Inverter

Inverter
Lecture 8!
ECEN 4517/5517
Experiment 4
Lecture 7: Step-up dcdc converter and PWM
chip
Lecture 8: Design of
analog feedback loop
Part I—Controller IC:
Demonstrate operating
PWM controller IC
(UC 3525)
Part II—Power Stage:
Demonstrate operating
power converter
(cascaded boost
converters)
Power Electronics Lab
Part III—Closed-Loop Analog Control System:
Demonstrate analog feedback system that
regulates the dc output voltage
Measure and document loop gain and
compensator design
1
Due dates
This week: Tuesday at noon (Mar. 8):
Prelab assignment for Exp. 4 (one from every student)
This week in lab (Mar. 9-10):
Start Exp. 4
This Friday at 5 pm (Mar. 11):
Exp. 3 part 2 report due
Power Electronics Lab
2
Discussion: Lab 4 prelab
Power Electronics Lab
3
Soft start and shutdown
The shutdown pin (10) turns off
the chip outputs. Ground this
pin to ensure that the outputs
are not shut down.
A capacitor can be connected
to the soft start pin (8). The
voltage on this pin limits the
maximum duty cycle. At turn on,
the capacitor will start at 0V,
and then will charge from the
50 μA current source. This
overrides the feedback loop
and starts the converter gently.
Power Electronics Lab
6
Outputs of the UC3525A
13
flip-flop
output Q
output A
flip-flop
output Q
11
VC
output B
14
output of
PWM
comparator
DTs
Ts
Output of PWM comparator
Flip-flop output Q
Flip-flop output Q
Output A
Output B
Outputs A and B can be OR-ed to restore the PWM pulses at the oscillator frequency.
Power Electronics Lab
Frequency of the
outputs is one
half the oscillator
frequency. Duty
cycle cannot be
greater than
50%.
Such outputs are
needed in some
types of switching
converters such
as “push-pull.”
OR-ing the outputs
+5V
A cheap way to OR the outputs of
the UC3525
VC
UC 3525
The + 5 V can be obtained from the 5 V reference of the UC3525
OUTA
OUTB
Bypass the + 5 V so that the
switching EMI of this circuit does not
disrupt the internal control circuitry of
the UC3525, which also uses the
+ 5 V.
Gate driver
More UC3525 tips:
•  You will need to ground the SHUTDOWN pin. Otherwise the UC3525 will shut
down.
•  RT must be greater than 2 kΩ; otherwise the UC3525 oscillator will not work
•  RD is usually a few hundred Ohms; RD must be substantially smaller than RT.
Power Electronics Lab
7
Exp. 4 Part III
Regulation of output voltage via feedback
•  Model and measure control-to-output transfer function Gvd(s)
•  Design and build feedback loop
•  Demonstrate closed-loop regulation of vHVDC
Power Electronics Lab
3
Negative feedback:
a switching regulator system
Power
input
Switching converter
Load
+
vg
+
–
iload
v
H(s)
–
Transistor
gate driver
Pulse-width vc
Gc(s)
modulator
Compensator
–+
Error
signal
ve
Reference
vref
input
ECEN 4517
11
Hv
Sensor
gain
Transfer functions of
some basic CCM converters
Table 8.2. S alient features of the small-signal CCM transfer functions of some basic dc-dc converters
Converter
buck
boost
buck-boost
Gg0
Gd0
D
1
D'
D
– D'
V
D
V
D'
V
2
D D'
0
1
LC
D'
LC
D'
LC
z
Q
C
L
D'R C
L
D'R C
L
R
D' 2R
L
D' 2 R
DL
where the transfer functions are written in the standard forms
Gvd(s) = Gd0
1 – s
z
1 + s + s
Q0
0
Gvg(s) = Gg0
2
1
1 + s + s
Q0
0
2
Flyback: push L and C to same side of transformer, then use buck-boost
equations. DC gains Gg0 and Gd0 have additional factors of n (turns ratio).
ECEN 4517
12
Bode plot: control-to-output transfer function
buck-boost or flyback converter example
80 dBV
Gvd Gvd 60 dBV
Gvd
Gd0 = 187 V
45.5 dBV
Q = 4 12 dB
f0
40 dBV
400 Hz
20 dBV
0 dBV
10 -1/2Q f0
300 Hz
0˚
Gvd
–20 dBV
–40 dB/decade
fz
0˚
2.6 kHz
RHP
fz /10
260 Hz
–40 dBV
10
f0
533 Hz
100 Hz
1 kHz
10 kHz
f
ECEN 4517
–90˚
–180˚
10fz
26 kHz
1/2Q
10 Hz
–20 dB/decade
13
–270˚
100 kHz
–270˚
1 MHz
Spice Simulation
Open-loop simulation of control-to-output transfer function
•  Replace boost converter switches with averaged switch model
•  CCM-DCM1 and other switch models are linked to course web site, inside
switch.lib file
•  Apply dc voltage (to set steady-state duty cycle) plus ac variation, to
terminal 5 of CCM-DCM1 model. Plot output voltage magnitude and phase
using ac analysis within Spice.
