Download COMPARISON OF LINEAR AND SWITCHING DRIVE AMPLIFIERS

AIAA-2002-1352
COMPARISON OF LINEAR AND SWITCHING DRIVE
AMPLIFIERS FOR PIEZOELECTRIC ACTUATORS
Douglas K. Lindner, Molly Zhu
Bradley Department of Electrical and Computer Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
(540) 231-4580
[email protected]
Nikola Vujic, Donald J. Leo
Center of Intelligent Material Systems and Structures, CIMSS
Virginia Polytechnic Institute and State University, VPI&SU
amplifier. These power considerations are important
when the total energy in the system is constrained,
such as in spacecraft.
Abstract
The power requirements imposed on the amplifier by
piezoelectric actuators is discussed. We consider a
two-degree-of-freedom mechanical system driven by a
piezoelectric stack for the purpose of analyzing power
flow and power dissipation of four amplifiers. Two of
the amplifiers are benchtop linear amplifiers. The other
two amplifiers are based on switching topologies. The
power consumption of all four of these amplifiers is
measured and compared. It is shown that the linear
amplifiers consume significantly more power than the
switching amplifiers. These measurements confirm
well-known analyses of these two amplifier topologies.
1.Introduction
In this paper we discuss the power requirements
imposed on the amplifier by piezoelectric actuators.
Piezoelectric actuators impose some special
requirements on the amplifier because their impedance
is primarily reactive. The reactive impedance implies
that the amplifier must handle significantly higher
voltages and circulating currents than suggested by
the real electrical/mechanical power requirements of the
actuator. The amplifier must be sized appropriately to
accommodate this circulating power. Furthermore, the
topology of the amplifier (linear or switching) has a
great impact on the power consumption of the
The analysis of power flow through the amplifier and
actuator has been discussed by Warkentin [1994], Leo
[1999], and Lindner and Zvonar [1998]. Warkentin
shows that actively damping the structure with a
controlled piezoelectric actuator causes the mechanical
power injected into the structure by the external
disturbance source to be absorbed by the structure
and funneled to the electrical source. Similar results
were presented by Chandrasekaran and Lindner [2000]
that show that the electrical power at the actuator
terminals has a negative real component, which
indicate that the actuator feeds electrical power back to
the source. Recent work by Chandrasekarn, Lindner,
and Leo [2000] has demonstrated that the type of
feedback control is a factor in determining the real and
reactive power flow for a controlled system.
We consider a simple mechanical system driven by a
piezoelectric stack. We investigate the power
requirements of the open loop system. We
experimentally determine the power dissipation of two
linear amplifiers, commonly found in the laboratory,
and two switching custom made amplifiers. It is shown
that the linear amplifiers require significantly more
power than the switching amplifiers. Furthermore, the
power dissipation of the linear amplifiers increases with
increasing frequency because the capacitors are
Copyright 2002 by the American Institute of
Aeronautics and Astronautics, Inc. All right reserved.
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drawing more current at higher frequencies. The
switching amplifiers show approximately constant
power consumption over frequency because they are
recycling the current through storage capacitors. The
constant power consumption represents (small) fixed
losses in the amplifiers.
2.Experimental Setup
In this paper we examine the power consumption of
several amplifiers driving a piezoelectric stack. The
Figure 1: Experimental setup
stack is attached to a mechanical load. A piezoelectric
actuator is fixed in from a base plate to a moving mass.
The moving mass is supported by two flexures
that are made from bolts that have been softened by
removing material from the center position. The moving
mass has a small amount of clearance underneath to
allow frictionless motion. This experimental setup is
shown in Figure 1. Several amplifiers were used to
drive this actuator, and the power consumed by each
amplifier was measured. The experimental schematic is
shown on Figure 2. All four amplifiers have been tested
under the same output conditions. Although the load
was the same, the input conditions to different
amplifiers topologies change. In order to establish a
realistic comparison on efficiency of different electrical
amplifiers, we are choosing the input power
Figure 2: Measurement schematic
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as the crucial parameter. As the mechanical load
(Figure 1) is constant during the experiment and the
output voltage of the amplifier is fixed to 100 V pp, the
output power of the stack is assumed constant. Each
amplifier is then driving the load with the periodic
voltage output with the fixed amplitude of 100 Vpp.
In the following we summarize the characteristics of
each of the four amplifiers tested.
Amplifier 1:
The Amplifier 1 is the PCB Piezotronics - AVC 790
Series linear topology amplifier. This amplifier is an offthe-shelf laboratory power amplifier designed to drive
piezoelectric actuators. It is able to drive different
capacitive loads (then different piezoelectric actuator).
