Optimization Project

MAE 550 ENGINEERING OPTIMIZATION PROJECT FALL 2009

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ELECTROMECHANICAL FIN CONTROL

SYSTEM PERFORMANCE OPTIMIZATION

Group Project

December 11, 2009

Vladimir Ten Santosh Rohit Yerrabolu Anirudh Pasupuleti Instructor: Dr. English


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1. Introduction These days Digital Signal Processing and FPGA technology have become affordable for almost any area where mechanical actuation is involved: from a portable CD player or power window/power lock in a car to thrust vector control in a Space Shuttle. In some power applications such as launch systems, re-entry vehicles or fin control electromechanical actuation is preferable to hydraulic actuation. The reasons for this are:

Electro mechanical actuators are more efficient per input power unit;

Electro mechanical actuators don’t utilize complex hosing systems;

Electro mechanical actuators do not require compression fluids (oil);

Electro mechanical actuators do not require complex valves and draining systems as a part of safety systems;

The hardware itself takes less volume and weight per output power. In this project we will be optimizing some major electromechanical control system parameters for given performance. The system provides a motive force required to move a fin in both directions, CW and CCW. 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 a majority of Aerospace applications. The proposed Actuator is a Ballscrew type actuator. The actuator provides an output shaft interface for control fin mounting. Fin movement is tracked using BLDC motor Hall Effect Device (HED) feedback. This simple feedback scheme, when combined with a lookup table in the controller, provides accurate positioning, reduces overall cost of the Control System (CS), and eliminates the contacting wiper element of an arc segment potentiometer. All four actuators are controlled by a single-board controller that receives commands from the flight computer, and power from the system battery. 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 of four flight control surfaces. The control architecture provides an outer position loop, an inner velocity loop, and a PWM pulse by pulse current limit. The FPGA manages communication with the Flight Computer, the CS operating mode control, and the interface to the analog to digital conversion device. The FPGA also provides commutation for the brushless DC motor based on the PWM and motor direction values calculated and the HED feedback from the motor. As


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a part of the commutation control, the FPGA also controls the motor modulation technique and the current limit. The FPGA also provides digital filtering on the HED state and current limit inputs to prevent noise induced false states from affecting the system’s operation. The controller consists of a low section, control circuitry board, and a high section, called power stage to provide brushless DC motor commutation using Insulated Gate Bipolar Transistors (IGBT).

2. System Design Analysis 2.1 Basic Operation/Description A functional schematic of the proposed electromechanical fin control system is shown in Figure 2.1-1. The CS receives commands from the missile flight computer via a serial bi-directional data link. Generally the industry standard RS-422 interface is being used for this type of application. The CS receives power from the system battery of 28 VDC. This should help simplify the missile-level electrical design, as the CS would use the same voltage as other systems and eliminate the need for a battery tap. The CS controller electronics convert the serial commands and battery power to PWM current and direction signals to each of four EM actuators. The actuators provide rotary motion to output shafts, which are mechanically fastened to four control fins, providing motion control to the vehicle. The fin position loop is closed by counting the state changes of HEDs in the actuator BLDC motors.

Fin Actuator # 1

BLDC Motor

Balscrew/Crankarm

Fin Actuator # 1

BLDC Motor

Balscrew/Crankarm

Fin Actuator # 1

BLDC Motor

Balscrew/Crankarm

Fin Actuator # 1

BLDC Motor

Balscrew/Crankarm

Control

Electronics

Flight

Computer

Battery

Fin # 1

Fin Lock

Fin # 4

Fin Lock

Fin # 3

Fin Lock

Fin # 2

Fin LockVladimir Ten

Santosh Rohit Yerrabolu

Anirudh Pasupuleti

Project MAE 550

Figure 2.1-1 The Control Electronics provides closed loop position control of four fin actuators based on commands received from RS-422 interface and actuator feedback,


