feedforward controller
Makes transient response faster.
Cancels plant nonlinearities.
Feedback controller
Reduces the effect of model uncertainties.
Good regulation in presence of disturbances.
Control Strategy

31. 31
Ruth and Joel Spira Laboratories of
Electromechanical System
SIMULATION RESULTSSIMULATION RESULTS

32. 32
Ruth and Joel Spira Laboratories of
Electromechanical System
PERFORMANCE SPECIFICATIONS
Performance specifications
Residual vibration level less than 10 m/s2
Cycle time less than 285.6 msec
Inputs used for performance comparison
Bang-bang
Ramped sinusoids
Results

33. 33
Ruth and Joel Spira Laboratories of
Electromechanical System
OPEN LOOP SIMULATION RESULTS
Input: Shaped torque
Problem: Drift in displacement
Solution: Feedback control
Results

34. 34
Ruth and Joel Spira Laboratories of
Electromechanical System
CLOSED LOOP SIMULATION RESULTS (WITH
FEEDBACK)
Results
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-2000
-1000
0
1000
Time (sec)
Accleration(m/sec2
)
0.118 0.12 0.122 0.124 0.126 0.128 0.13 0.132 0.134 0.136 0.138
-100
0
100
200
Time (sec)
Accleration(m/sec2
)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-10
-5
0
5
x 10
-3
Time (sec)
Displacement(m)
Input: Shaped torque
Problem: Residual vibration
Solution: Feedforward control

35. 35
Ruth and Joel Spira Laboratories of
Electromechanical System
CLOSED LOOP SIMULATION RESULTS (WITH
FEEDBACK AND FEEDFORWARD)
P
L L
s
G
J s b
=
+
Results
( )( ) ( ) ( , ) ( )m loadJ J b Lτ θ θ θ θ θ θ τ θ= + + − +&& & &&
Feedforward control strategies
Linear feedforward
Rigid body inversion
Linear plant inversion
Nonlinear feedforward
Rigid body inversion
Nonlinear plant inversion
(computed torque)

36. 36
Ruth and Joel Spira Laboratories of
Electromechanical System
CLOSED LOOP SIMULATION RESULTS (WITH
FEEDBACK AND FEEDFORWARD)
Results
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-1000
-500
0
500
1000
Time (sec)
TipAccleration(m/sec2
)
Closed Loop Acceleration of Nonlinear Model with Nonlinear Feedforward
Closed Loop Acceleration of Nonlinear Model with Linear Feedforward
0.17 0.172 0.174 0.176 0.178 0.18 0.182 0.184 0.186 0.188 0.19
-15
-10
-5
0
5
10
15
Time (sec)
TipAccleration(m/sec2
)
Closed Loop Acceleration of Nonlinear Model with Nonlinear Feedforward
Closed Loop Acceleration of Linear Model with Linear Feedforward
Reduction in residual vibration.
Does not satisfy performance
specification.

37. 37
Ruth and Joel Spira Laboratories of
Electromechanical System
BANG-BANG vs. RAMPED SINUSOID INPUT
INPUT COMPARISON
Results
Bang-bang input profile
Better available torque
utilization.
Better time-optimality.
Ramped sinusoid input profile
Better vibration suppression
capability.
More robust to plant
uncertainties.

38. 38
Ruth and Joel Spira Laboratories of
Electromechanical System
BANG-BANG vs. RAMPED SINUSOID INPUT
CLOSED LOOP ACCELEARTION COMPARISON
Results
Bang-bang input is time-optimal
Ramped sinusoid input has lesser
vibration level.
Tradeoff
Time-optimality vs. Vibration
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-1000
-500
0
500
1000
Tim e (sec)
TipAccleration(m/sec2
)
0.045 0.05 0.055 0.06
-15
-10
-5
0
5
10
15
Tim e (sec)
TipAccleration(m/sec2
)
nonlinear model with bang-bang input
nonlinear model with ramped sinusoid
nonlinear model with bang-bang input
nonlinear model with ramped sinusoid

39. 39
Ruth and Joel Spira Laboratories of
Electromechanical System
ROBUSTNESS TO PARAMETER VARIATIONS
Investigate the system performance when the following
parameters are varied:
Rigid body viscous damping
Rigid body inertia
Natural frequency
Damping
Results

40. 40
Ruth and Joel Spira Laboratories of
Electromechanical System
± 10% VARIATION IN RIGID BODY DAMPING
Results

41. 41
Ruth and Joel Spira Laboratories of
Electromechanical System
± 10% VARIATION IN RIGID BODY INERTIA
Results

42. 42
Ruth and Joel Spira Laboratories of
Electromechanical System
± 5% VARIATION IN NATURAL FREQUENCY
Results

43. 43
Ruth and Joel Spira Laboratories of
Electromechanical System
± 5% VARIATION IN MODAL DAMPING
Results

44. 44
Ruth and Joel Spira Laboratories of
Electromechanical System
BONDING CYCLE
ATTRIBUTES
CURRENT
WAVEFORM
OPTIMIZED-
TIME
WAVEFORM
BANG-BANG
PROFILE
RAMPED
SINUSOID
PROFILE
Total time for
5 moves (msec)
122.80 55.72 29.10 40.87
Saving in total
move time (msec)
--- 54.63% 76.30% 66.72%
Total non-move
time (msec)
160.8 160.88 162.8 163.03
Total bonding cycle
time (msec)
285.6 216.6 191.9 203.9
Time saving per
Cycle
--- 24.15% 32.8% 28.6%
Highest Residual
Vibration Amplitude
(m/s2
)
2 40 5 5
QUANTITATIVE SUMMARY
Results

45. 45
Ruth and Joel Spira Laboratories of
Electromechanical System
CONCLUSIONS
Developed approach is likely to work for nonlinear systems in which:
Nonlinearities are tied in with the rigid-body mode.
Resonant mode is well defined.
Robustness to modeling errors in natural frequency and damping ratio
can be incorporated into the design of shaped commands.
The effective control strategies combine shaped command, feedback,
and feedforward controller to achieve fast motion with minimum
residual vibration.
Wire bonder performance can be significantly improved as
A better level of residual vibration has been achieved.
Bonding cycle time has been reduced.
Conclusion

46. 46
Ruth and Joel Spira Laboratories of
Electromechanical System
FUTURE WORK
Generate synchronized controlled motions using X, Y and Z servos
which complete the bonding process, as z-axis model and control
strategies have been developed.
Implement developed control strategies on the actual system.
Modify current approach to accommodate negative velocity regions in
the profile where bonding force is applied.
Use nonlinear model for the optimization technique to generate shaped
motion profiles.
Future Work

47. 47
Ruth and Joel Spira Laboratories of
Electromechanical System
QUESTIONS ?