5807 matlabsimulink intro

8/13/2019 5807 MATLABSimulink Intro

1/37

Introduction to Switched-Mode Converter Modeling

using MATLAB/Simulink MATLAB: programming and scripting environment

-

Motivation: Powerful environment for system modeling and simulation

More sophisticated controller models, analysis and design tools

But*: - ,

Not a traditional circuit simulator; specialized physics-based Spicedevice models or component libraries are not readily available

*Various add-ons to Simulink are available to allow traditional circuit diagramentry and circuit simulations (e.g. SimPowerSystems, PLECS), or to embed

ECEN5807 1

. -and will not be used in ECEN5807.


2/37

Introduction through an example

iLoadig Ron1

+ _vL

Synchronous buck converter

+

voutvg

+

_

Resr

C

+

_v

L

Ron2 iCBode Diagram

-20

0

20

40From: vc To: SyncBuck/vout

gnitude(dB)

PWM

v

dTs

TsVM

c

1 2 3 4 5 6-180

-135

-90

-45

0

Ph

ase(deg)

-80

-60

-Ma

5

Vg

v gv

v

Switching model

Averaged model

Frequency (Hz)

0

0.36

Vc

v c

iLoad

vout

i

vout

Small-signal linearization andfrequency responses

See MATLAB/Simulink a e on the course

ECEN5807 2

iLoad

g

SyncBuckScope

ig

Simulink model: syncbuck_OL.mdl

website (Materials page) for complete step-by-

step details, and to download the example files


3/37

Synchronous Buck Converter

iLoadig Ron1

+ _vL

+

voutvgResr

C

+

v

L

Ron2 iC

dTs

__

c

PWMTsVM

c

Inputs: vg, iLoad, vc

ECEN5807 3

ou, g

State variables: v, i


4/37

Converter state equations

iLoadig

+L RL

Ron1+

_vL

i

+ voutvg

_

esr

C+

_v

Ron2 iC

PWM

dTs

TsVM

c

vc

State equations Output equations

)0(

)1(

2

1

c

c

viRR

viRRv

dt

diLv

outLon

outLong

L)0(

)1(

0

c

ciig

ECEN5807 4

LoadC ii

dt

vCi Loadesrout iiRvv


5/37

Simulink

model

5

Vg

v gv

v

SyncBuck subsystem block

0.36

Vc

v c

i

vout

i

vout

iLoad

oaig

SyncBuckScope

ig

1

v

1

scapacitor integrator

v c c2

1

vg

dv /dt v

c

SyncBucksubsystem

blockinternals

3

2

i

1

s

inductor integrator

PWM

u yCCMbuck

CCM buck

3

iLoad

vc

idi/dt

yu

c

4

ig

vout

ig

ECEN5807 5


6/37

Synchronous buck (SyncBuck) subsystem

1

Integration of

state variables

1

v

1

1


v c c

PWM

2

vc

dv /dt v

c

cInputs

subsystem

3

is

inductor integratoru yCCMbuck

CCM buck

3

iLoad

idi/dt

vout

yu Outputs

4

igig

Converter

state

equations

ECEN5807 6


7/37

PWM operation and model

cc

1

c

1

vc

PWM ramp

Comparator

ECEN5807 7

Simulink PWM model


8/37

Converter state equations: embedded MATLAB script

3

vout

2

i

1

v

1

s

inductor integrator

1

s

capacitor integratorvc c

PWM

u yCCMbuck

CCM buck

3

iLoad

2

vc

vg

dv /dt v

idi/dt

vout

yu

c

c

u = inputs = [vg c iLoad v i]y = outputs = [ic/C vL/L vout ig]