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which is derived from the motor HEDs. The actuator control algorithm includes both position and velocity loops implemented in firmware and an active current limit implemented in hardware. Telemetry and Built-in-Test (BIT) data are sent from the Control Electronics over the RS-422 communications interface in response to every valid position command message. The entire CS is powered by +28VDC. The low voltage section of the Control Electronics is powered by two on-board switching power supplies, a +28V to +12V regulator and a +28V to +3.3V regulator. Other small signal voltages are provided by linear regulators. The output stage, which drives the fin actuator motors, is also powered by +28 VDC supplied by the actuator battery, a great benefit, as it allows the whole system to be powered by a single, standard voltage battery. At power-on, +28VDC is supplied to the CS. After completing a robust Power on Reset (POR), the CS will initially perform Power-On BIT testing. After successful completion of Power-On BIT, the controller enters Ready Mode. Once in this mode, the CS accepts and responds to the RS-422 commands, from the application Flight Computer. The CS also begins to run its Continuous BIT check. As a part of the CS pre-launch check, the Control Electronics could be instructed to run its Commanded BIT test. This comprehensive check would provide a high degree of confidence that the CS will successfully perform during flight. The integrity of the motor drive circuitry, HED feedback, and motor can be completely checked. The CS is then ready for flight and will respond to position commands from the application Flight Computer over the RS-422 communications link. The proposed electromechanical fin control solution takes its roots from well known existing designs already developed by the industry. 2.2 System Sizing

In sizing an EM actuator for any given application, we typically look to minimize the size of the motor component in relation to the available envelope and dynamic performance requirements. So the first step in sizing the actuator is to find the optimal brushless motor performance to obtain the torque necessary for the application.


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3 Component Analysis and Constraints 3.1 Actuator

3.1.1 Rotary to Linear Conversion of a Screw System (RPM to in/sec)

3.1.2 Rotary to Linear Conversion of a Screw System (Torque to Force)

Lead

Screw

Rodx

)(

)(

)/(

4.25*24.25*60

mmLead

RPMS

Secinchx

LeadLeadSx

Screw

Rod

ScrewScrewRod

Sec

Rad

v

Rad

Sec

Min

Min

v

SecRadToRPMOfConversion

Min

v

MinRad

v

Sec

Rad

RPMToSecRadOfConversion

Re

2*

60*

Re

/

Resec60*

2

Re*

/

sec/7.154.25*60

54800

RPM4800 Speed Motor with

mm 5 Lead Screw Ball

:ithactuator wan for speedoutput Linear calculate Example,

inchxSpeedOutput Rod

Lead

ScrewT

RodF

Actuator

onaticFrictiActuatorStT

ActuatorScrewRodLead

TF 4.25

2T onaticFrictiActuatorSt

lbFRod

Actuator

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8.0

lb-inch 6T

lb-inch 75.2 T TorquePeak Motor with


:ithactuator wlinear afor force) end (rodoutput ForcePeak Calculate Example,

onaticFrictiActuatorSt

Screw


6

3.1.3 Rotary to Linear Conversion of a Screw System (Acceleration)

3.1.4 Reflected Inertia of Linear Actuation System

Lead

Screw

Rodx 4.252

Lead

x ScrewRod

2

2

2

2

2

sec/3861:

'62.1sec/386

sec/627:'

sec/6274.25*2

520000

rad/sec 20000 on accelerati rotational (screw)Motor


:ithactuator wlinear afor on accelerati end rod calculate Example,

inchgNote

sginch

ginchsnGExpressedI

inchxtionarAcceleraOutputLine Rod

JActuator

Lead

JActuator JLoad

WLoad

JTotal

2

*4.25*2

GR

Lead

g

wJ Load

Load

2

2

2

Load

2

Actuator

sec0034.00024.0001.0

sec0024.04.25*2

20

386

60

1GR

20mmLead

60lbW

sec001.0J

.centerlinemotor the toreflected as inertia system equivalent

thecalculate end, rod the tocoupleddirectly load pound 60

a and screw ball mm 20 aith actuator wlinear aFor :Example

lbinJ

JJActuatorJ

lbinJ

lbin

Total

TotalTotal

Load


7

3.1.5 Rotational Acceleration

LoadActuatorTotal JJJ

JActuator

Lead=20mm

JActuator

0.001

JLoad 0.0024

WLoad=60 pounds

JTotal 0.0034

4.25*2

T

: torque)effective increasedfriction down slowing(when on Decelerati

T

: torque)effective reducesfriction ngaccelerati(when on Accelerati

:tionRepresenta General

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Leadx

J

T

J

T

J

T

ScrewRod

Total

PeakMotor

Motor

Total

PeakMotor

Motor

Total

PeakMotor

Motor

Peak

Peak

Peak


8

3.1.6 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

JTotal

PeakMotorMotorPeakTStatictionSystemFricT

sginxLinear

radJ

TRotational

sginxLinear

radJ

TRotational

sginxLinear

radJ

TRotational

lbinJ

lbin

lbin

Rod

Total

PeakScrewScrew

Rod

Total

PeakScrewScrew

Rod

Total

PeakScrewScrew

Total

Peak

Peak

Peak

'9.7sec/30594.25*2

2024412:

sec/244120034.0

677T:

:onDeceleratiPeak

'8.6sec/26174.25*2

2020882:

sec/208820034.0

677T:

:onAcceleratiPeak

'4.7sec/28384.25*2

2022647:

sec/226470034.0

77:

:onAccelerati Nominal

sec0034.0

20mmLead

60lbW

sec001.0J

6T

lb-in 77TpeakMotor

:ithActuator wLinear afor on valuesaccelerati Caluclate Example,

2

2onaticFrictiActuatorSt

2

2onaticFrictiActuatorSt

2

2

2

Load

2Actuator



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3.1.7 Equivalent Rotor Equations

3.2 Motor Description and Analysis In the analysis of electric servo drive motors, the equations for the motor indicate the presence of two time constants. One is a mechanical time constant and the other is an electrical time constant. Using Kirchhoff law motor current can be represented as:

𝑑𝑖𝑎𝑑𝑖𝑡

= −𝑟𝑎𝐿𝑎

𝑖𝑎 −𝑘𝑒

𝐿𝑎𝜔𝑟 +

1

𝐿𝑎𝑢𝑎

The mechanical part of the system yields:

𝑇 = 𝐽𝛼 = 𝐽𝑑𝜔

𝑑𝑡

Where 𝐽 - is a rotor Inertia and 𝑑𝜔

𝑑𝑡 - is acceleration of the rotor

Electromechanical Torque per motor current can be defined as:

𝑇𝑒 = 𝑘𝑡 𝑖𝑎

AAAM

AAAM

AAAM

AAAM

AAAM

JbTsKFT

JbTsKFKT

JKbKKTsKTF

KJbTsTF

LeadLetK

LeadJbTsTF

/

][

][

4.252

4.252][

TM = Motor Torque (in-lb)

TsA = Torque due to static friction (in-lb)

TvL = Torque due to viscous friction (in-lb)

bA =Actuator viscous friction (in-lb-s)/r

JA = Actuator Inertia (in-lb-s2)

Composite Efficiency including screw/bearings (%)

Lead = Screw lead (mm)

F = Rod end force (lb)

V = Rod end velocity (ips)


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Friction Torque can be defined as:

𝑇𝑣𝑖𝑠𝑐 = 𝐵𝑚𝜔𝑟

Where 𝐵𝑚 - is friction coefficient and 𝜔𝑟 - is a rotor speed

𝑑𝜔𝑟

𝑑𝑡=

1

𝐽 𝑇𝑒 − 𝑇𝑣𝑖𝑠𝑐 =

1

𝐽 𝑘𝑡𝑖𝑎 − 𝐵𝑚𝜔𝑟 =

𝑘𝑡

𝐽𝑖𝑎 −

𝐵𝑚

𝐽𝜔𝑟

Finally we will have a system of two differential equations:

𝑑𝑖𝑎𝑑𝑖𝑡

= −𝑟𝑎𝐿𝑎

𝑖𝑎 −𝑘𝑒

𝐿𝑎𝜔𝑟 +

1

𝐿𝑎𝑢𝑎

𝑑𝜔𝑟

𝑑𝑡=

𝑘𝑡

𝐽𝑖𝑎 −

𝐵𝑚

𝐽𝜔𝑟

So State Space Form yields:

𝑑

𝑑𝑡 𝑖𝑎𝜔𝑟

=

−

𝑟𝑎𝐿𝑎

𝑘𝑒

𝐿𝑎

𝑘𝑡

𝐽−

𝐵𝑚

𝐽

𝑖𝑎𝜔𝑟

+

1

𝐿𝑎

0

𝑢𝑎

With output form:

𝑦 = 1 0 𝑖𝑎𝜔𝑟

3.3 Controller Operation Description/PI Compensator Implementation

The basic theory behind electronic motor controls is that the motor’s speed, torque and direction are managed by electronically switching or modulating the voltages to the motor. The current level to the motor can also be managed indirectly by modulating the motor’s voltage. Pulse Width Modulation (PWM) is the most commonly used method to vary the average voltage to the motor. The motor’s inductance, which is partially set by the number of turns used in the motor’s windings, will integrate or smooth out the PWM voltages. For example, if 28 VDC is applied to the motor at 50 percent duty cycle, the average motor voltage will be 14 VDC. This is the basic principle used to vary average voltage in most electronic motor control systems. There are many aspects to PWM for motor control. The duty cycle of the PWM directly affects the amount of energy applied to the motor. The frequency of the PWM waveform will also influence the motor’s operation and the long-term reliability of the power electronics. In most motor controls, the PWM frequency remains constant while its duty cycle varies from 0 to 100 percent. Since the motor is a dynamic machine with the armature and mechanical loads acting as a flywheel, the PWM frequency can be fairly low -


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100Hz or less, before the motor starts to pulsate noticeably in synchronization with the PWM frequency. All servo drives require some form of compensation, often referred to as proportional, integral, and differential (PID). The process of applying this compensation is known as servo equalization or servo synthesis. In general, servo drives use proportional and integral compensation (PI). PI-type control algorithms found to be straightforward and well understood, reliable, and efficient for solving the motion control problems for both linear and nonlinear electromechanical systems.

System output with a PI compensator can be defined as:

𝑢 𝑡 = 𝑘𝑝𝑒 𝑡 + 𝑘𝑖

𝑒(𝑡)

𝑠= 𝑘𝑝𝑒 𝑡 + 𝑘𝑖 𝑒 𝑡 𝑑𝑡

Laplace Transform of PI takes place:

𝑠 = 𝑘𝑝 +𝑘𝑖

𝑠 𝐸(𝑠)

Finally the system PI Transfer Function can be written as:

𝐺𝑃𝐼 𝑠 =𝑈(𝑠)

𝐸(𝑠)=

𝑘𝑝 𝑠 + 𝑘𝑖

𝑠

𝐺 𝑠 =𝑌(𝑠)

𝑅(𝑠)=

𝐺𝑠𝑦𝑠 𝑠 𝐺𝑃𝐼(𝑠)

1 + 𝐺𝑠𝑦𝑠 𝑠 𝐺𝑃𝐼(𝑠)

3.4 Controller Operation Description/PI Compensator Implementation 3.4.1 DC Motor Representation

Using the Laplace transformation we can separate the mechanical and electrical parts of the DC motor as shown in Figure 3.4.1 below. This is an essential procedure for closed loop position and current control.

tttt RSL

1

BJS

K t

eK

wi

vbemf

v

Figure 3.4.1 DC Motor with feedback


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3.4.2 Velocity Loop

In this section we are implementing motor velocity PI regulator. Note, the velocity loop has its own feedback coefficient and it can be different from the internal one.

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+

-

+

-

Figure 3.4.2 Velocity Loop

3.4.3 Current Loop

Finally to meet torque requirement we are closing PI current control loop as shown below. The focus of this stage of the development is to finalize Block diagram for both a velocity loop and a current loop.

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

Figure 3.4.3 Current Loop

3.4. 4 Design Variables and Standard Optimization Form

After a brief description of a basic operation of electromechanical control system the following design variables will be considered in this optimization project.

System Component Design Variable

BLDC Motor Speed, Torque, Current, 𝑘𝑡𝑘𝑒

Actuator Gear Ratio, Total Inertia

Controller 𝑘𝑖 , 𝑘𝑝

All dimensions are in SI units suitable for MATLAB/SIMULINK simulation


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X1=Motor Speed, 𝑟𝑎𝑑

𝑠𝑒𝑐

X2=Motor Torque, 𝑁𝑚 ) X3=Motor Current, 𝐴𝑚𝑝

X4=Motor𝑘𝑡 , 𝑁𝑚

𝐴𝑚𝑝

X5=Motor𝑘𝑒 , 𝑉

𝑟𝑎𝑑 /𝑠𝑒𝑐

X6=Gear Ratio, − X7=Total Inertia, 𝑘𝑔 ∙ 𝑚2 X8=Velocity Loop 𝑘𝑝 (Proportional Coefficient))

