ADAPTIVE PIEZOELECTRIC ENERGY HARVESTING TECHNIQUE

 The need for a wireless electrical power supply has spurred an interest in piezoelectric energy harvesting, or the extraction of electrical energy using a vibrating piezoelectric device. Examples of applications that would benefit from such a supply are a capacitively tuned vibration absorber ,a foot-powered radio” tag and a Pico Radio .A vibrating piezoelectric device differs from a typical electrical power source in that its internal impedance is capacitive rather than inductive in nature, and that it may be driven by mechanical vibrating amplitude and frequency. While there have been previous approaches to harvesting energy generated by a piezoelectric device there has not been an attempt to develop an adaptive circuit that maximizes power transfer from the piezoelectric device. The objective of the research described herein was to develop an approach that maximizes the power transferred from a vibrating piezoelectric transducer to an electromechanical battery. The paper initially presents a simple model of piezoelectric transducer. An ac-dc rectifier is added and the model is used to determine the point of optimal power flow for the piezoelectric element. The paper then introduces an adaptive approach to achieving the optimal power flow through the use of a switch-mode dc-dc converter. This approach is similar to the so-called maximum power point trackers used to maximize power from solar cells. Finally, the paper presents experimental results that validate the technique. 

 

2. DESIGN

2.1. OPTIMAL POWER FLOW OF PIEZOELECTRIC DEVICE

fig.1  piezoelectric element model dc-dc converter

To determine its power flow characteristics, a vibrating piezoelectric element is modeled as a sinusoidal current source i_p (t) in parallel wit its internal electrode capacitance Cp. This model will be validated in a later section. The magnitude of the polarization current I_P varies with the mechanical excitation level of the piezoelectric element, but is assumed to be relatively constant regardless of external loading. A vibrating piezoelectric device generates an ac voltage while electromechanical batteries require a dc voltage, hence the first stage needed to be the output harvesting circuit is an ac-dc rectifier connected to the output of the piezoelectric device, as shown in the Fig. 1. In the following analysis, the dc filter capacitor Crect is assumed to be large; enough so that the output voltage Vrect is essentially constant; the load is modeled as a constant current sourceload ; and the diodes are assumed to exhibit ideal behavior.

The voltage and current waveforms associated with the circuit are shown in Fig 2. These waveforms can be divided into two intervals. In interval 1, denoted as u, the polarization current is charging the electrode capacitance of the piezoelectric element. During this time, all diodes are reverse-biased and no current flows to the output. This condition continues until the magnitude of the piezoelectric voltage vp (t) is equal to the output voltage Vrect. At the end of the communication interval, interval 2 begins, and output current flows to the capacitor Crect and the load.

				| sin (Tt) |.
							(2)
		+ io (t) ,   =
							(3)

By assuming C_rect  >> C_p , the majority of the current will be delivered as output current

 

The dc component of i_o (t) can be shown to be

The output power can be shown to vary with the value of the output voltage V_rect as follows

	+ P (t) ,   =
					(4)

It can then be shown that the peak output power occurs when

			(5)

Or one-half the peak open circuit voltage of the piezoelectric element

Fig.2 Voltage, current waveforms of a piezoelectric device

 

2.2. ENERGY HARVESTING CIRCUITRY

The magnitude of the polarization current I_p generated by the piezoelectric transducer, and hence the optimal rectifier voltage, may not be constant as it depends upon the vibration level exciting the piezoelectric element. This creates the need for flexibility in the circuit. i.e., the ability to adjust the output voltage of the rectifier to achieve maximum power transfer. To facilitate the attainment of the optimal voltage at the output of the rectifier, a dc-dc converter is shown in Fig. 3. Typically the controller of such a converter is designed to regulate the output voltage [11]; however, in this circuit the converter will be operated to maximize power flow into the battery. If effective, the piezoelectric element would be at peak power, which corresponds to the output voltage of the rectifier V_rect being maintained at its optimal value, approximately one-half the open circuit voltage, as described previously.

         The purpose of this circuit is to maximize the power flowing into the battery. As the battery voltage is essentially constant or changes very slowly, this is equivalent to maximizing the current into the battery, I_battery. By sensing this current, the duty cycle can be adjusted to maximize it. A control scheme such as this is general enough to be effective for many dc-dc converter topologies. To illustrate the theoretical principle of maximum power transfer and the control of the converter will be discussed in this paper. Fig. 4 shows a representation of the steady state battery current-duty cycle relationship using a step-down converter.

         In order to achieve peak battery current, an appropriate method of controlling the duty cycle is to incrementally increase or decrease the duty cycle as determined by the slope of the battery current curve JI/JD. The duty cycle is now the sum of the present duty cycle and the increment

D_i+1 = D_i  + K _sgn (JI/JD)

Where K is the assigned rate of change of the duty cycle and sgn() is the signum function which returns the sign of the quotient JI/JD.