u y

4

igig

Converter

stateequations

)0(

)1(

0

c

ciig

Loadesrout

)1( cviRRvdi

LoadC iidt

dvCi

ECEN5807 8

)0(2

cviRRdtv

outLon

L


9/37

Numerical example

iLoadig

+R

L RL

Ron1+

_vL

i

Switching frequency:fs = 1MHz

+

voutvg

_C

+

_v

Ron2 iC

c

Iout = 0

Vg = 5 V

PWM

vc

s

TsVM L = 1 H

RL = 10 m Ron1 = Ron2 = 20 m

C= 200 F5

Vg

v gv

v

Resr = 0.8 m PWM ramp amplitude

V = 1 V

0.36

Vc

v c

vout

i

vout

ECEN5807 9

Vc

= 0.36, D= 0.36iLoad

ig

SyncBuckScope

ig

Simulink model: syncbuck_OL.mdl


10/37

Numerical example: synchronous buck converter model

5

Vg

v gv

v

0.36

Vc

v c

i

vout

i

vout

iLoad

iLoadig

SyncBuckScope

ig

Masking a Simulink subsystemallows parameterization

Same subsystem model can bere-used

Models and MATLAB scri ts can

ECEN5807 10

be collected in a library


11/37

Switching simulation: open-loop start-up transient

v

i

vout

ig

ECEN5807 11

,


12/37

Averaged model

)0(

)1(

2

1

c

c

viRR

viRRv

dt

diLv

outLon

outLong

L

Switching modelLoadC ii

dt

Ci

)1(

ci

ig

Loadesrout iiRvv

State-s ace avera in review Textbook Sections 7.1-7.3

sssss

s

s ToutTLonToutTLonTg

T

TL viRRdviRRvd

dt

idLv 21 1

ss

s

s TLoadT

TTC

iidt

Ci

ss TTg

idi

Large-signalaveraged model

ECEN5807 12

ssss TLoadTesrTTout

iiRvv


13/37

Converter averaged state equations: MATLAB

The MATLAB function stays exactly the same, except d (duty-cycle) replaces c (switch control)

ECEN5807 13


14/37

Synchronous buck (SyncBuck) subsystem:

switching or averaged model

1

Integration of

state

variablesInputs

1

v

1

sw

constant

1


v c c

PWM2

vc

vg

dv /dt v

d

c

3vout

is

inductor integratorSwitchPWM Gain

uyCCMbuck

CCM buck

3

iLoad

idi/dt

v out

yu

d

4

igig

stateequations

Averagedmodel of the

PWM

ECEN5807 14


15/37

Start-up transient simulations

Switching model Averaged model

v

i

vout

ig

ECEN5807 15


16/37

Linearization of the large-signal averaged model

Large-signal (nonlinear) averaged model

LVgd iLRL

+

R

+

vvg+

D vgD iL

Resr Small-signal

avera edC

Iod model

The small-signal model can be solved for all important converter transfer functions:

vsGvd

)( vg

vsG

)( out

vsZ

)(

ECEN5807 16

g oa

Control-to-output Line-to-output Output impedance


17/37

Synchronous buck converter exampleReview textbook Chapter 8

LVgd iLRL

vsG ovd

)(

Buck SSM

+

C

R v

vg+

D vg

Iod

D iL

Resr

1 esr

s

VsG

Gvd(s)

11

oo

ss

Q

d

kHz112

1

CLfo

dBV14V5 vdoG

a r o po es:

Low-frequency gain:

1

dB2.73.2/

Lesr

lossRR

CLQ 5

/

CL

RQload ESR zero:

ECEN5807

z2

esr

esrCRdB2.73.2||

loadloss

loadlossloadloss

QQQQQ

17


18/37

Magnitude and phase Bode plots of Gvd

60dB

80dB

(1/VM)Gvd(s)

20dB

40dB

dB145)/1( Mvdo VG dB2.73.2 Q

0dB

-20dB

kHz11ofdB/dec40

0o

of10

-90oMHz1esrf

2/1

dB/dec20

ECEN5807

100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz

-180o

esro

18


19/37

Linearization and frequency responses inMATLAB/Simulink

5

Vg

vg v

vg v

0.36

Vc

vc

i

vout

vc

i

vout

1. Set transfer

function inputand outputpoints

0

iLoad

iLoadig

SyncBuck Scope

iLoadig

2. MATLAB scri t BodePlotter_scri t.m com utes DC o eratin oint linearizes themodel, computes and plots the transfer function magnitude and phase responses

ECEN5807 19


20/37

Magnitude and phase Bode plots of GvdBode Diagram

20

40From: vc To: SyncBuck/vout

-20

0

gnitude(dB)

0-80

-60

-M

-90

-45

se(deg)

101

102

103

104

105

106

-180

-135Ph

ECEN5807 20

Frequency (Hz)


21/37


22/37

Closed-loop SMPS block diagramReview Textbook Chapter 9

Control objectives: tight output voltage regulation

tat c or ynam c stur ancesInput (line) voltage vg

Load current iload

ECEN5807

Component tolerances

22


23/37

Small-signal model: loop gain T

T(s)

Loop gain: T(s) = H(s)Gc(s)(1/VM)Gvd(s)

ECEN5807 23


24/37

Small-signal model: closed-loop responses

T(s)

ECEN5807 24


25/37

Feedback loop design objectives

T(s)

