1. ELECTROMECHANICAL FIN CONTROL SYSTEM
PERFORMANCE OPTIMIZATION
Santosh Rohit Yerrabolu
Anirudh Pasupuleti
Vladimir Ten
MAE 550 Engineering Optimization

2. Introduction
• In this project we will be optimizing some major electromechanical control system
parameters for given performance.
• The system consists of an electromechanical actuator, electronic control unit (ECU
or Controller) and associated interconnecting cables between an actuator and a
controller.
• The proposed Motor is a Brushless DC motor (BLDC). The reason the group
selected a BLDC motor over a conventional brushed motor is that a delivery of
minimum amount of Total Harmonic Distortion is one of the most critical factors in
most Aerospace applications.
• The proposed Actuator is a Ballscrew type actuator.
• The proposed Controller is an FPGA based controller. The FPGA performs all of the
high speed logic and algorithmic functions. The FPGA provides several important
functions to the system. First and foremost, it provides the closed loop control for
complex system.
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 2

3. Basic Concept of the System
• The Control Electronics provides closed loop position control of four fin actuators
based on command received from Flight Computer and Actuators Feedback:
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 3

4. System Component Analysis
Reflected Inertia Rotational Acceleration
Total System Inertia General Representation
Lead
JActuator
WLoad
TSystemFriction Static TMotorPeak Motor Peak

JTotal
JActuator JLoad
General Representation :
T
Motor  MotorPeak

Peak
J Total
Acceleration (when accelerating friction reduces effective torque) :
T T
w 
2 Motor  MotorPeak SystemStaticFriction

Lead 
J Load  Load  J Total
Peak
JTotal 
g  2 * 25.4 * GR  Deceleration (when slowing down friction increased effective torque) :
T T
Motor  MotorPeak SystemStaticFriction

Peak
J Total
Lead
Rod  Screw
x 
2 * 25.4
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 4

5. System Component Analysis
Equivalent Actuator Free Body Diagram:
• Once the rod end force (F) and speed (V) requirements are defined, we can work
backwards through the actuator to estimate motor torque and speed.
• The peak torque is then compared to motor peak torque/speed curves to make
sure it is within peak capabilities and then the RMS current is calculated based on
duty cycle and compared to the RMS current rating of the motor (actuator) to
determine if this cyclic operation can be maintained continuously.
Lead
Tm TsA TvL
F
Ja Rod End
V
bA 
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 5

6. System Control Analysis
Motor and Compensator Description:
Mechanical part of the system System output with PI compensator can be defined as:
yields:
Using Kirchhoff law motor current/electrical part
can be represented as:
S S
wcmd + 1 icmd + 1 Vs v + 1 i Kt w
Z mvff Z iff
K mvff K iff Vmod Ltt S  Rtt JS  B
- S - S -
vbemf
So State Space Form Ke
yields: K ifb
K mvfb
 J  B  RB  K t K e 
icmd +
S
1 
 RB  K K  ( s  J ) 
  i
Vs v  
Z iff  t e  LJ
With output form:
K iff Vmod LB  RJ RB  K t K e
- S s 
2
s
LJ LJ
K ifb
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 6

7. Design Variables and Constraints
Design Variables :
Constraints :
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8. Transfer Function Optimization
We made several attempts to optimize our system parameters using different
optimization methods however after plugging in the data into our model none of
them would give us data that we could consider valid for implementation. We tried
to consider Multi-objective parameter estimation using particle Swarm
optimization method, however due to complexity of the system, the nature of the
physics of the process and time invariant approach the method is very difficult to
apply. Finally we are optimized our parameters using the time cancelation method
going from time domain into frequency domain and then back to time domain.
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 8

9. Performance Verification
Step Response Bode Plot
Unit Step Response of 6278 s 2 + 5.012e006 s + 6.814e007/s 3 + 6872 s 2 + 5.872e006 s + 6.814e007 Bode Diagram
1 0
System: CurrentClosedLoop
System: CurrentClosedLoop System: CurrentClosedLoop
Peak amplitude >= 0.996
Settling Time (sec): 0.171 Overshoot (%): 0
Peak gain (dB): -2.89e-015
0.9
At time (sec) > 0.3 -5 At frequency (rad/sec): 2.35e-007
System: CurrentClosedLoop
Rise Time (sec): 0.000334
0.8
Magnitude (dB)
-10
0.7
-15
0.6
-20
Output y
0.5
-25
45
0.4
0.3 0
Phase (deg)
System: CurrentClosedLoop
Phase Margin (deg): -180
0.2 Delay Margin (sec): Inf
-45
At frequency (rad/sec): 0
Closed Loop Stable? Yes
0.1
0 -90
0 0.05 0.1 0.15 0.2 0.25 0.3 0 1 2 3 4 5
10 10 10 10 10 10
t (sec) Frequency (rad/sec)
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10. System Simulation
Motor Velocity
20
The simulation is done based 18
Motor Velocity
Velocity Command
on Optimized System Parameters 16
14
Motor Velocity, rad/sec
12
10
8
6
4
2
0
0 0.05 0.1 0.15
The simulation is done based on Optimized Time, sec
System Parameters 15
Motor BEMF
Phase A
Phase B
10 Phase C
5
Voltage, volts
0
-5
-10
-15
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Time, sec
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 10

