PEDS 2007
Digital Control Generations -- Digital Controls for
Power Electronics through the Third Generation
Philip T. Krein
Grainger Center for Electric Machinery and Electromechanics
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois
Abstract - Digital control in power electronics can be divided
into three "generations." First-generation digital controls use
digital "outside the loop" in communications, setup, and
supervisory roles. Second generation digital controls use digital
processes "inside the loop," including discrete-time feedback
loops and sometimes even digital signal processing. Today,
first-generation digital methods are expanding quickly, as new
communication protocols and adjustable analog loops become
common. Even companies that continue to design analog
controls for power electronics often include these types of digital
processes. Second-generation digital controls are a hot topic
right now, as real-time digital controllers become feasible. In
third-generation digital controls, the digital process functions
directly with individual switches to push performance up to the
physical limits of power electronics. A digital switch decides
when it must turn on or off. The control is on direct switch
timing rather than a converter duty ratio or a setting. Extreme
performance is possible with this approach, such as converters
that do not exhibit output disturbances when confronted with
load or line step changes. The talk compares these different
arenas, all of which are current active topics in power electronics,
and shows what can become possible as the third generation
develops
I. INTRODUCTION
Digital control in power electronics, treated now as a hot
topic area and debated in many forums, has a long history.
The general approaches and contexts are perhaps better
understood by dividing the developments into three
"generations." In this paper, the concept of digital control
generations is introduced. The emphasis is on
third-generation techniques that are beginning to capture
interest in research laboratories. Although the general value
of digital control continues to be a matter of debate, the broad
question of how control adds value in a power electronic
system, and whether digital techniques offer special value, is
the underlying issue that motivates this work. The concepts
in this paper may be of value in discussions of digital control.
As digital control is discussed, it is important to keep in
mind the fundamental analog processing to be accomplished.
We are not free to create arbitrary digital representations of
energy, in contrast to most communications and information
1 This paper is provided under the Distinguished Lecturer Program of the
IEEE Power Electronics Society. This material is based in part upon work
supported by the U.S. National Science Foundation under Grant No.
ECS-062 1643.
61801 USA
processing applications. Power electronics in the end is
characterized by large-signal nonlinear systems with analog
functions. No matter how much digital processing is
involved, its merit is always determined by the ability to better
perform these analog functions.
The generations are defined as follows:
* First-generation digital control: digital processing
outside a control loop, in a management or supervisory
role.
* Second-generation digital control: digital processing
inside a control loop. The ultimate formulation includes
digital loop designs and real-time control processes.
* Third-generation digital control: digital processing is
responsible for the moment-by-moment direct action of
active switching devices in a converter. The ultimate
formulation is a digital switch with built-in computational
capability that functions in real time as the device
operates.
Although the digital control generations defined in this
paper have a certain time evolution sequence, they are not
meant to imply obsolescence. First-generation digital
controls, which have the longest history, are quickly becoming
dominant and are not likely to leave the stage in the
foreseeable future. Second-generation digital controls seem
to be at the heart of present debates. Third-generation
controls open the way to unique performance improvements,
but are rare.
II. FIRST-GENERATION DIGITAL CONTROL IN POWER
ELECTRONICS
The earliest power electronics controllers, dating to the
TL494 and similar chips, were some of the first mixed-mode
integrated circuits. These ICs include simple logic along
with oscillators and amplifiers, and thus combine digital and
analog functions. In this sense, digital control has been a
fundamental aspect ofpower electronics for 40 years or more.
In this paper, first-generation digital controls are assumed
to be more than just mixed-mode circuits. In first-generation
digital controls, a digital process manages a power electronic
process. The objectives typically include communication,
programming, or protection. Motor drives were an early
example of first-generation controls. When electronic
1-4244-0645-5/07/$20.00©2007 IEEE P-1
adjustable-speed drives emerged in the 1970s, many already
had displays and internal interactions governed by digital logic.
Modern drives are designed with dedicated digital signal
processors [1, 2], which often manage nearly all the power
electronics through computer control. A more recent
example is the PMBusTm architecture for power supply
communications and interaction [3].
Today, first-generation digital controls for power
electronics are widespread. In addition to the PMBus
architecture, various smart battery charging interfaces and
other communication configurations are becoming common.
Dc-dc converters for processors often have external digital
settings to support adaptive output voltage. Even those
manufacturers "dedicated" to analog power management have
embraced digital communication and control interfaces. As a
result, first-generation techniques are not really part of the
present debate about digital control, and should be taken as a
routine extension of other control methods in power
electronics.
First-generation controls provide a wide array of
advantages. Two crucial advantages are the ability to
managing event-driven actions and the ability to provide
numerical settings. Event-driven actions, such as responses
to overloads, transitions among various modes, or even the
ability to control different converter topologies bring
fundamental performance advantages to this class of control.
Since real-time performance demands are avoided in digital
part of the system, these capabilities are possible without
compromise in dynamic performance. Numerical settings,
including gains, output reference values, or operating
frequency add software-like flexibility to hardware devices.
Other potential advantages include communications interfaces
and control buses, memory for various programming functions,
and the ability for IC designers to add new features as blocks.