To meet the control objectives, design Tas large as possible in aswide frequency range as possible, i.e. with as high fc as possible

ECEN5807

Limitation: stability and quality of closed-loop responses

25


26/37

Uncompensated loop gain Tu

L

iL(t)

+ +

Iout

+

Vg

_

vo

_

C R

Gvd(s)-

_

+PWM Compensator

s= 1 MHz

error

duty-cyclecommand

sense =(in this

example)

Vref

+Gc(s) = 11/VM

Tu(s) = Hsense(1/VM)Gvd(s)

Plot magnitude and phase responses of Tu(s) to plan how to design Gc(s)

ECEN5807 26


27/37

Magnitude and phase Bode plots of Tu

60dB

80dB

Tu(s) = Hsense(1/VM)Gvd(s)

20dB

40dB

dB145)/1( senseMvdouo HVGT dB2.73.2 Q

0dB

-20dB

kHz11ofdB/dec40

2

ofT

0o

of10

target fc

cf

-90oMHz1esrf

2/1

dB/dec20

ECEN5807


-180o

esro

27


28/37

Lead (PD) compensator design

om 53

kHz100cf1. Choose:

2. Compute:

z

kHz003

2 2

3. Find Gco to position the crossover frequency:

1 z

p

co

c

ouofGfT dB1545.5 p

z

o

c

uoco

ffTG

ECEN5807

Magnitudeof Tu at fc

Magnitudeof Gc at fc

28


29/37

Lead (PD) compensator summary

11

s

dB1545.5 coG

21

11

)(

pp

coc

ss

GsG

z

kHz3001pf

c sLead

compensatorHF pole

MHz12f = f = f in this exam leAdded high-frequency pole:

High-frequency gain of the lead compensator: Gcofp1/fz = 49 (34 dB)

ECEN5807 29


30/37

Loop gain with lead (PD) compensator

60dB

80dB

11

z

s

20dB

40dB

dB7.297.28 couoGT

21 11 pp

coc

sss

0dB

-20dB

kHz100cf

kHz10zf

0o

kHz300pfkHz33zf

-90o

ECEN5807


-180o

om 53

30


31/37

Add lag (PI) compensator

Integrator at low frequencies

Choose 10fL < fc so that phase margin stays approximately the same: fL = 8 kHz

ECEN5807

- . cmcoc

31


32/37

Adding PI Compensator

60dB

80dB

20dB

40dB

0dB

-20dB

L kHz100cf

0o

Lf10

-90o

Lf10/1

PI compensator phase

ECEN5807


-180

om 53

32


33/37

Complete PID compensator: summary

dB1545.5 cmG

kHz8Lf

kHz33zf

kHz3001pf

MHz12pf

kHz100cf (=1/10 of fs)Crossover frequency:

ECEN5807

53omPhase margin:

33


34/37

Magnitude and phase Bode plots of T

60dB

80dB

20dB

40dB

0dB

-20dB

kHz100cf

0o

ase o uncompensate u

-90oPhase of compensated T

ECEN5807


-180o

om 53

34


35/37

Closed-loop voltage regulator in Simulink

5 vg v

vg v

Simulink model: syncbuck_CL.mdl

Vg

vc

ii

x

iLoadig

Step

iLoad

vout

ig

SyncBuck

1H

vyvx

PID compensator

1.8

Vref

1/(2*pi*33e3)s+1

1/(2*pi*300e3)s+1

PD Compensator

1

Injectionpoint

1

1/(2*pi*1e6)s+1

HF pole

5.45

Gcm

1/(2*pi*8e3)s+1

1/(2*pi*8e3)s

Inverted zero

y

ECEN5807 35

Input and output linearization points for finding the loop-gain, T= -vy/vxThe output point (y) should be Open Loop , as shown by an x symbol next to the output arrow


36/37

Loop gain and stability margins

MATLAB script

BodePlotter_scriptT.m

(computes dc op,

near zes, ca cu a esand plots frequency

response and stabilitymargins)

Bode Diagram

50

100From: x To: Gcm/y

(dB

)

= , = . .

-100

-50

0

Magnitude

-

-90

- 5

hase(deg)

ECEN5807 36

102

103

104

105

106

107

-180

P

Frequency (Hz)


37/37

Closed-loop 0-5 Astep-load transient responses

Averaged model Switching model

v

i

vout

ig

ECEN5807 37

See MATLAB/Simulink page on the course website (Materials page)for complete step-by-step details, and to download the example files

5807 matlabsimulink intro

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