sthxfhxfgj

1. Sensorless Current Mode Control - An Observer-BasedTechnique for
De-De Converters
Pallab Midya
Motorola, Inc.
Chicago Corporate Research Lab
Schaumburg, Illinois
Abstract - Sensorless current mode (SCM) control is an
observer method that provides the: operating bene€its of
current mode control without current sensing. SCM has
significant advantages over both conventional peak and
average current-modecontrol techniquesin noise susceptibility
and dynamic range. The method supports both line and bulk
load regulation, and reduces control complexity to a single
loop. The static and dynamic performance of SCM are
analyzed and verified experimentally for dc-dc converters.
Performancein continuousand discontiinuousmodescompares
favorably to conventional techniques when noise is not a
factor, but is significantly better when noise and wide load
ranges are a concern. The SCM method encompasses one-
cycle control as a special case; the general SCM method is
introduced here as a public domain control technique.
I. INTRODUCTION
Background
It is desirable that controls for power converters be robust
to noise, have good dynamic performance, and be simple to
design. Current mode control [1] is based on sensing an
inductor current and using this signal in place of a triangle
carrier. It is equivalent to providing current feedback, with
the objective of maintaining the induictor current equal to a
reference current. The reference cunrent is generated by an
addiiional control loop that compares the output voltage to a
reference voltage [2]. Two-loop current-mode control is well
known to have good dynamic response to converter input and
output disturbances, provided an extra r,ampis added to avoid
subharmonic instability beyond 50% duty ratio.
There are three important drawbacks 80 this conventional
peak current-mode technique:
1. Switching takes place at the peak (of the inductor current,
anid noise sensitivity is therefore relatively high. The noise
trouble is inherent in the current feedback process [3].
2. A current sensor is required. Resistive sensing is the
usual practice, since it is less expensive than Hall effect
sensing. Resistive pickups are a problem in low-voltage
high-current applications. In olhe1 applications, the
resistive sensor often has low diffwential-mode potential
and high common-mode potential.
3. Converter action is related to the dynamic range of the
current signal. A converter intended tlo supply a 100:1 load
Matthew Greuel Philip T. Krein
University of Illinois
Urbana, Illinois
Department of Electrical and Computer Engineering
range, for example, must sense and react to currents over
this entire range.
Average current mode control [4] improves the noise
robustness by filtering the current signal. A related control
scheme, charge control [5],integrates the current and further
improves the noise performance. Both of these approaches
retain a current sensor.
Sensorless current mode control description
An alternative to the various current-mode methods is to
use observer techniques. These have been employed with
good results in motor drive and UPS systems [6-81 but are
unusual in dc-dc converters. Recall that an observer method
constructs a model of the system to be controlled, and uses
state: information from the model among the control inputs.
In sensorless current mode (SCM) control, observer
information is used to reconstruct an inductor current from
voltage information, and the current sensor is avoided. The
inductor voltage in a dc-dc converter is usually a much larger
signal than the output of a current sensor, and its range does
not change much as a function of loading. The integral of the
inductor voltage contains all the dynamic information of the
current signal.
In its simplestform, the SCM control approachreconstructs
an inductor current directly by integrating the inductor
voltage. The integral can substitute for ac inductor current in
a conventional eurrent-mode controller. A description of this
simple form and some applications can be found in [9]. A
comprehensive form that takes into account the dc operating
needs of a converter involves a more complete observer
implementation, and supports direct line and bulk load
regulation in the whole range of dc-dc converter applications.
The (comprehensiveform is the subject of this paper.
Thle general SCM technique contrasts with one-cycle
control [10,11], and it will be shown here that one-cycle
control is a restricted case of SCM. Recently, feedforward
controls that extend the one-cycle method were described by
Arbetter and Maksimovic [12].
General approach
Consider a dc-dc converter, of any particular type, in which
an inductor current state is of interest. The case of a boost
converter is shown in Figure 1. The figure shows both a
0-7803-3840-5/97/$10.00
Q 1997IEEE 1!
3
7

2. I
I .
Boost converter
' Rniiip
I
V I W i i t / l Y e 1
Fig. 1. Boost converter model for SCM.
circuit diagram and a block diagram that emphasizes the
inductor current. Here vSwllch
represents the forward drop
across the active switch when it is on.
The block diagram can be simplified significantly.
