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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. 1 American Institute of Aeronautics and Astronautics 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 2 American Institute of Aeronautics and Astronautics 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. 3 American Institute of Aeronautics and Astronautics 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 4 American Institute of Aeronautics and Astronautics 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. 5 American Institute of Aeronautics and Astronautics