Chapter 11
Current Programmed Control
Buck converter
L
is(t)
iL(t)
The peak transistor current
replaces the duty cycle as the
converter control input.
+
Q1
vg(t) +
–
v(t)
C
D1
R
–
Measure
switch
current
is(t)
Clock
0
is(t)Rf
Control
input
Ts
S Q
+
–
ic(t)Rf
Control signal
ic(t)
Analog
comparator
m1
Latch
Current-programmed controller
0
dTs
Transistor
status:
Compensator
Switch
current
is(t)
R
–+
Rf
on
Clock turns
transistor on
v(t)
Ts
t
off
Comparator turns
transistor off
vref
Conventional output voltage controller
Fundamentals of Power Electronics
1
Chapter 11: Current Programmed Control
Chapter 11
Current Programmed Control
Buck converter
L
is(t)
iL(t)
The peak transistor current
replaces the duty cycle as the
converter control input.
+
Q1
vg(t) +
–
v(t)
C
D1
R
–
Measure
switch
current
is(t)
Clock
0
is(t)Rf
Control
input
Ts
S Q
+
–
ic(t)Rf
Control signal
ic(t)
Analog
comparator
m1
Latch
Current-programmed controller
0
dTs
Transistor
status:
Compensator
Switch
current
is(t)
R
–+
Rf
on
Clock turns
transistor on
v(t)
Ts
t
off
Comparator turns
transistor off
vref
Conventional output voltage controller
Fundamentals of Power Electronics
1
Chapter 11: Current Programmed Control
The main idea behind
CMC is that the inductor
can be turned into a
current source, thus
eliminating the dynamics
of the inductor in the loop.
The controller sets a
current reference and a
fast inner-loop follows this
reference cycle by cycle.
Current programmed control vs. duty cycle control
Advantages of current programmed control:
• Simpler dynamics —inductor pole is moved to high frequency
• Simple robust output voltage control, with large phase margin,
can be obtained without use of compensator lead networks
• It is always necessary to sense the transistor current, to protect
against overcurrent failures. We may as well use the
information during normal operation, to obtain better control
• Transistor failures due to excessive current can be prevented
simply by limiting ic(t)
• Transformer saturation problems in bridge or push-pull
converters can be mitigated
A disadvantage: susceptibility to noise
Fundamentals of Power Electronics
2
Chapter 11: Current Programmed Control
Chapter 11: Outline
11.1
Oscillation for D > 0.5
11.2
A simple first-order model
Simple model via algebraic approach
Averaged switch modeling
11.3
A more accurate model
Current programmed controller model: block diagram
CPM buck converter example
11.4
Discontinuous conduction mode
11.5
Summary
Fundamentals of Power Electronics
3
Chapter 11: Current Programmed Control
11.1 Oscillation for D > 0.5
•
The current programmed controller is inherently unstable for
D > 0.5, regardless of the converter topology
•
Controller can be stabilized by addition of an artificial ramp
Objectives of this section:
•
Stability analysis
•
Describe artificial ramp scheme
Fundamentals of Power Electronics
4
Chapter 11: Current Programmed Control
Inductor current waveform, CCM
Inductor current slopes m1
and –m2
iL(t)
ic
iL(0)
m1
0
– m2
dTs
Fundamentals of Power Electronics
iL(Ts)
Ts
t
5
buck converter
vg – v
m1 =
– m2 = – v
L
L
boost converter
vg
vg – v
m1 =
– m2 =
L
L
buck–boost converter
vg
m1 =
– m2 = v
L
L
Chapter 11: Current Programmed Control
Steady-state inductor current waveform, CPM
First interval:
i L(dTs) = i c = i L(0) + m 1dTs
Solve for d:
i – i (0)
d= c L
m 1T s
Second interval:
i L(Ts) = i L(dTs) – m 2d'Ts
= i L(0) + m 1dTs – m 2d'Ts
iL(t)
ic
iL(0)
m1
0
– m2
dTs
iL(Ts)