X9=Velocity Loop 𝑘𝑖 (Integral Coefficient) Time Domain Constraints

𝒙𝟏 > 0; 𝒙𝟐 − 𝒙𝟒𝒙𝟑 > 0;

𝒙𝟒−𝒙𝟓 > 0; 𝒙𝟕 ≤ 0.000062;

𝒙𝟔 ≤ 𝟒; 𝒙𝟖 − 0.081𝒙𝟗 > 0;

Inverse Laplace Transform Function Minimization:

𝑭 = 𝟔𝟐𝟕𝟖∙𝑺𝟐+𝟓.𝟎𝟏𝟐∙𝟏𝟎𝟔∙𝑺+𝟔.𝟖𝟏𝟒∙𝟏𝟎𝟕

𝑺𝟑+𝟔𝟖𝟕𝟐𝑺𝟐+𝟓.𝟖𝟕𝟐∙𝟏𝟎𝟔∙𝑺+𝟔.𝟖𝟏𝟒∙𝟏𝟎𝟕 ∞

𝟎𝒆𝒔𝒕𝒅𝒔

4 Optimization Process 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 were considering Multi-objective parameter estimation of induction motor using particle swarm optimization method, however due to complexity of the system, a 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 by going from time domain to frequency domain and then back to time domain.


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% Group Project MAE 550 Engineering Optimization, Fall 2009 % Electromechanical System Performance Optimization % % Group Members: % % Santosh Rohit Yerrabolu % Anirudh Pasupuleti % Vladimir Ten

clear all close all clc

Npoles = 8; % [-] Number of Poles Kt = (1.184); % [Nm/Arms] Kt Torque Constant psi_ = (sqrt(2)/3*Kt)*2/Npoles; % [kg-m2/s^2-Amp] Motor Flux Kt_pk = 3*psi_/2*(Npoles/2); % [Nm/Apk] Kt Peak Torque Constant Ke = 1.1163; % [V/rad-sec] Ke BEMF Constant Ltt = 0.025; % [H] Inductance terminal to terminal Rtt = 14.5; % [Ohm] Phase resistance terminal to terminal Jnet_actuator = (0.62*0.0001); % [kg-m^2] Inertia, Actuator J = (0.62*0.0001); % [kg-m^2] Inertia Bm = (0.000857859); % [Nm-sec/rad] Damping

Kifb = 1; % Current feedback scaling Kmvfb = 1; % Velocity feedback scaling Kposfb = 1; % Position feedback scaling

%PI for Current Loop - cancel electrical time const and for the gain we %set for high frequency asymptote

Ki_p = 2.9065e2/Kifb; Ki_i = 228000/Kifb; Kiff = Ki_i; Ziff = Ki_i/Ki_p;

%piff = 0;

%PI for velocity loop we cancel mechanical time constant

Km_p = 7.8537e-2*Kifb/Kmvfb; Km_i = 9.66e-1*Kifb/Kmvfb; Kmvff = Km_i; Zmvff = Km_i/Km_p;

Vbatt = 540; %Bus voltage Vmod = 1000; %Modulation Gain

%Current Loop PlantGain=(J/(Rtt*Bm+Kt*Ke))*((Rtt*Bm+Kt*Ke)/(Ltt*J)); num2=[0 1 Bm/J]; den2=[1 ((Ltt*Bm+Rtt*J)/(Ltt*J)) ((Rtt*Bm+Ke*Kt)/(Ltt*J))]; Plant = PlantGain*tf(num2, den2);


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CurrentGain=Kiff; num1=[0 1/Ziff 1]; den1=[0 1 0]; CurrentCompensator = CurrentGain*tf(num1, den1); CurrentOpenLoop=(Vbatt/Vmod)*series(CurrentCompensator, Plant); CurrentClosedLoop=feedback(CurrentOpenLoop,Kifb); system1_ss=ss(CurrentClosedLoop) %System's State Space - current loop system1_tf=tf(CurrentClosedLoop) %System's Transfer Function - current loop figure step (CurrentClosedLoop); grid on xlabel('t') ylabel('Output y') title('Unit Step Response of 6278 s^2 + 5.012e006 s + 6.814e007/s^3 + 6872

s^2 + 5.872e006 s + 6.814e007') figure bode (CurrentClosedLoop); grid on impulse(CurrentClosedLoop); grid on %Velocity Loop VelocityGain=Kmvff; num3=[0 1/Zmvff 1]; den3=[0 1 0]; VelocityCompensator = VelocityGain*tf(num3, den3); VelocityOpenLoop=series(VelocityCompensator, CurrentClosedLoop); VelocityClosedLoop=feedback(VelocityOpenLoop, Kmvfb); figure step (VelocityClosedLoop); grid on figure bode (VelocityClosedLoop); grid on impulse(VelocityClosedLoop); grid on