The latter allows a vendor to create comprehensive product
families from a single base design.
Many present first-generation implementations emphasize
communication and basic settings, but a range of opportunities
remain. Potential innovations include variable-gain tuning,
in which gain settings depend on actual line or load conditions,
frequency tuning to or from resonances, and various types of
control tuning. On-line calibration and active digital
trimming, common in many drive applications, can be
extended to most power converters. The use of various
frequency-domain techniques, such as Fourier Transforms for
compensation [4], nonlinear filters [5], and more sophisticated
signal processing for fault detection, has been a topic of
previous study that is well worth a closer look.
III. SECOND-GENERATION DIGITAL CONTROLS IN POWER
ELECTRONICS
In second-generation control, the digital process moves
inside the control loop and operates a power converter in real
time. Like first-generation approaches, the basic technique is
not new. Once motor drives moved to digital PWM
processes more than a decade ago, many of them used
complete digital loops for operation and control. At the
research level, complete digital controls were presented almost
twenty years ago [6]. In motor drive applications,
computation time is usually ample and computation cost is a
modest fraction of total system cost. The net result has been
early adoption of all-digital implementations in that industry.
In power supplies and dc-dc converters, real-time
operation tends to work against second-generation designs,
which are often characterized by intensive analog-digital
(A-D) conversion requirements and short computation time
windows. The development of second-generation digital
controls for these applications is perhaps the most active topic
in digital control for power electronics and is the subject of
controversy. Many designers still question the value of
digital implementations compared to conventional analog
hardware.
To see the rate challenge, consider a counter-based digital
PWM generator intended to support 250 kHz switching for a
dc-dc converter. If this device provides 0.1% pulse-width
resolution, its clock must run at 250 MHz or more. A PWM
generator to support 500 kHz switching with 16-bit
pulse-width resolution demands 31 ps time resolution. This
requires a 33 GHz clock. Resolution and operating
requirements such as these, which have little meaning in the
context of analog controls, quickly become unwieldy in a
digital application. Digital controls of this type can chatter
and operate in limit cycles [7], although known methods such
as integral controls can help avoid the problems.
Many second-generation digital controls involve a direct
mapping from analog implementations to discrete-time
implementations. This practice supports the numerical
setting advantages of digital controls, but does not
fundamentally alter performance compared to analog
implementations. Much of the controversy about digital
control in power electronics today is concerned with whether a
discrete-time implementation offers special advantages over
an analog version given a conventional average-model
controller. In this paper, the controversy is not entirely
germane: there are valid analog controls that use external
digital management, as in first-generation digital control, and
evolution towards digital control need not place real-time
digital processing inside a loop.
A. Discussion ofsampling issues
Given the linkage between second-generation digital
control and A-D/D-A conversion, sampling challenges
become a significant aspect. One relatively misunderstood
aspect is the Nyquist rate, which reflects the results of
sampling theory. As is well known [8], a bandlimited signal
can be reconstructed perfectly from properly selected samples
taken at higher than the Nyquist rate. This rate is normally
taken as half the period associated with the signal band limit.
It is tempting to infer that any periodic signal can be
reconstructed from samples taken at half the period, but this is
not correct.
P-2
1111111111111111111111111
Sample times
Fig. 1. A square wave with arbitrary duty ratio cannot be reconstructed from
uniform samples. Here samples taken five times per switching cycle are not
adequate.
Consider a square wave of unknown (but constant) duty
ratio, as might be measured as the voltage drop across a switch
in a power converter or as the ESR jump on a capacitor. As
Fig. 1 shows, no set of uniform samples, no matter how often
they are taken, will permit the waveform to be sampled and
reconstructed perfectly. This is because for arbitrary duty
ratio the probability of sampling exactly at the switching
instant is zero. What does the Nyquist rate not apply here?
A square wave is not a bandlimited signal, so conventional
sampling theory does not apply.
Curiously, the fundamental Nyquist rate problem
associated with the square wave in Fig. 1 can be circumvented.
The integral of the square wave yields a triangle wave, as in
Fig. 2. This waveform, although also not bandlimited, is
easy to reconstruct if the sampling rate is sufficient to ensure
two samples during each rising portion and two during each
falling portion. This means that for any duty ratio between 0
and 1, a sampling frequency suitable to permit perfect
reconstruction can always be found. Indeed, the underlying
square wave can be reconstructed from the same samples by
taking the derivative of the computed triangle. The sampling
frequency is not really a Nyquist rate in the conventional sense,
but waveform reconstruction is possible. It is also clear that
non-uniform samples can be used to advantage: if samples
are taken just before and just after each switch operation, the
information needed to reconstruct the waveform will be
available.
The possibility of reconstructing square waves from
limited samples gives rise to the notion of integral sampling
[9], but in contrast to the hold process in [9], samples are to be
taken during the integration process. The addition of a single
analog block - the integrator - adds considerable signal
processing capability to a power converter since it support
signal reconstruction from a small number of well-place
samples. Notice that the process uses general knowledge
about the shape of the waveform ( a square wave or triangle)
instead of knowledge about its frequency limits. In effect, a
time-domain sampling theorem has been identified in place of
a more conventional frequency-domain theorem.