Ts
t
In steady state:
0 = M 1DTs – M 2D'Ts
M2 D
=
M 1 D'
Fundamentals of Power Electronics
6
Chapter 11: Current Programmed Control
Perturbed inductor current waveform
iL(t)
i L(0)
ic
i L(T s)
m1
I L0 + i L(0)
IL0
– m2
m1
– m2
Perturbed
waveform
dT s
0
D + d T s DTs
Fundamentals of Power Electronics
Ts
7
Steady-state
waveform
t
Chapter 11: Current Programmed Control
Change in inductor current perturbation
over one switching period
magnified
view
ic
m1
i L(T s)
i L(0)
m1
dT s
– m2
– m2
Steady-state
waveform
Perturbed
waveform
i L(0) = – m 1 dTs
i L(Ts) = i L(0) – D
D'
i L(Ts) = m 2 dTs
m2
i L(Ts) = i L(0) –
m1
Fundamentals of Power Electronics
8
Chapter 11: Current Programmed Control
Change in inductor current perturbation
over many switching periods
i L(Ts) = i L(0) – D
D'
i L(2Ts) = i L(Ts) – D = i L(0) – D
D'
D'
2
i L(nTs) = i L((n – 1)Ts) – D = i L(0) – D
D'
D'
i L(nTs) →
For stability:
Fundamentals of Power Electronics
0
∞
n
when – D < 1
D'
when – D > 1
D'
D < 0.5
9
Chapter 11: Current Programmed Control
Example: unstable operation for D = 0.6
α = – D = – 0.6 = – 1.5
D'
0.4
iL(t)
ic
2.25i L(0)
i L(0)
IL0
– 1.5i L(0)
0
Ts
Fundamentals of Power Electronics
– 3.375i L(0)
2Ts
10
3Ts
4Ts
t
Chapter 11: Current Programmed Control
Example: stable operation for D = 1/3
α = – D = – 1/3 = – 0.5
D'
2/3
iL(t)
ic
i L(0)
IL0
– 1 i L(0)
2
0
Ts
Fundamentals of Power Electronics
1 i (0)
4 L
2Ts
11
– 1 i L(0)
8
3Ts
1 i (0)
16 L
4Ts
t
Chapter 11: Current Programmed Control
Stabilization via addition of an artificial ramp
to the measured switch current waveform
Buck converter
L
is(t)
iL(t)
ia(t)
+
Q1
vg(t) +
–
C
D1
v(t)
–
Measure is(t)
switch
Rf
current
ma
++
0
ia(t)Rf
Artificial ramp
Analog
comparator
ic(t)Rf
Control
input
0
Ts
Ts
2Ts
t
i a(dTs) + i L(dTs) = i c
S Q
+
–
ma
Now, transistor switches off
when
Clock
is(t)Rf
R
R
Latch
or,
i L(dTs) = i c – i a(dTs)
Current-programmed controller
Fundamentals of Power Electronics
12
Chapter 11: Current Programmed Control
Steady state waveforms with artificial ramp
i L(dTs) = i c – i a(dTs)
(ic – ia(t))
ic
– ma
iL(t)
m1
IL0
0
Fundamentals of Power Electronics
– m2
dTs
Ts
13
t
Chapter 11: Current Programmed Control
Stability analysis: perturbed waveform
(ic – ia(t))
ic
m1
iL (T
s)
)
i L(0 m
1
I L0 + i L(0)
IL0
– ma
– m2
Steady-state
waveform
– m2
Perturbed
waveform
dT s
0
D + d T s DTs
Fundamentals of Power Electronics
Ts
14
t
Chapter 11: Current Programmed Control
Stability analysis: change in perturbation
over complete switching periods
First subinterval:
i L(0) = – dTs m 1 + m a
Second subinterval:
i L(Ts) = – dTs m a – m 2
Net change over one switching period:
m –m
i L(Ts) = i L(0) – m 2 + ma
1
a
After n switching periods:
m –m
m –m
i L(nTs) = i L((n –1)Ts) – m 2 + ma = i L(0) – m 2 + ma
1
a
1
a
Characteristic value:
m –m
α = – m 2 + ma
1
a
Fundamentals of Power Electronics
i L(nTs) →
15
0
when α < 1
∞
when α > 1
n
= i L(0) α n
Chapter 11: Current Programmed Control
The characteristic value α
ma
1– m
2
α=–
D' + m a
D m2
•
For stability, require | α | < 1
•
Buck and buck-boost converters: m2 = – v/L
So if v is well-regulated, then m2 is also well-regulated
•
A common choice: ma = 0.5 m2
This leads to α = –1 at D = 1, and | α | < 1 for 0 ≤ D < 1.
The minimum α that leads to stability for all D.
•
Another common choice: ma = m2
This leads to α = 0 for 0 ≤ D < 1.
Deadbeat control, finite settling time
Fundamentals of Power Electronics
16
Chapter 11: Current Programmed Control