         Note a few features of this control: First, as the control algorithm is based upon the sign of a rate of change, the duty cycle must continuously change in practice. Ideally, once the controller has settled, this will amount to small perturbations about the optimal operating point. Furthermore, as the control algorithm is based upon steady-state behavior of piezoelectric element and the dc-dc converter, a two time scale approach must be used when designing the controller [12]. Using two-time-scale analysis techniques, convergence of the controller can be assured provided the dynamics of the control algorithm are set to be “slow” enough such that the piezoelectric device and converter can be assumed to always be operating under steady state conditions. However, this also places limitations on the bandwidth of the controller.

 

2.3. CONTROL IMPLEMENTATION

         fig.5

The adaptive controller is implemented using a dSPACE DS1102 controller board. The board includes a Texas Instruments TMS320C31 floating point digital signal processor(DSP), analog-to-digital (ADC) converter for sampling measurements, and pulse-width modulated (PWM) signal outputs for controlling the converter. The control algorithm was developed in MATLAB 5.3 using the graphical interface Simulink 3.0 and the Real-Time Workshop to generate the controller code for the DSP.

         Fig. 5 shows a block diagram of the controller implementation. The initial duty cycle is set at 10% for circuit startup. The resulting battery current is evaluated using a current sense resistor in series with the battery and sampled by an A/D converter. The current signal is then low-pass filtered to attenuate noise and reduce the current ripple effect caused by the switching of the MOSFET. The derivative of the signal is then taken and divided by the derivative of the duty cycle. Dividing the derivative of the current by the derivative of duty cycle provides JI/JD. Which is used to determine the controller’s position n the battery current-duty cycle curve shown in Fig. 4.

                          

                                                       fig.4

          The sign of the quotient, JI/JD. is used by a 0-threshold block to increment the duty cycle by a set rate, in our case 21 mill percent /s (21-m%/s). This rate was determined to produce a measurable change in the battery current that could be used to evaluate the effectiveness of the new duty cycle. The resulting sign(+/-) of the division block, not its numerical magnitude, is all that is used by the 0- threshold block to increase or decrease the duty cycle. If either input signal would be zero, resulting in a zero or undefined quotient, the threshold block will decrease the duty cycle as a default. This default decrease allows the control to migrate to lower duty cycle values when the battery current might not be measurably changing, as is the case of circuit startup. Experimentation showed that, at a switching frequency of 1kHz, the current changes little at duty cycles above 10%, whereas optimal duty cycles occurred around 3-5%.

        

The duty cycle is then filtered and used to generate the PWM signal for the driver circuitry of the step-down converter. The additional filtering of the PWM signal is necessary to slow the rate of change of the duty cycle so the change in current can be measured and evaluated. Without the LPF, the controller is prone to duty cycle oscillations, as the perturbing signal reacts faster than the finite settling time of the battery current signal.

3. EXPERIMENTAL SETUP

         A Quickpack® QP20W purchased from Active Control eX-perts(ACX), Cambridge, MA, was used as the piezoelectric energy source. It is a two layer device that generates an ac voltage when vibrated in a direction perpendicular to its mid-plane. Device specifications and diagram are shown along with the piezoelectric element properties.

Fig.7

            The experimental setup is shown in Fig 7. The piezoelectric device is secured to an electric-powered shaker, which provides variable mechanical excitation in response to a sine wave input. The magnitude of the mechanical excitation of the piezoelectric element will be characterized by the open-circuit voltage that is measured across the unloaded rectifier capacitor, Voc. A small mass was added to the free tip of the bimorph to enhance the external stress and increase the tip deflection, thus providing a larger open-circuit voltage.

         The step-down converter consists of a MOSFET switch with a high breakdown voltage rating, a custom wound inductor with inductance of 10.03 mH, a Schotty diode, and a filter capacitor. The voltage across the current-sense resistor is amplified with a precision op-amp (powered by he 3V battery), and then sampled by the A/D converter on the controller card. The controller card then generates the PWM signals at the calculated duty cycle that is fed to a high side MOSFET driver. The driver was powered by an external dc power supply. Due to the low power levels expected from the piezoelectric element [2] – [4],[6], it is assumed that the converter will operate in discontinuous current condition mode at the chosen because switching losses in the experimental setup comprised a significant fraction of the power flow from the element.

4. RESULTS

         Experimental data were taken to illustrate the theories presented in this paper and to demonstrate the performance of the adaptive control algorithm. The first experiment was conducted in order to determine the validity of the piezoelectric model presented in the Fig.1. Various resistive loads were placed across the output of the excited piezoelectric element, as shown in fig. 8., and the output voltage was measured. The frequency of the excitation was adjusted to the resonant mode of the system for each resistor. This was done to ensure a relatively constant mechanical excitation level of the element throughout the experiment as the resistive load has a dampening effect on the amplitude of the mechanical vibrations. The output voltage for the circuit is given by

Ö1+ ( w CpR )2

 

(7)

R

Ip

Vo =

   

         A least squares fitting of the data to (7)resulted in I_p  equal to 2.2 mA_rms and C_p  equal to 0.184mF. Substituting these values into(7), the theoretical output voltage of the circuit can be compared to the measured output voltage over a range of load resistance as shown in Fig. 9.