Consider that in a practical converter, the capacitor voltage vc
is not really intended to act as a state variable. Instead, it
should match a specific reference value. In the dc case, the
reference value Vrcl can be used to replace vc. Now, an
integral process emerges when the inductor voltage vL is
considered. The inductor voltage integral
(1)
b
i
n - qlv$wirch- q2vref dt
represents a flux error that should be driven to zero. The
appropriate control law based on current-mode control is to
set a latch at the beginning of the switching period and turn
on the active switch. Then the integral is computed. When
it rises above a value (which could be given by Vref,
an
external stabilizing ramp, or even just a zero level), the latch
i s reset and the switch turns off.
Table I lists the SCM integrals for five common dc-dc
converters. In the boost-buck (Cuk) and SEPIC cases, either
inductor yields the same integral value if the ideal transfer
TABLEI. SCM INTEGRALS FOR MAJOR DC-DCCONVERTERS.
capacitor voltage is used in the observer. Figure 2 shows a
generic SCM controller that takes the integral and implements
a PWh4 converter control with ramp.
" I v i
Switching
function
Fig. 2. Generic SCM process for PWM control.
II. ANALYSIS
Operational stability
Stability can be evaIuated with a recursive approach for any
given converter. First, we assume that the reference level is
produced either open-loop or with a stable closed-loop
feedback controller. The question is how the SCM system
affects local stability. Consider the integral value vI(t)in
Figure 2. At the beginning of the Nth cycle of converter
operation, the value is v,(NT), where T is the switching
period. Let the duty ratio at cycle N be D,. The reference
ramp has slope mR. The switch turns off when the integral
value reaches the ramp level, at time NT + D,T,
v,(NT + DNr) mp,T (2)
Define the derivative of vI to be -monwhen the converter's
active switch is on and +m,,, when the switch is off. These
choices account for the negative signs in (1). At cycle N+l
in continuous conduction mode,
(3)
v,(NT+T+D,&,T)= v,(NT+D,T) + moJl -D,)T - mOnDN-,T
The difference between cycle N+l and cycle N is
mo&l -DN)T - monDN-,T= mR(D,+,-DN)T (4)
A difference equation for DN+,
can be obtained as
(5)
mR- m m
' N + I OffD, + O f f
mR + mm mR ' m m
198

3. For any realistic converter, the inductor voltage increases
when the active switch is on and decreases when it is off, and
the values moi,and m,,, are both poisitive. The pole of
difference equation (5) occurs at (mn a- ,~n,,)/(m,+ won).
The
SCM action will be stable if the pole is within the unit circle.
This condition is met if the ramp slope is at least equal to
mR= (m,,,,- m,,)/2. If the slope is zero (a constant reference
with no ramp), instability occurs for m(Jff
5-y
n
,
,
,
, corresponding
to D > 0.5, just as in current-mode conlrol. An especially
good choice of ramp is to select m
R = to move the pole
to the: origin in z domain. One advantage of SCM is that the
ramp choice is independent of the storage element values in
the converter. This is a considerable robustness advantage,
and loop design is much simplified.
Discontinuous mode introduces a third configuration in
which the slope of v, is zero. The stability issue can be
addre,ssedby definingan equivalentramp mOf;that defines the
average slope over the total off intervall. For all positive mor[,
the value mof; cannot exceed the actual value mOfpTherefore,
if mR2 (m,,, - m,,)/2, it is also true that mR> (qIff’
- mJ2.
Any controller that is stable in continuous mode will remain
stable if it enters discontinuous mode,
Flux balancing
Since SCM uses an integration of an inductor voltage, the
voltage vI serves as a flux observer a!; well as a current
observer. Flux control is very effective for various
transformer-coupled forward converters. A full-bridge
example is given in [13].
Peformance
The stability analysis suggests that !$CM acts very much
like conventional current-mode control. ]However, there is
very substantial improvement in noise performance. Thee
aspects,contribute to the improvement:
1. The inductor voltages are large-signal switching
waveforms, spanning the full range of the converter’s input
and output voltages. Compared to a 1% per unit resistive
sensor, the signals are about 40 dB higher.
2. Since the sensing is based on voltage rather than current,
the signal magnitude is independlent of dc current
magnitude and load. In conventional current-mode control,
it is a challenge to cover a wide dyn,arnic range of loads.
With SCM, a 10O:l or higher load range offers no special
challenge. A resistive or Hall effect sensor intended for a
1OO:ll load variation offers only 1% (of nominal signal at
light load. At the worst-case load point, SGM would offer
a signal advantage of 40 dB.
