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Battery-Conscious Task Sequencing for Portable Devices Including Voltage/Clock Scaling
Battery-Conscious Task Sequencing for Portable Devices
Including Voltage/Clock Scaling
 
Daler Rakhmatov and Sarma Vrudhula
Center for Low Power Electronics
ECE Department, University of Arizona
Tucson, Arizona 85721
daler/sarma@ece.arizona.edu
Chaitali Chakrabarti
Center for Low Power Electronics
EE Department, Arizona State University
Tempe, Arizona 85287
chaitali@asu.edu
ABSTRACT
Operation of battery-powered portable systems can no longer be
sustained once a battery becomes discharged. Maximization of the
battery lifetime is a difcult task due to nonlinearity of battery be-
havior that depends on the characteristics of the system load prole.
We address the problem of task sequencing without and with volt-
age/clock scaling that shapes the prole so that the battery lifetime
is maximized. We developed an accurate analytical battery model
and validated it with measurements taken on a real lithium-ion bat-
tery used in a pocket computer. We use the model as a basis for a
unique battery-conscious cost function and utilize its properties to
develop several novel algorithms, including insertion of recovery
periods and voltage/clock scaling for delay slack distribution.
Categories and Subject Descriptors
J.6.2 [Computer-Aided Engineering]: Computer-Aided Design
General Terms
Algorithms, Performance, Design
Keywords
Battery, modeling, low-power design, scheduling, voltage scaling
1.
INTRODUCTION
In portable battery-powered electronic systems maximizing the
battery lifetime is an important problem. Consequently, a designer
needs an accurate model of a battery. Previously, we have pro-
posed a high-level analytical model that produces accurate lifetime
predictions and permits a trade-off between the accuracy and the
amount of computation performed [9]. The present work shows
how this model can be utilized for single-processor load schedul-
ing without and with voltage/clock scaling.
 
This work was carried out at the National Science Foundations
State/Industry/University Cooperative Research Centers (NSF-
S/IUCRC) Center for Low Power Electronics (CLPE). CLPE is
supported by the NSF (Grant EEC-9523338), the State of Arizona,
and a consortium of companies from the microelectronics industry
(visit the CLPE web site http://clpe.ece.arizona.edu).
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for prot or commercial advantage and that copies
bear this notice and the full citation on the rst page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specic
permission and/or a fee.
DAC 2002, June 10-14, 2002, New Orleans, Louisiana, USA.
Copyright 2002 ACM 1-58113-461-4/02/0006 ...
$
5.00.
Several published papers have considered the battery issues to
improve system operation [2, 5, 6]. The authors of [2] used the
VHDL-based simulation model from [1] to expose the impact of
different dynamic power management policies on the battery life-
time. Both single-battery and dual-battery powered systems were
considered. In [6] the authors addressed static scheduling of tasks
with real-time constraints. Evaluation of the proposed method was
based on the battery model combining Peukerts law [4] and empir-
ical analysis due to [8]. Lifetime improvements reported in [2, 6]
must be interpreted with care, since the results are heavily biased
by the properties of a model used to represent the battery. Power-
aware scheduling under timing constraints was described in [5].
The authors used a NASA/JPL Mars Pathnder rover as a motivat-
ing application with the two power sources: a battery and a solar
panel. The objective was to utilize the solar panel (the free energy
source) as much as possible and minimize the energy drawn from
the battery. However, the scheduler was only aware of the presence
of an alternative energy source, not battery behavior itself.
In this paper, we propose an approach to battery load prole syn-
thesis based on the high-level battery model from [9]. This model
not only accurately predicts the battery lifetime under various dis-
charge conditions, but also provides an analytical expression that
can be used as a cost function to guide the battery lifetime opti-
mization process. The specic problems that we address are (1)
task sequencing without voltage/clock scaling and (2) task sequenc-
ing with voltage/clock scaling. While tackling these problems, we
account for and take advantage of charge recovery effects. We also
demonstrate that predictions of the model are in close correspon-
dence with measurements performed on a real lithium-ion battery
used in a pocket computer.
