Electric and Hybrid Drive Systems homework

2019QnsReviewHomeworkAssignmentC0.docx

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ECE 4/5630 Electric & Hybrid Drive Systems Prof Ka C Cheok

PWM Sound Playback (5 pts)

An FPGA chip can be programmed to produce a 250 KHz 8-bit PWM signal. A low pass filter circuit then smooths the “square” PWM into a usable audio waveform. This driver technique is used in MP3 audio sound players.

Given the digital output below, sketch the filtered analog waveform Vout, using your imagination. The analog signal should be as representative as possible (ie., include small wavy ripples).

Electronic Power Converter - PWM duty cycles and sketch (15 pts)

You are asked to turn on & off the switches so the 3-phase inverter would produce PWM voltage that is equivalent to [V]. The PWM frequency is 1 kHz and the DC power supply to the inverter is . Sketch the waveforms of the variables and complete the missing info for the duty cycles in the following timing diagram.

Space Vector Modulation (20 pts)

You are asked to control the switches so the 3-phase inverter would produce a SVM sequence and timing & that is equivalent to [V]. The SVM frequency is 1 kHz, and the 3-phase inverter DC power supply is . Sketch the waveforms for the variables and complete the timing information in the following diagram.

Electromotive force (voltage) (20 pts)

Faraday discovered that an electromagnetic force (voltage) is produced when a conductor moves through a magnetic field. Faraday’s law is described by the expression, where

= the magnitude of induced emf (voltage) in the conductor

= the velocity of the conductor

Brush up on cross product and dot product.

See the role of these vectors.

= the magnetic field

= the direction and length of the conductor

the symbols are cross product and dot product operators. The law can be split up into two operations:

This Matlab program implements the two operations, and plot and print the eVector & eMagnitude, for the case, &

B = [0 0 1]'; v = [0 1 0]'; l = [1 0 0]';

eVector = cross(v,B); e = dot(eVector,l);

close all;

plot3([0 B(1)],[0 B(2)],[0 B(3)],'b','linewidth',3); hold on, grid on

plot3([0 v(1)],[0 v(2)],[0 v(3)],'g','linewidth',3);

plot3([0 eVector(1)],[0 eVector(2)],[0 eVector(3)],'r','linewidth',3);

text(B(1),B(2),B(3)*1.3,['B^t = ',num2str(B')],'color','b')

text(v(1),v(2)*1.3,v(3),['v^t = ',num2str(v')],'color','g')

text(eVector(1)*1.2,eVector(2),eVector(3),['eVec^t = ',num2str(eVector')],'color','r')

text(-1.7,0.0,0.5,'eVec = cross(v,B)','fontweight','bold')

plot3([0 eVector(1)],[0 eVector(2)],[0 eVector(3)]-1.5,'r','linewidth',3);

plot3([0 l(1)],[0 l(2)],[0 l(3)]-1.43,'k','linewidth',3);

text(eVector(1)*1.1,eVector(2),eVector(3)-1.5,['eVec^t = ',num2str(eVector')],'color','r')

text(l(1),l(2),l(3)-1.43,[' l^t = ',num2str(l')])

text(-1.7,0.0,-1.0,'eMag = dot(eVec,l)','fontweight','bold')

text(-1.7,0.0,-1.3,['eMag = ',num2str(e)])

xlabel('x'), ylabel('y'), zlabel('z')

axis('equal'), axis([-1 1 -1 1 -1 1]*1.5), view(20,20)

Copy and paste this m-script in your own Matlab editor and execute the program.

Illustration: The case of cutting perpendicularly into the magnetic field

Show these as your results

Modify the Matlab program, and find the and interpret the results for each of the following cases:

a) The case of stabbing motion into the magnetic field

Computer plot ?

b) The case of parallel motion to the magnetic field

c) .

The case of general motion to the magnetic field (example with = [1 1 1]’)

c) .

Electromechanical force (20 pts)

Lorentz’s law is given by where are force, current and magnetic field vectors. Below is an illustration of when , resulting in . Superscript t denotes transpose of a vector. The Matlab m-script in the box was used to compute the Lorentz’s law and plot the results . The were then interpreted & hand sketched in the diagram next to it.

B = [0 0 1]'; i = [1 1 1]'; l = 1; li = l*i; f = cross(li,B);

close all;

plot3([0 B(1)],[0 B(2)],[0 B(3)],'b','linewidth',3); hold on, grid on

plot3([0 li(1)],[0 li(2)],[0 li(3)],'g','linewidth',3);

plot3([0 f(1)],[0 f(2)],[0 f(3)],'r','linewidth',3);

text(B(1),B(2),B(3)*1.5,['B^t = ',num2str(B')])

text(li(1),li(2)*1.5,li(3),['li^t = ',num2str(li')])

text(f(1)*1.5,f(2),f(3),['f^t = ',num2str(f')])

plot3([2 0 0 0 0],[0 0 2 0 0],[0 0 0 0 2])

xlabel('x'), ylabel('y'), zlabel('z')

axis('equal'), axis([-1 1 -1 1 -1 1]*2), view(20,10)

Your task is to investigate the case when . Modify and run the Matlab program to produce the computer result. Interpret the result and hand sketch, as accurately as you can, the arrow (blue), arrow (green) & the arrow (red) for the case.