3. The integration process itself is robust to noise. The SCM
method inherently provides noise advantages like those of
average current-mode control without the associated time
delay.
When these three are taken into account, SCM can be seen to
offer signal-to-noise improvements on the order of 80 dB or
more compared to average current mode control, and much
higher improvements compared to conventional peak current
mode control.
It is known that audio susceptibility can be nulled in peak
current mode control with the proper choice of stabilizing
ramp [141. The optimal SCM ramp slope mR= moffalso nulls
the audio susceptibility. This is considerably easier to achieve
under SCM than under peak current mode control, since the
noise is low and the slopes are unrelated to uncertain values
such as component values. A null audio susceptibility
indicates an ideal feedforward compensation for the source
voltage. Notice that for the observer method, this applies to
all dc-dc converters, not just to buck topologies.
One-cycle control as a special case
A general block for one-cycle control (from [lo])is shown
in Figure 3. [n this circuit, an inductor operates into a fixed
voltage-source load. It has been discussed for buck converters
and far the output stage of boost-buck converters. The switch
turns on at the beginning of the cycle, then turns off, with an
integrator reset, when the integrator level meets the reference
level. Since the inductor operates a fixed load, the integrator
provides a representation of the ac current in the inductor.
The focus of the one-cycle method is source regulation. The
average voltage over a cycle is controlled and set eo a
specified value such that source effects are eliminated. This
is similar to a dead beat technique [151. Except for the
integrator reset, the one-cycle block is the samc as SCM for
the buck case.
One-cycle control does not apply to boost converters or
other topologies, since in these cases the inductor is not
driving a fixed load. The integrator reset is problematic. It
avoids instability caused by duty ratios beyond 50% by
eliminating dependence on past cycles, at the expense of
eliminating the advantages of past behavior in
Fig. 3. Basic one-cycle control block (from [IO])
error
1991

4. correction. Consider for example the effects of delay in the
comparator. This will cause the switch to be on somewhat
too long, producing a small dc offset error. With the reset in
place, there is no mechanism to correct for this error.
Elimination of intercycle memory does not give the best
possible load regulation: after a large load transient, there are
cycles when the output error is not eliminated and it would be
beneficial to carry over this error. Current mode and SCM
controls can carry over any output error and are capable of
handling large load disturbances effectively. In one reference
[16], a version of one-cycle control without reset is described.
It is again identical to SCM in the buck case, but does not
apply to general dc-dc converters.
In [121,the feedforward concept from conventional voltage
feedforwardPWM control is extended beyond buck converters
and made generally applicable. The gain of the PWM block
is made constant and independent of the input voltage. As in
one cycle control, an integrator with a reset is the key
building block. This approach represents an improvement
over conventional PWM in terms of the ease of closing the
feedback loop. There remain issues with the integrator reset.
The switch voltage vSWlfEh,
which is the only directly
controlled voltage in a power converter, is affected
significantly by factors other than the input voltage and the
PWM duty cycle. These include voltage across the switch,
the switching transition and delay, and also the possibility of
discontinuous mode. These require additional attention in
feedforwardtechniques. In SCM, since v,,,~~,,
is directly used
in the integration process, these effects are already factored in.
Regulation
The various SCM integral control laws provide near-ideal
line regulation for all types of dc-dc converters. Load
regulation is limited by dc parasitics in devices that appear
between the controlled switch and the load. For example, in
a buck converter, the load regulation is limited by the
parasitic resistance of the output inductor. In a boost
converter, the output diode’s voltage drop is the only load
regulation issue. In a boost-buck converter, either inductor
gives rise to the same control law. Sensing based on the
input inductor will give excellent line regulation, but the load
regulation will be limited by the transfer capacitor ESR and
the output inductor parasitic resistance. Sensing based on the
output inductor will give better load regulation. Similar
arguments apply to SEPIC and higher multi-stage converters.
The implication of the regulation behavior is that the
observer-based SCM method provides primary line and load
regulation without the need for a separate control loop. This
is a significant advantage of the approach. A conventionalPI
loop can be implemented around the SCM control law, but
this PI loop need only perform very fine adjustments to
compensate for the inductor dc drop. The combination of
inherently good load regulation and near-ideal line regulation
supports very high performance designs.
Sensorless current mode limitations
A possibledrawback of SCM is that the current information
is really ac information. This drawback (as in one-cycle
control) affects the ability to react to overcurrent conditions
and to support current sharing. However, the true observer-
based approach does not really eliminate all the dc
information. If the current rises sharply because of a short
circuit, the integral of inductor voltage will rise until
saturation is reached. If a large current flows in the active
switch, the integral process will detect the extra voltage drop.