The output waveform of this amplifier tracks the input
reference waveform (sinusoidal, square, triangular,
ramp). The limitations are provided by the maximum
voltage and current outputs (see Table 1). As a
majority of commercial amplifiers, it has a standard
electrical network inputs (120/220 VAC, 60/50 Hz),
which means that it has an internal rectifying circuit
that converts AC network signal into DC. The DC
voltage is then used to drive the linear amplifier that
supplies the output signal of the amplifier.
Amplifier 2:
Amplifier 2 is the Trek model 50/750 (which is no longer
commercially available). The main difference with
Amplifier 1 is that this is a high-voltage power amplifier
with an available voltage range of 0 to 750 V (see Table
1). Very similar to Amplifier 1, it contains a rectifying
circuit to adapt the standard AC electrical network to
DC signal, which drives a linear amplifier. The output
waveform will track the input waveform.
Both Amplifiers 1 and 2 may be modeled as linear
amplifier as shown on Figure 3. In Lindner, Vujic and
Leo [2001] these two amplifiers are modeled, simulated
and experimentally tested. Note that when the load
(piezoelectric actuator modeled as a
capacitor) is driven with a sinusoidal signal, the
Amplifier
Designation
Max Voltage
AMP 1
PCB AVC
200 V
AMP 2
TREC
750 V
AMP 3
DSM 1
135 V
AMP 4
SWITCHING
90 V
Table 1: Amplifiers characteristics
energy stored in the capacitor during half of the cycle
is returned to the amplifier during the second half of
the cycle to be dissipated as heat in the transistors.
Figure 3: Electrical representation of a linear
amplifier driving a piezoceramic actuator
Amplifer 3:
Amplifier 3 is the Dynamic Structures and Materials
(DSM) custom made amplifier. It was designed on a
hybrid topology. This amplifier requires a DC electrical
power input (the unit doesn’t contain a AC/DC
rectifier). Also the output signal is limited to a square
wave signal due to the fact that this amplifier was
designed for a current controlled operation.(see Table
1) It requires two inputs signals, one specifying the
frequency and the other specifying the current
magnitude.
Amplifier 4
Amplifier 4 is a switching amplifier fabricated at Virginia
Tech. The power stage is the APEX chip SA-12. The
inductor and control circuitry were designed such that
the amplifier could drive the piezoelectric actuator at
100 V over a 400 Hz bandwidth. The APEX chip is
limited to 0-100 Vdc output. Similarly
to Amplifier 3, this is a custom made (not commercially
distributed) unit, which requires a 100 Vdc power
Max Current
100 mA
50 mA
1.5 A
2.0A
Topology
Linear
Linear
Hybrid
Switching
Input
120 V/60 Hz
120 V/60Hz
80 Vdc
100 Vdc
supply. The output voltage waveform will track the
input reference waveform.
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Comparison of Input Powers for different amplifiers
100
Amp
Amp
Amp
Amp
90
80
1
2
3
4
70
60
Power in [W]
Figure 4 shows the topology of this switching
amplifier. The two transistor switches are controlled so
that the appropriate voltage waveform is delivered
to the load. The current circulates between the
piezoelectric actuator and the capacitor at the input of
the amplifier. The losses in this amplifier are
attributable to the stray resistance loss, the turn-on
and turn-off of the transistors, and the losses in the
magnetics.
50
40
30
20
10
L
Vdc
0
0
ACTUATOR+
STRUCTURE
gating signals
H f (s)
+
_
Pulse Width Modulator
_
H c (s )
+
Σ
Controller
Figure 4 Switching amplifier
3.Results and analysis
The amplifiers were tested by exciting the actuator with
sinusoidal waveform (0-100V) for the two linear
amplifiers and triangular waveform with same peak-topeak voltage for the switching amplifier. At the same
time the input power drawn by the amplifier was
measured with a power meter and the output voltage
and current were sensed by a data acquisition board.
As no load was placed on the structure the only work
done by the actuator was the work to overcome the
internal dissipations, which we consider small in the
current test configuration.
The dissipated power in amplifiers is shown on Figure
5.