11. System Simulation
Feedback Response and Motor Position
Motor Current Command & Feedback Motor Position
1.6 1.8
Current Command
1.4 Actual Motor Current 1.6
1.2 1.4
1.2
Motor Postition, rad
1
Current, Amps
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-5 0 5 10 0
Time, sec -3
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
x 10 Time, sec
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 11

12. Digital Filter Design
• After we confirmed the optimal controller coefficients we ran a real motor control
test. The Initial Signal was obtained based on coefficient optimization
performance. Coefficients were taken into real motor control system and raw test
data was recorded into MS Excel Spreadsheet thru 4 channels digital 500MHz
Tektronix oscilloscope. Due to noises, such as power source, motor winding
imperfection, EMI issues etc. the sine wave is never perfect. The last part of this
project is to design such a digital filter that clears up all possible noises to make
design suitable for real life mission.
• For digital filter design implementation we were using 50,000 points test data that
was recorded in 2 milliseconds.
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13. Digital Filter Design
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 13

14. Digital Filter Design
We examined the spectrum of the phase voltage and it is almost non-zero from
1kHz up to 5kHz so we designed an elliptic filter, which allows frequencies up to
1kHz and stops frequencies from 5kHz and up. The intermediate response of the
filter (from 1kHz to 5kHz) is transitive with increasing attenuation as we move from
1kHz to 5kHz. This setting provokes no problem because the initial signal does not
have any frequencies inside the transition band. In a different case a more precise
filter would be required. In the design passband ripple Apas=1dB and stopband
attenuation Astop=80dB I kept by default choice. Had we chosen 60dB the
difference would be very small since both 60dB and 80dB is a huge attenuation.
Ideally we would like Apass=0dB, so as the amplitude of all the frequencies in the
passband to remain unaltered (that would be a perfect passband). However is not
possible and so Apass=1dB means that a small amplitude distortion up to 1dB is
allowed.
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 14

15. Digital Filter Design
December 12, 2009 V. Ten, S-R. Yerrabolu, A. Pasupuleti 15

16. Digital Filter Design Conclusion
When you design filter the performance is very sensitive on the coefficients
accuracy. You may notice that coefficients have many decimal digits. And here is a
trade off. If I reduce the accuracy the filter may become unstable namely it's poles
may jump out off the unit circle. And that is the problem with IIR filters. You will
need to break the transfer function in second order so to achieve numerical
stability. The advantage of the elliptical filter is that for given allowable ripple in
the passband and a minimum attenuation in the stopband, the width of the
transition band is minimized. And here we successfully implemented dual stage
digital elliptic filter:
%section 1
b1 = [1 -1.9969664834094429384 1]';
a1 = [1 -1.9965824396882807523 0.99658967925051866743]';
G1 = .21269923678879777522e-2;
%section 2
b2 = [1 -1.9994686288012706310 1.0000]';
a2 = [1 -1.9986105563553899778 0.99863550105005205459]';
G2 = .46944009614010177855e-1;
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17. Outcome of the Optimization
Due to complexity of the selected system we learned that the system breakdown
and detailed investigation of the components of the system (Motor, Actuator, and
Controller) is critical to determine the system’s Optimization Transfer Function. We
needed accurate transfer function in order to run optimization. That is why we
took really significant amount of efforts and time to investigate the system on a
component level with the detailed mathematical derivations, descriptions and
physics processes inside the system. We learned that swarm optimization method
for multi objective function is very difficult to implement. We also learned that
other methods such zero, first and second order are very difficult to implement as
well, due to high nonlinearity of the systems. Since the system is in active and all
parameters are function of time, in this project we were using frequency transform
approach, so we could reduce the order of the system and work directly with
frequency domain.
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18. Recommendations For Next Step
In controls/parameter estimation of multi disciplinary systems, such as an electro
mechanical, it is very difficult to implement standard optimization methods that
we discussed in the class so far. This is including multi-objective swarm
optimization method which is based on searching space and processing stochastic
data. When it comes to electro mechanical parameters estimation and controls,
the problem begins after integration all three parts into one cost function as a
transfer function and this function becomes highly nonlinear. For example in our
simple case we were dealing with polynomials of third order differential equations.
Moreover each and every parameter of the system has its own operating time
domain and limitations and it cannot be liberalized due to a different state
transitioning matrix, which is highly nonlinear as well. When the system is in
differential mode (servo) and the steady state is not an option, the only reasonable
approach of optimizing cost function is to convert a system of Ns order differential
equations time domain into frequency domain. And this optimization approach we
finally selected in this project to optimize our electro mechanical control system.
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19. Reference
1. George Younkin - Industrial Servo Control Systems: Fundamentals and
Applications;
2. Richard Valentine - Motor Control Handbook, 1998;
3. Sergey Lyshevski - Electromechanical Systems, Electric Machines, and Applied
Mechatronics;
4. Chi-Tsong Chen - Linear System Theory and Design, 3rd edition, 1999;
5. Garret Vanderplaats - Numerical Optimization Techniques for Engineering Design
4th edition;
6. Ravindran, K.M. Ragsdell, G.V. Reklaitis – Engineering Optimization Methods and
Applications, 2nd edition;
7. V.P. Sakthivel Multi-objective parameter estimation of induction motor using
particle swarm optimization;
8. D. Lindenmeyer An induction motor parameter estimation method;
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