optimization presentation

ELECTROMECHANICAL FIN CONTROL SYSTEM PERFORMANCE OPTIMIZATION

Santosh Rohit Yerrabolu

Anirudh Pasupuleti

Vladimir Ten

MAE 550 Engineering Optimization

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.

2V. Ten, S-R. Yerrabolu, A. Pasupuleti December 12, 2009

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:


System Component Analysis

Reflected Inertia

Total System Inertia

Rotational Acceleration

General Representation

JActuator

Lead

JActuator JLoad

WLoad

JTotal

2

*4.25*2

GR

Lead

g

wJ Load

Load

JTotal

PeakMotorMotorPeakTStatictionSystemFricT

4.25*2

T

: torque)effective increasedfriction down slowing(when on Decelerati

T

: torque)effective reducesfriction ngaccelerati(when on Accelerati

:tionRepresenta General

icFrictionSystemStat

icFrictionSystemStat

Leadx

J

T

J

T

J

T

ScrewRod

Total

PeakMotor

Motor

Total

PeakMotor

Motor

Total

PeakMotor

Motor

Peak

Peak

Peak


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.

Tm TsA TvL

Ja

Lead

F

V

bA

Rod End


System Control Analysis

Motor and Compensator Description:

Using Kirchhoff law motor current/electrical part

can be represented as:

Mechanical part of the system

yields:

So State Space Form

yields:

With output form:

System output with PI compensator can be defined as:

S

Z

S

Kiff

iff

1

S

Z

S

Kmvff

mvff

1

ifbK

mvfbK

modV

Vswcmd icmd

-

+

tttt RSL

1

BJS

K t

eK

wi

vbemf

v+

-

+

-

LJ

KKRBs

LJ

RJLBs

LJ

KKRB

J

Bs

KKRB

J

et

et

et

2

)(

S

Z

S

Kiff

iff

1

modV

Vs v+

-

icmd i

ifbK


Design Variables and Constraints

Design Variables :

Constraints :


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.


Performance Verification

Step Response Bode PlotUnit Step Response of 6278 s2 + 5.012e006 s + 6.814e007/s3 + 6872 s2 + 5.872e006 s + 6.814e007

t (sec)

Outp

ut y

0 0.05 0.1 0.15 0.2 0.25 0.30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

System: CurrentClosedLoop

Rise Time (sec): 0.000334


Settling Time (sec): 0.171


Peak amplitude >= 0.996

Overshoot (%): 0

At time (sec) > 0.3

Bode Diagram

Frequency (rad/sec)

100

101

102

103

104

105

-90

-45

0

45

System: CurrentClosedLoopPhase Margin (deg): -180Delay Margin (sec): InfAt frequency (rad/sec): 0Closed Loop Stable? Yes

Phase (

deg)

-25

-20

-15

-10

-5

0

System: CurrentClosedLoopPeak gain (dB): -2.89e-015At frequency (rad/sec): 2.35e-007

Magnitude (

dB

)


System Simulation The simulation is done based

on Optimized System Parameters

The simulation is done based on Optimized System Parameters

0 0.05 0.1 0.150

2

4

6

8

10

12

14

16

18

20Motor Velocity

Time, sec

Moto

r V

elo

city,

rad/s

ec

Motor Velocity

Velocity Command

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-15

-10

-5

0

5

10

15Motor BEMF

Time, sec

Voltage,

volts

Phase A

Phase B

Phase C


System Simulation Feedback Response and Motor Position

-5 0 5 10

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6Motor Current Command & Feedback

Time, sec

Curr

ent,

Am

ps

Current Command

Actual Motor Current

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Motor Position

Time, sec

Moto

r P

ostition,

rad


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.



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 stopbandattenuation 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.


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;


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.


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.


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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