These factors can be used for protection purposes on a cycle-
by-cycle basis. Furthermore, the parasitic resistance of the
inductor has a measurable dc drop that can be obtained by
averaging, then used for protection or sharing purposes. We
have used the inductor dc drop approach to obtain current
sharing at about the 10%level [9].
111. PERFORMANCE
COMPARISONS
Experimental results
Experiments have compared SCM control to current mode
control and voltage mode control for a 5 V to 2 V buck
converter, as well as other types of converters. In the buck
converter, operation over a load current dynamic range of
about 400:1 was achieved with no special difficulties. With
an outer voltage PI loop, combined line and load regulation
below 0.02% was measured over this load range. Table I1
lists some measured results from this converter. Figure 4
shows the transient response to a 4 V to 6 V line step
imposed on the nominal 5 V to 2 V buck converter. The
output effect isjust barely discernible during the transient, and
there is no noticeable output change when steady state is
reached. Conventional current mode control can match this
high performance only if noise is not an issue.
TABLE
11. DATA
FOR SCM BUCK CONVERTER, L=7 uH, C=660 uF. T=10us.
Input voltage
4.0 V
4.0
4.0
4.0
5.0
5.0
5.0
5.0
6.0
6.0
6.0
6.0
Output voltage,
no outer loop
1.9958 V
1.9538
1.9133
1.8720
1.9958
1.9526
1.9121
1.9958
1.9510
1.9107
1.8680
1.a675
Output voltage
with outer loop
1.9974V
1.9973
1.9973
1.9972
1.9974
1.9973
1.9972
1.9973
1.9972
1.9971
1.9971
1.9971
0.04 A
0.04
10
15
200

5. Fig. 4. Line transient response, S V to 2 V converter with SCM control.
Top: input, 1 V/div. Bottom: output, 20 mV/div. Time: 50 pddiv.
Figure 5 compares large-signal load transient performance
for a buck converter under single-loop SCM control and
conventional two-loop current-mode control. The load swing
is sufficient to drive the converter into discontinuous mode.
The current-mode controller has been tuned for good
performance in this load range; the current-mode and SCM
traces are indistinguishable.
, . .
i.. ..L-..L i-_F 1 ~ - - ~ . . _ J
a) One-loop SCM control, load step from discontinuous mode. Top:
output voltage, 50 mV/div. Bottom: load current, 2 Ndiv. Time: 50 ps/div.
b) Load transient under two-loop current-mode control. Top. output
voltage, 50 mV/div. Bottom: output current, 2 Ndiv Time, SO ps/div.
Fig. S Buck converter load transient under one-loop SCM and under
two-loop current-mode ccntrol
Figure 6 shows a boost convertler designed
nominal output of 210 V from a 72 V battery
to provide
bus. This
Fig. 6. 72 V to 210 V boost converter with open-loop SCM control.
ccmverter operates without an outer loop, and has been tested
0ve.r a load range of more than 250:l without difficulty. At
nominal load of 60 W, the output voltage in this converter
changes by no more than 7 V over a 40 V input swing. At
a laad of 0.25 W, the output voltage changes by no more than
10 V over a 40 V input swing. The output voltage change
over this load range was also less than 10 V.
Fiigure 7 shows inductor current and observer comparisons
for a boost converter operating in continuous and
discontinuous modes. The observer output is intended to be
a scaled copy of the negative of the current, and the figure
confirms this relationship.
(canuinuausmode) (discontinuous mode)
Inductor current (1 Ndiv) (upper)
V, (1 V/div)(lower)
X axis: Time (5 pddiv)
Inductor current (0.5 Mdiv) (upper)
V, (0.5 V/div)(lower)
X axis: Time (5 pddiv)
Fig. 7. Inductor current and observer output comparisons for 72 V
to 210 V boost converter at two load levels.
Figure 8 shows waveforms for sensorless current mode
control in a push-pull forward converter application. In this
case, the integral corresponds to the magnetizing current
rather than the transformer winding current. It is more
physically correct to consider the integral term to be a flux
observer. It is straightforward to operate the push-pull
converter by enforcing hard limits on the flux.