50
100
150
200
250
Frequency [Hz]
300
350
400
Figure 5: Measured Input powers
Figure 5 shows two different behaviors versus
frequency. Amplifiers 1,2 and 3 exhibit linear
dependence with frequency because the piezoelectric
actuators are drawing more current at higher
frequencies. Also note that Amplifier 2 draws much
more power than Amplifier 1 because the output
voltage of 100 V is closer to the rated voltage of
Amplifier 1 (200 V) than the rated voltage of Amplifier 2
(750 V). The amplifier 4 exhibits a completely different
behavior versus frequency. The switching amplifiers
show approximately constant power consumption over
frequency because they are recycling the current
through storage capacitors. The constant power
consumption represents (small) fixed losses in the
amplifiers.
We notice that for the first three amplifiers a constant
amount of power is drawn. We assign these power
losses (offset) to the dissipation in the AC/DC rectifier
and other control and protection circuits present in the
amplifier. Therefore the major power loss in the system
comes from the linear amplifier circuit. Hence in order
to compare the power dissipation of the first three
amplifiers when driving a PZT we will subtract out this
constant amount of power to examine the frequency
dependence of the measurement. The extrapolated
linear relations between the normalized power versus
frequency are:
in
PAMP
1 = 0.2019 ⋅ f − 0.0799
in
PAMP
2 = 0.8367 ⋅ f + 2.5779
in
PAMP
3 = 0.0218 ⋅ f + 1.1024
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The constant power losses are estimated by
extrapolation to 0 Hz and subtracted and the
normalized efficiencies are plotted on Figure 6.
Acknowledgement
This work was supported in part by Air Force under
grant 00-05-6889.
Comparison of Normalized Input Powers
60
References
Saturation Amp 1
50
Amp 1
Extrapolated-Amp1
Amp2
Extrapolated-Amp 2
Amp 3
Extrapolated-Amp3
Power in [W]
40
30
1.
Chandrasekaran, S. and D. K. Lindner, "Power
Flow Through Controlled Piezoelectric Actuators,"
Journal of Intelligent Material Systems and
Structures, Vol. 11, No. 6, June 2000, pp. 469 - 481.
2
Chandrasekaran, S., D. K. Lindner, and D. Leo,
"Effect of Feedback Control on the Power
Consumption of Induced-Strain Actuators,"
Proceedings of the Adaptive Structures and
Materials Systems Symposium, ASME
International Mechanical Engineering Congress
and Exposition, Orlando, Florida, November 5-10,
2000, pp. 65 – 76; to appear in Journal of Intelligent
Material Systems and Structures
3.
Warkentin. D. J, Crawley. E.F, 1994, “Power Flow
And Amplifier Design For Piezoelectric Actuators
In Intelligent Structures,” Proceedings of the
SPIE, The International Society for OpticalEngineering, vol. 2190, pp. 283-94.
4.
Leo, D.J., 1999, "Energy Analysis Of PiezoelectricActuated Structures Driven By Linear Amplifiers,"
Proceedings of the Adaptive Structures and
Materials Symposium, ASME AD-vol. 59,
November, Nashville, TN, pp. 1-10.
5.
Zvonar, G. A. and D. K. Lindner, 1998 "Power Flow
Analysis of Electrostrictive Actuators Driven by
Switchmode Amplifiers," Journal on Intelligent
Material Systems and Structures, special issue on
the 3rd Annual ARO Workshop on Smart
Structures, Vol. 9, No 3, pp. 210 - 222.
6.
D. K. Lindner, N. Vujic, and D.J. Leo, 2001
"Comparison of drive amplifiers for piezoelectric
actuators ”Journal on Intelligent Material
Systems and Structures”, Proceedings of the
SPIE, The International Society for OpticalEngineering, vol. 4332, pp. 281-91.
20
10
0
0
20
40
60
80
100
120
Frequency [Hz]
Figure 6: Normalized Comparison of
Amplifiers 1,2 and 3
This extrapolated results shows that hybrid amplifier
(AMP3) has a ten times lower slope then AMP1. Also
the total power drawn into the AMP3 is 38 % less then
AMP1 and 80 % less then AMP2 (in current saturation
mode). This gap is proportionally increasing with
frequency.
4.Conclusions
In this paper we have examined the power
consumption of four amplifiers when these amplifiers
are driving a piezoelectric actuator. All amplifiers
exhibit a fixed amount of power dissipation due to
internal energy management components. In addition,
the amp lifier may have additional power dissipation
due to the topology of the amplifier. Linear amplifiers
will dissipate all of the regenerated energy as heat.
This energy dissipation increases as the difference of
the peak output voltage and maximum voltage of the
amplifier increase. Switching amplifiers, properly
configured, will recycle the regenerative energy from
the piezoelectric actuator, thus minimizing the losses in
the amplifier. The cost of a more efficient switching
amplifier is increased complexity.
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