Figure 4.1 Step Response with compensating gains

Unit 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


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Figure 4.2 Bode Plot with compensating gains

5 System Design Analysis using MATLAB/SIMULINK

5.1 Electromechanical System Top Level After detailed system analysis and its performance investigation we created a model of our control system using Simulink.

Figure 6.1 System Top Level

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

Magnitu

de (

dB

)

System Analysis : Motor Control Evaluation Sinedrive Motor , 3-Phase Implementation

Motor

Vabc [V]

Motor Velocity [V]

Motor Position [V]

Line Currents [amps]

Controller

Cmd Input [V]

Motor Velocity [V]

Motor Pos . [ rad, V]

Iabc [A]

Vabc [V]Command

Generation

Cmd [V]double

double (3)

3

double (3)

double

double


17

5.2 SINE Drive Control Algorithm We selected Sine commutation (versus 6-step) because it would give us better voltage utilization and less total harmonic distortion, so our system will be more efficient and less noisy (both system and audible)

Figure 6.2 Sine Commutation

5.3 Power Stage Power stage is utilizing IGBTs for motor phase switching. Block diagram is presented in Figure 6.3

Figure 6.3 Power Stage

Generic Analog Sinedrive Controller

Id_cmd

Iq_cmd

Vabc

[V]

1

Npoles/2

-K-

dqo 2abc

dq

the

abc

abc2dqo

the

abc

dq

Vector

Limiter

xy xy _lim

MotorCurrentFdbk

MotorVelocityFdbk

MotorVelocityCommand MotorCurrentCommand

Terminator

Power Stage 1

fdc

Iabc

Vabc

Ibus

PI1k=Kiff

z=ziff

(1/z)s+1

k ––––––

s

PI

k=Kmvff

z=zmvff

(1/z)s+1

k ––––––

s

Modulation

Gain

1/Vmod

1/Kifb1/Kmvfb

Current

Sensor

Scaling

Kifb

0

Iabc

[A]

4

Motor Pos .

[rad , V]

3

Motor

Velocity

[V]

2

Cmd Input

[V]

1double

double

double

double

double (2)double (2) double (2)

double

double

2

2

double (2)

double

3

3

double (3)

double

double (3)

double (2)

double (3)

2

2

double (2)

double (3)

double

double

double

Terminal

VoltagesPower Stage-Vs/2 to Vs/2

±1

Battery

Draw

Ibus

2

Vabc

1

0.5

0.5

Rbatt

MotorPower

BusPower

BusCurrent

BusVoltage

Dot Product

0

Vbatt

Iabc

2

fdc

1 double (3)

double

double (3)double

3

3

double (3)

3

3

double (3)

double

double

double double

double double

double

3

3

double (3)


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6.3 Motor Subsystem Now we are ready to integrate DC motor, power stage and phase switching logics. Motor subsystem is presented in Figure 6.4

Figure 6.4 Motor Subsystem

6.4 Motor Phases This is one of the most important analytical blocks. After we design our system, we want to see if motor phases commutate properly. Later we will run a test based on optimal coefficients we derived analytically. We want to see a perfect Sine wave in the end. If our wave is noisy we no other choice but create a filter to meet harmonics distortion requirements.