201

6. Transformer voltage (2V/div) (upper) V, (2 Vldiv) (upper)
Transformer Current (0.1 i/div)(lawer) TransformerCurrenr (0.1 A/div)(lower)
x axis: '%IC (1 psldiv) X axis. Tme ( i psidiv)
Fig. 8. Waveforms in a push-pull forward converter under SCM control.
'v. CONCLUSION
Sensorless current mode control uses an observer approach
both to reconstruct an inductor current state and to control a
dc-dc converter based on a current-mode technique. SCM is
a very attractive option for the control of dc-dc converters.
It offers the operating performance merits of current mode
control without the need for current sensing. It provides near-
ideal source compensation even over extreme load variations.
Ht also provides bulk load regulation, and a low-performance
PI[ outer loop produces a complete high-performance
converter.
The noise performance of SCM is dramatically enhanced
compared to current-mode techniques. The difference in
signal level between SCM and current mode controls is large
and a difference in signal level of 80 dB is not unusual for
wide load ranges.
The SCM approach applies to all major types of dc-dc
converters, and the appropriate control laws for buck, boost,
buck-boost, boost-buck, and SEPIC converters were listed.
The general SCM approach is a public domain technique for
control of dc-dc converters.
ACKNOWLEDGEMENTS
This work was supported in part by Sorensen Company and
through a grmP from the Collins Avionics and Communi-
cations Division of Rockwell International. Portions of this
paper axe based on the PhD. dissertation of Midya [13].
REFERENCES
[l] C. W. Deisch, "Simple switching control method changes power
converter into a current source," in IEEE Power Electronics Specialists
Con$ Rec., 1979, pp. 300-306.
R. D. Middlebrook, "Topics in multiple-loop regulators and current-
mode programming," in IEEE Power Electronics Specialists Con$ Rec.,
1985, p. 716.
P. Midya, P. T. Keein, "Closed-loop noise properties of PWM power
converters," in IEEE Power Electronics Specialists Conf Rec., 1995.
W. Tang, F. C. Lee, and R. B. Ridley, "Small-signal modeling of
average currest-mode control," lEEE Trans. Power Elec., vol. 8, no. 2,
[
2
]
[3]
141
pp, 112-119, 1993.
[5] W, Tang, F. C. Lee, R. B. Ridley and I. Cohen, "Charge control:
modeling, analysis and design," lEEE Trans. Power Elec., Vol. 8,No. 4,
T. G. Habetler, D.M. Divan, "Control strategies for direct torque
control using discrete pulse modulation," IEEE Trans. Indmtry
Applications, vol. 27, no. 5,pp. 893-901, 1991.
K. H. Kim, S.K. Chung, I. C. Baik, M. J. Youn, "Parameter estimation
and control for permanent magnet synchronous motor drive using model
reference adaptive technique," in Proc. 1995 IEEE Int'l. Con$ Indus.
Elec., pp, 387-392, 1995.
Y. Ito, S. Kawauchi, "Microprocessor-based robust digital control for
UPS with three-phase PWM inverter,'' IEEE Trans. Power Elec., vol. 10,
no. 2, pp. 196-204, 1995.
P. T. Krein, P. Midya, U. Ekambaram, "A distributed low-voltage
power converter," Technical Report UILU-ENG-93-2563, University of
Illinois at Urbana-Champaign, July 1993.
[lo] K. M. Smedley and S. Cuk, "One cycle control of switching
converters,'' IEEE Trans. Power Elec., vol. 10, No. 6, pp. 625-633, 1995.
[I I] K. M. Smedley and S. Cuk "Dynamics of one cycle controlled Cuk
converters," IEEE Trans. Power Elec., vol. 10, No. 6, pp. 634-639, 1995.
[12] B.Arbetter, D. Maksimovic, "Feedforward pulse width modulators for
switching power converters," IEEE Trans. Power Elec., vol. 12, no. 2, pp.
[131 P. Midya, "Nonlinear control and operation of dc to dc switching power
converters," Ph.D. thesis, University of Illinois at Urbana-Champaign,
1995.
[14] R. Ridley, "A new, continuous-time model for current-mode control,"
IEEE Trans. Power Elec., vol. 6, no. 2, pp. 271-280, 1991.
[I51 G.C. Goodwin, K. S. Sin, Adaptive Filtering, Prediction and Control.
Englewood Cliffs, NJ: Prentice Hall, 1984.
[16] K. M. Smedley, "One-cycle controlled switching circuit," U.S. patent
5,278,490, January 1994.
pp. 396-403, 1993.
[6]
[7]
[8]
[9]
361-368, 1997
202