B. Real-time limitsfor second-generation controls
In second-generation designs, real-time digital control
must push the limits. Concerns include the conversion speed
of A-D and D-A converters, the time needed for computation,
and time needed to obtain low-noise samples. Precision,
both in terms of time resolution and quantization, becomes an
11 1 1I1 1 1 1 11
Sample times
Fig. 2. The integral of the square wave (a triangle) can be reconstructed if
two samples are available during each rising and falling portion.
important issue. A fundamental question is how a control
can determine whether the output has reached the desired
value and that the converter should enter steady state.
A important way to manage extreme resolution
requirements is to employ dithering or noise shaping methods
[10, 11]. In both approaches, a large number of switching
periods is used as a group to deliver the desired pulse width.
For example, a PWM process with only 10% resolution can
deliver effective 1% output resolution if a group of ten cycles
is employed. In dithering, the local duty ratio variation
needed to deliver higher resolution is randomized. Thus, a
desired 5400 duty ratio in a process that can deliver only 500O
and 60% values would be obtained by random combinations
of 5000 and 60% in the right proportions. In noise shaping,
the process is not random, and instead is characterized by a
high-pass filter that shifts the output quantization noise away
from the baseband duty ratio modulation.
As microprocessors improve, real-time computational
limits become less important in second-generation controls.
Today's DSPs, for instance, perform multiple complicated
arithmetic steps in a single clock cycle. At clock frequencies
above 100 MHz, there is time for several hundred
computations per switching period, even for dc-dc converters
operating at up to 500 kHz. One commercial product [12]
processes six inverter channels for high-fidelity audio output
based on a complete second-generation implementation.
Other vendors provide sophisticated adaptive controls in
second-generation devices [13]. These examples suggest that
second-generation digital controls will continue to be an area
of active growth for years to come.
IV. THIRD-GENERATION DIGITAL CONTROLS IN POWER
ELECTRONICS
In any switching power converter, the true control
actuation is the time at which switches operate. At the most
basic level, the control question is to determine when to
operate each switching device in the network to achieve a set
of performance objectives. Beyond the implementation of
real-time digital control in a closed-loop power converter is
the challenge of direct switch control to address this question.
The issue can be considered in a manner analogous to
averaging: in second-generation digital controls, the control
generally computes a desired duty ratio. A counter
P-3
implements the final step of a PWM process. The control is
altering pulse width, rather than direct timing.
Third-generation digital controls act on information to
determine specific time-domain action of each switching
device. The ultimate objective is the digital switch, an
intelligent switching device that operates at just the right times
to achieve objectives. The objectives could represent any
performance aspect needed by the user. Many of them do
not lend themselves to analog controls. For example, in a
given dc-dc converter, the detailed performance objectives
might include the following:
* Deliver an output voltage that is within 0.5% of a
specified reference.
* Do not allow the current to exceed a given dynamic limit.
* Deliver the voltage while minimizing internal converter
losses.
* Avoid certain frequency bands to prevent noise problems.
* Respond to load changes as rapidly as possible while
continuing to meet output tolerance requirements.
Objectives like these mix steady-state, dynamic, and
protection requirements. They imply computation challenges
such as those associated with loss minimization and
electromagnetic interference (EMI). At the most basic level,
performance objectives translate into difficult control
requirements: determine when to operate the next switching
device in a sequence, such that loss is minimized, EMI is
avoided, and steady-state requirements are met. In general, it
might be possible to formulate an optimal control problem for
a set of objectives:
Optimal controlproblem formulation
Given a set of n switches and a time interval T, find times
ti n for these switches to minimize a performance objective
function J(x,t) that is a function of states x and time.
With enough constraints and well-defined objective functions,
this problem can be solved. For example, in a dc-dc
converter in which there is one active switch and the switching
period is constrained to be fixed, there is a unique time that
delivers the correct output in steady state. This is just the
well-known average duty ratio. The general problem deals
with dynamics rather than steady state, and a suitable problem
formulation should have the switching frequency as a
dependent variable rather than a constraint, but at least the
steady-state operation is relatively well defined. The general
problem, in which there are many performance objectives
representing both static and dynamic requirements, may not be
tractable, however.
Third-generation controls are the subject of present
research in a few groups. An early example that follows the
general approach is given in [14], although the geometric
controls introduced much earlier by Burns [15] are
straightforward to represent in terms of third-generation digital
methods. Dead-time optimization [16, 17] is a partial
a)
ct
0 10 20 30 40 50
Time (us)
Fig. 3. Hysteresis controlled buck converter responding when a 150 kHz
line disturbance is imposed at 20 pts. Top trace: input voltage.
Triangle: inductor current. Dotted trace: output voltage across capacitor.
Output capacitor is small to show ripple.
third-generation example, in which detailed switch timing is
controlled inside a loop to minimize loss.
Fig. 3 provides a hint - based on an analog control - of
what might be possible with third-generation controls. The
waveforms shown are the input voltage, output voltage, and
output current for a buck converter. The converter operates
with a hysteresis control to maintain the output at 5 V. The
steady-state switchin