Power Electronics Lab
4
The loop gain T(s)
More loop gain ||T|| leads
to better regulation of
output voltage
Power
input
Switching converter
+
vg
+
–
iload
v
H(s)
–
Transistor
gate driver
Error
signal
ve
Pulse-width vc
Gc(s)
modulator
Compensator
Reference
vref
input
T(s) = Gvd(s) H(s) Gc(s) / VM
Gvd(s) = power stage control-to-output transfer function
PWM gain = 1/VM. VM = pk-pk amplitude of PWM sawtooth
ECEN 4517
Load
–+
Loop gain T(s) = product
of gains around the
feedback loop
14
Hv
Sensor
gain
Phase Margin
A test on T(s), to determine stability of the feedback loop
The crossover frequency fc is defined as the frequency where
|| T(j2fc) || = 1, or 0 dB
The phase margin m is determined from the phase of T(s) at fc , as
follows:
m = 180˚ + (T(j2fc))
If there is exactly one crossover frequency, and if T(s) contains no
RHP poles, then
the quantities T(s)/(1+T(s)) and 1/(1+T(s)) contain no RHP poles
whenever the phase margin m is positive.
ECEN 4517
15
Example: a loop gain leading to
a stable closed-loop system
T
60 dB
T
T
40 dB
fp1
fz
20 dB
0 dB
Crossover
frequency
fc
T
0˚
–90˚
–20 dB
m
–40 dB
–180˚
–270˚
1 Hz
10 Hz
100 Hz
f
(T(j2fc)) = – 112˚
m = 180˚ – 112˚ = + 68˚
ECEN 4517
1 kHz
16
10 kHz
100 kHz
Transient response vs. damping factor
2
Q = 50
v(t)
Q = 10
Q=4
1.5
Q=2
Q=1
1
Q = 0.75
Q = 0.5
Q = 0.3
Q = 0.2
0.5
Q = 0.1
Q = 0.05
Q = 0.01
0
0
5
10
c t, radians
ECEN 4517
17
15
Q vs. m
20 dB
Q
15 dB
10 dB
5 dB
0 dB
Q = 1 0 dB
m = 52˚
–5 dB
Q = 0.5 –6 dB
m = 76˚
–10 dB
–15 dB
–20 dB
0
10
20
30
40
50
m
ECEN 4517
18
60
70
80
90
9.5.2. Lag (PI) compensation
Gc(s) = Gc∞
|| Gc ||
ω
1 + sL
– 20 dB /decade
Improves lowfrequency loop gain
and regulation
Gc∞
fL
10fL
∠ Gc
0˚
+ 45˚/decade
– 90˚
fL /10
f
Fundamentals of Power Electronics
42
Chapter 9: Controller design
Example: lag compensation
original
(uncompensated)
loop gain is
Tu0
Tu(s) =
1 + ωs
0
compensator:
ω
Gc(s) = Gc∞ 1 + sL
40 dB
|| T ||
Gc∞Tu0
20 dB
fL
|| Tu ||
Tu0
f0
fc
0 dB
f0
–20 dB
–40 dB
90˚
∠ Tu
0˚
10fL
Design strategy:
choose
∠T
10f0
–90˚
ϕm
Gc∞ to obtain desired
crossover frequency
ωL sufficiently low to
maintain adequate
phase margin
Fundamentals of Power Electronics
–180˚
1 Hz
10 Hz
100 Hz
1 kHz
10 kHz
100 kHz
f
43
Chapter 9: Controller design
8.4. Measurement of ac transfer functions
and impedances
Network Analyzer
Injection source
vz
magnitude
Measured inputs
vz
frequency
vy
vx
vx
input
vy
input
+
+
–
–
+
–
vz
output
Fundamentals of Power Electronics
Data
94
vy
vx
17.3 dB
Data bus
to computer
– 134.7˚
Chapter 8: Converter Transfer Functions
Swept sinusoidal measurements
• Injection source produces sinusoid vz of controllable amplitude and
frequency
• Signal inputs vx and vy perform function of narrowband tracking
voltmeter:
Component of input at injection source frequency is measured
Narrowband function is essential: switching harmonics and other
noise components are removed
• Network analyzer measures
vy
vx
Fundamentals of Power Electronics
and
vy
∠v
x
95
Chapter 8: Converter Transfer Functions
Measurement of an ac transfer function
Network Analyzer
Injection source
vz
magnitude
Measured inputs
Data
vz
frequency
vx
input
vy
input
+
+
–
vy
vx
–
+
–
vz
output
vy
vx
Data bus
to computer
–4.7 dB
– 162.8˚
vy(s)
= G(s)
vx(s)
DC
blocking
capacitor
input
output
G(s)
• Injection sinusoid
coupled to device
input via dc blocking
capacitor
• Actual device input
and output voltages
are measured as vx
and vy
VCC
DC
bias
adjust
• Potentiometer
establishes correct
quiescent operating
point
• Dynamics of blocking
capacitor are irrelevant
Device
under test
Fundamentals of Power Electronics
96
Chapter 8: Converter Transfer Functions
9.6.1. Voltage injection
–
Block 1
Z1(s)
0
vref (s)
+–
ve (s)
G1 (s) ve (s) +
–
vz
+
Zs(s)
–
Block 2
i(s)
+
vy (s)
vx (s)
+
–
Z2(s)
G2 (s) vx (s) = v(s)
Tv (s)
H(s)
• Ac injection source vz is connected between blocks 1 and 2
• Dc bias is determined by biasing circuits of the system itself
• Injection source does modify loading of block 2 on block 1
Fundamentals of Power Electronics
64
Chapter 9: Controller design
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