Show your modified Matlab code & computer 3D plot here1

3 –phase stator with sinusoidal distributed winding (10 pts)

The currents in a 3-phase stator can be described by

Node voltage

Kirchoff’s current law said that Show (with detail equations) that this leads to the central node voltage:

Steady state stator currents

Suppose that , , and . What is the steady state value of the currents ?

Clarke Transform

Field to 3-phase transformation – Inverse Clarke transform

Given a desired field oriented voltage , what is the equivalent non-negative 3-phase voltage vector ? Why do we require these voltage to be nonnegative?

3-phase to field transformation – Clarke transform

Given a desired field oriented current , what is the equivalent field oriented current vector ?

Back emf in 3 phase winding stator (10 pts)

A permanent magnet rotor spins in a 3-phase stator with sinusoidal distributed winding, Phase A winding would experience a back emf given by. What would be the back emf representation for Phase B and Phase C?

Phasor and space vector (10 pts)

A phasor is a complex variable of the form , where are the magnitude and phase angle, and is the unit imaginary component. A space vector is a real variable of the form , which is a 2-D Cartesian coordinate. Both can be used to represent the same quantity (think polar and Cartesian coordinates).

If , what is

If , what is?

Permanent magnet synchronous motor (PMSM) (10 pts)

The torque generated by a PMSM can be described by (refer to lecture notes). are the magnitude and phase angle of the stator current phasor .

Suppose you were told that the stator current is , the rotor angle is , and the motor parameters are , , , . What is the torque generated by the motor?

What is the dq component - Park transform (20 pts)

The effective stator field current is and the rotor field magnet is oriented at angle. What is the direct and quadrature components for the . Sketch in the diagram below to illustrate the relationship between .

8

6

Torqueing similarity/differences between PMSM, FOC BLDC motors and SEDC/PMDC motors (15 pts)

The torque generated by a PMSM by, is the (positive) magnitude of . If we control the angle such that , hence , then the PMSM becomes a Field Oriented Control BLDC motor generating the torque as . On the other hand, the torque generated by a separately excited dc motor can be expressed by (refer to lecture notes). For permanent magnet DC motor, .

BLDC vs SEDC

Describe in detail terms how and are similar. (Which term corresponds to which).

BLDC vs PMDC

Describe in detail terms how and are similar.

PMSM vs PMDC

Explain the difference between and . Explain why we don’t refer PMSM as a BLDC or DC motor.

BLDC Torq/Current Control loop. (15 pts)

Explain the role of and in the current loop controller .

Software

Power

Electronics

&

Sinusoidal

Wound

Stator

Permanent

Magnet Rotor

Explain why is set to 0.

If a torque = 10 Nm is generated when we set = 1A, what value should be set to if =30 Nm is desired?

Integration of Speed Control BLDC Motor and Q-Car model (20 pts)

Connect the block diagrams/equations for the quarter car system to the speed control BLDC motor drive.

Gear

Software

Permanent

Magnet Rotor

Power

Electronics

&

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Wound

Stator

Wheel

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Speed Controller for a FOC BLDC Motor Electric Vehicle (30 pts)

The figure below shows the speed control scheme for a car. Suppose that the sports car is powered by a field oriented control brushless DC motor and can be approximately model as the plant transfer function shown in the figure. You are asked to use Matlab auto-tuning PID design capability and design a PID controller such that it drives the car from 0 to 60 mph in 3 seconds with .

A Simulink model for the PID control scheme is shown below. You are to build this Simulink model.

Submit a diagram of your Simulink model that satisfies the specs.

Change it to show your name and the date you worked on it.

Note: A step command for 0 to 60 mph.

Running the model with the shown PID setting yields the response with overshoot and a settling time of about 1 second.

Interpret the curves shows that the speed response is too fast and has a slight overshoot.

Submit the scope result from the best run you make.

Click on the PID Controller block and select auto tuning feature.
Submit the PID Control Prameters for the best run you make.

Use the tuner to to adjust the parameters and design a PIDN controller that satisfies the specs. 3 seconds

Desired Specs:

Go from 0 to 60 mph in 3 seconds with no overshoot

Submit the PID Tuner Info for the best run you make.

2019 Qns Review Homework Assignment B.docx 1 23 June 2019

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