2.
MOTIVATING EXAMPLE
In this section we demonstrate, by simple examples, the impact
of task sequencing on a battery. Moreover, we also provide justi-
cation for the use of the battery model from [9] in our algorithms.
All the results are obtained by performing experiments with a real
battery.
The experimental setup consisted of a lithium-ion battery used
in the ITSY pocket computer [10], the programmable electronic
load Agilent 6060B, and the host computer recording experimen-
tal data. The open-circuit voltage of the battery was 4.2 V and
the cutoff voltage was set to 3.0 V. The electronic load operated
in the constant-current mode. Variable-current proles were gen-
erated as a piece-wise constant-current prole (a staircase). The
battery voltage was sampled every second, and once the voltage
dropped below the cutoff level the load was disconnected from the
battery. Recharging was performed in the constant-current mode
at 800 mA, until the battery voltage recovered to its open-circuit
value.
First, we conducted ten constant-current discharge experiments
to estimate parameters for our battery model and to see how well
the model predicts battery lifetime under constant loads. The dis-
charge currents ranged from 1011 mA to 123 mA, and the life-
times ranged from 30 minutes to over 300 minutes. The model t is shown in Figure 1. The maximum error of lifetime predictions is
4%, with
¡
the average of 2%.
100
200
300
400
500
600
700
800
900
1000
1100
10
1
10
2
10
3
Load, mA
Lifetime, min
Lifetimes under ConstantCurrent Discharge
measured
predicted
Figure 1:
Lifetimes for Various Constant-Current Loads.
Next, we generated ve variable-current proles shown in Fig-
ure 2. We selected four currents of certain duration (1011 mA for
10 minutes, 814 mA for 15 minutes, 518 mA for 20 minutes, and
222 mA for 15 minutes) and sequenced them in different order to
obtain proles P1-P4. The length and total charge demand of each
of the four prole is 60 minutes and 36010 mA-min, respectively.
Note that in P1, after all the four currents were applied, the battery
was discharged under the constant rate of 222 mA until the cutoff
voltage was reached. The sole purpose of the last load 222 mA is
to determine how much residual charge is left.
Measured
Predicted
Lifetime
Charge
Prole
L
m
C
m
L
p
C
p
Error
Error
min
mA-min
min
mA-min
%
%
P1
64.9
37098
66.9
37542
3.1
1.2
P2
54.0
29944
54.4
30348
0.7
1.3
P3
55.8
32591
55.0
31940
1.4
2.0
P4
58.4
35181
57.5
34715
1.5
1.3
P5
67.5
34965
67.0
34706
0.7
0.7
Table 1:
ITSY Lifetime and Delivered Charge.
According to these experiments, prole P1 is the best, and pro-
le P2 is the worst sequence for the battery. Note that load currents
in P1 (P2) are decreasing (increasing). This important result is ac-
curately predicted by the battery model. In P1 the battery survives
all the four loads and remains operational for extra 4.9 minutes un-
der 222 mA (residual 1088 mA-min charge). In P2, however, the
battery fails to service the last 6.0 minutes under 1011 mA (un-
delivered 6066 mA-min charge). For these two proles, the dif-
ference in the total delivered charge is as much as 20% of 36010
mA-min. The other alternatives P3 and P4 are neither better than
P1 nor worse than P2, as predicted by the model and demonstrated
by the measurements.
Voltage/clock scaling plays a critical role in minimizing energy
consumption, thus improving the battery lifetime. To obtain prole
P5, for example, we took P2 and changed the failing 10-minute load
of 1011 mA to a 20-minute load of 518 mA to reect a hypothet-
ical change in the system voltage.
1
The prole length increased
from 60 minutes to 70 minutes, and the battery failed after 67.5
minutes. The total delivered charge is 34965 mA-min, which is an
improvement over P2 with 29944 mA-min.
Table 1 shows the measured/predicted lifetimes (L
m
and L
p
, re-
spectively) and the measured/predicted delivered charges (C
m
and
C
p
, respectively) for the proles P1-P5. Note tha