Figure 6.5 Motor Phases

Motor Subsystem

Position

[rad ]

3

Velocity

[rad /s]

2

Iabc

[amps]

1[rad ]

1

s

[rad /s]

1

s

Torque Generation

3 Phase Sinewave

Speed [rad/s]

Vabc [V]

Pos [rad]

Torque [Nm]

Iabc [A]

MotorDrag

MotorPositionMotorVelocity

MotorTorque

Motor

FrictionBm

Coulomb Friction

Vel [rad /s]

Torque [lbf in ]Friction [lbf in ]

Armature

Inertia

(inverse )Nm/Jnet_actuator

-K-

Torque

[Nm]2

Vabc

[V]

1

double

doubledouble

double

double doubledoubledouble

double (3)

double (3)

double

double

Line

Currents

Sinewave Drive Motor -- Individual Phases

Iabc [A]

2

Torque [Nm ]

1

Torque

Id

IqMotorCurrent

MotorVoltage

BackEMF

Number of Pole Pairs

Npoles /2

Motor Line Currents

Back EMF

Line Voltages

Motor Currents [amps]

Max Flux

Linkage

psi_

3-Phase

Sinusoids

abc 2dqo

abc

the

dq

Number of Pole Pairs

Npoles /2

Pos

[rad ]

3

Vabc

[V]

2

Speed

[rad /s]

13

3

double (3)

3

3

3

3

double (3)

3

3

double (3)

double (3) double

double

double (3)double (3)

3

double

3

3

double (3)

double

double

doubledouble (2)


19

7 Results from the Analysis 7.1 Motor Velocity

Figure 7.1 Motor Velocity

7.2 Motor Current Command & Feedback

Figure 7.2 Motor Current

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

-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


20

7.3 Motor Torque

Figure 7.3 Motor Torque

7.4 Motor BackEMF

Figure 7.4 Motor BackEMF

-5 0 5 10

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4Motor Torque

Time, sec

Moto

r T

orq

ue,

Nm

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


21

7.5 Motor Position

Figure 7.5 Motor Position

8 Digital Filter Implementation

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 clear up all possible noises to make design suitable for real life mission.

Filter Design Summary for Real Life Implementation

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

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


22

not possible and so Apass=1dB means that a small amplitude distortion up to 1dB is allowed. For digital filter design implementation we were using 50,000 points test data that was recorded in 2 milliseconds. Due to size of the data we are providing here only a computer short screen:

Figure 8.0 50000 points 2usec phase voltage test data


23

MATLAB Script of Elliptic dial section digital filter:

% Group Project MAE 550 Engineering Optimization, Fall 2009 % Electromechanical System Performance Optimization % % Group Members: % % Santosh Rohit Yerrabolu % Anirudh Pasupuleti % Vladimir Ten

clear all; close all; clc;

%test data, raw initial signal x = xlsread('real_raw_test_data_for_MAE550_vladimir_ten.xls' ,

'D4419:E33255'); %the second column contains the dependent variable and consequently all the

information x = x(:,2); %FFT setting based on the raw voltage test data N = length(x); %number of samples for FFT Fs = 10^7 / 8; %sampling rate fft_resolution = Fs / N %FFT resolution

X_mag = abs(fft(x));

f = [0 : fft_resolution : Fs - fft_resolution]'; %Filter design %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;

x_filtered = G1 * filter(b1,a1,x); x_filtered = G2 * filter(b2,a2,x_filtered);

X_filtered_mag = abs(fft(x_filtered));

%visualization subplot(221); plot(x,'g'); grid on title('initial signal');

subplot(222); plot(f,X_mag,'g*');grid on title('spectrum of initial signal')


24

subplot(223); plot(x_filtered,'r');grid on title('filtered signal');

subplot(224); plot(f,X_filtered_mag,'r');grid on title('spectrum of filtered signal')

Figure 8.1 Raw Signal of the phase voltage and Signal after filtering 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.


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9 Challenge of the Project

In this project we are working on a system that has 4 (four) different Engineering disciplines:

Electrical

Mechanical

Controls

Engineering Optimization

One of the biggest challenges was integrating both Electrical and Mechanical parts of the system into a single closed loop feedback transfer function which has several design variables. The second biggest challenge was selecting an appropriate Controls algorithm and compensation technique to meet performance criteria. Our system has two subsystem loops. Each subsystem has its own compensation gains, namely current loop gains - to meet torque requirements and velocity loop gains - to meet fin response. Finally the last challenge was implementing all theoretical development work into the model that can be used in real life. We successfully implemented dual stage digital Elliptical filer.

10 Lessons Learned

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 transfer function. We needed an 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 is very difficult to implement as well, due to high nonlinearity of the systems. The result of using any of these methods wouldn’t give us satisfied accuracy, especially in this sort of applications when we are dealing with a 0.25 degrees accuracy of motion.

11 Solution Approach Selected and 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


26

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.

12 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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