power electronic class. electrical engneer

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ECE 4763 Project #2 Due: Tuesday, April 24, 2018 in class

Buck Converter Control Design

Vg

48Vdc

H

Gm

Vref 5.1Vdc

C 47u

R 1.44

Rc 200m

d+ d-

a

c

p Av gPWMsw2 FS = 100kHz L = 10uH

Gc

L

10uH

Fig. 1. Closed-loop buck converter diagram

Design the feedback control loop for the 100 W buck converter depicted above with the following component values:

Vg = 48 V, Vo = 12 V, R = 1.44 Ω, fs = 100 kHz. C = 47 μF, RC = 200 mΩ, L = 10 μH

and using a saw-tooth modulator with peak-to-peak voltage, V

ramp(pk-pk) = 1.8V and a

precision reference voltage, V ref

= 5.1V.

The compensator design is to meet the following specifications:

• Loop-gain Cross-over Frequency: f c ≥ 10 kHz

• Gain Margin: G M

≥ 12 dB

• Phase Margin: φ M

≥ 60º

• Output voltage transient response to a 1 V step change in the input voltage or to a 1 A step change in the load current to meet the following:

o Peak Instantaneous v o

change: ≤ 0.25 V

o Settling-Time of v o

within 10 mV of steady-state, τs: ≤ 0.25 ms

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Your design procedure and report should follow the following steps:

1. Outline of your design with problem specifications 2. Derive the small signal model for the buck converter shown above and give the

analytical expression of Gvd(s), Gvg(s) and Zo(s) open loop. 3. By using MATLAB

 Create M-File with all your transfer functions derived in part 1.  Plot the following open loop transfer functions:

o Duty cycle to output Gvd(f) o Audio susceptibility Gvg(f) o Output impedance Zo(f)

4. Design the compensator (Gc) in MATLAB (SISOTOOL)  Find the sensor gain H and Gm  Import the transfer function you need by using the command “sisotool (x)”  Find the values of the poles, zeroes and the gain of the compensator in

order to meet the design specification  Plot the compensator transfer function C(f) = H · Gc( f ) · Gm  Plot the loop gain T(f)

5. Plot the following closed loop transfer functions:  Duty cycle to output Gvd_CL(f)  Audio susceptibility Gvg_CL(f)  Output impedance Zo_CL(f)

Plots comment: You should plot the magnitude in dB and the phase for each one, moreover the X-axis should start at 100Hz to 1MHz. Use same Y-axis scaling factors for open- and closed-loop plots of audio-susceptibility and output impedance. Mark the crossover frequency, gain and phase margins

6. Verify the transient response using time-domain (transient) analysis in Matlab/SimPowerSystems toolbox:

 Plot the closed loop transient of Vg(t), Vo(t), Io(t), IL(t) and d(t) when: o Input voltage Vg steps from 48 V to 49V and back o Output current io steps down from 8.33A to 7.33A and back

(Mark the maximum instantaneous peak and settling time of vo)

7. Discuss the frequency and time domain results with emphasis on if working simulation values differ from calculated ones and why.

(All plots must have sufficient X- and Y-axis resolutions to clearly see necessary details.

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ECE4763 Power Electronics Spring 2018 Project 2 Report Guideline

The report should be concise, self-explanatory, and well documented. It should include:

Cover page: (course no., course name, project title, your name, your student no., date completed, and statement that it is your own work)

Abstract or Executive Summary An abstract of the report with no more than 300 words

Introduction • Task statement • List of desired input, output, and other specifications (design objectives)

Design and Verification • Design approach • Complete circuit diagrams • Design process (equations, steps, ...) • Tabulated design results • Simulation verification

Summary, Conclusions, and Comments Summary of design results Discussion on how well the design meets the objectives Comments on relevant issues

The grading guideline: • Technical (80 pts) • Structure and organization of the report (5 pts) • Grammar, spelling, vocabulary, word usage (5 pts) • Presentation quality (including tables and figures) (5 pts) • Overall (subjective) impression on the technical content and style (5 pts) ALL WORK MUST BE YOUR OWN. You are allowed to discuss design procedures and PSpice/MATLAB usage with other students, teaching assistants, and the instructor. You are NOT allowed to work in teams or compare the results.