         The next experiment was performed to validate the piezoelectric element-rectifier circuit optimal power transfer theory. Fig. 10 shows a plot of the output power versus the voltage maintained at the output rectifier for a vibrating piezoelectric element. The piezoelectric device was driven at a constant frequency of 53.8Hz and resistors of various values were inserted across the rectifier capacitor (see Fig. 1) to provide the load. At open-circuit condition, a voltage of 45.0 V was measured across the rectifier V_rect. The plot of power dissipated in the resistor at various voltages shows that the maximum power of 18.0mW is available with a 24.0kW resistor at a voltage of 20.57 V. this represents the maximum power available for a set level of execution and shows that maximum power occurs at a specific output voltage. The optimal rectifier voltage of the piezoelectric element. A possible reason for this discrepancy is unmodeled loss mechanisms in the piezoelectric device and/or rectifier.

         Using the same circuit and conditions, the output current io(t) of the piezoelectric element was measured using a 10W current sense resistor between the rectifier and the capacitor. The waveforms for load resistor of 430 kW to 0.51 kW across the rectifier capacitor. As the resistance is decreased, the communication interval u becomes smaller and the current waveform is closer to a rectified sine wave.

         To demonstrate that a dc-dc converter is capable of attaining the point of maximum power transfer, the step-down converter was operated with manually varied duty cycle. Fig. 10 revels that the battery current has a definite maximum with respect to the duty cycle. With a 45.0 V open-circuit voltage, the maximum current of 4.3 mA was measured at a duty cycle of 3.18%. at this point, the voltage at the rectifier bus capacitor was measured at 20.4 V(2V below one-half the open-circuit voltage). The current remained above 4mA for duty cycles between 2.5 and 4.5% and quickly decreased outside this range. The power stored by the 3 V batteries was 13.0 mW at the optimal duty cycle as compared to the previous experiment, which showed 18.0mW of power available with a resistive load. Power converter losses are therefore estimated to be 5mW. For comparison, direct charging of the battery across the rectifier capacitor yielded.5mA or 4.5 mW of power harvested.

         The adaptive controller was then used to show that the algorithm could find and maintain the maximum power into the battery at circuit startup and adjust itself aas the excitation varied. The initial duty cycle was set at 10%and the controller decreased the duty cycle linearly as the current increases. With an open-circuit voltage of 45.8 V, the controller settled to the maximum current of 4.3 mA. The controller then maintained maximum power transfer, while pertubing the duty cycle slightly.

         The settling time illustrates the duty cycle rate of change, 21-m%/s, and its effects. The value allows meaningful changes to the current to be measured without large oscillations around the maximum power point. This value does limit the controller speed at startup, taking almost 6 min to achieve maximum current, but once the optimum duty cycle is determined, it limits the oscillations that would increase the time away from the optimum duty cycle. Smaller rates of change that were investigated did not allow changes in the current to be reliably measured and larger rates cost inefficient harvesting due to the increased duty cycle oscillations.

           

5.APPLICATION

SHOE-POWERED RF TAG SYSTEM

         To demonstrate the feasibility and utility of scavenged shoe power, we developed a simple application circuit. The design is a self-powered, active radio frequency (RF) tag that transmits a short-range, 12-bit wireless identification (ID) code while the bearer walks. This system has immediate application in a smart environment, in which multiple users transmit their identities to the local surroundings. The IDs, for example, can enable a central server to make dynamic, near-real-time decisions to personalize the environment or route appropriate information to mobile users. Most previous work in this area relied on battery-powered infrared (IR) badges.9 Our RF-based design, however, requires no line of sight to the reader and therefore can be mounted in a shoe, operating without a battery under the power of a piezoelectric insert. Figure 11 shows a functional prototype pair of self-powered RFID sneakers.

Figure 11. Piezoelectric-powered RFID shoes with mounted electronics.

Figure 12 shows the RF tag system schematic. This design uses scavenged energy from either the PVDF or PZT source to encode and transmit a periodic, On/Off-keyed RFID signal using devices developed for automotive keyless entry systems. A local base station receives the transmission and emits an audible chirp upon identifying the transmitter. The signal from the piezoelectric source is full-wave rectified through 500-mA diode bridge D1. As the source signal ramps up, charge transfers to electrolytic bucket capacitor C1 whenever the source voltage overcomes the voltage already supported by this capacitor (plus two diode drops). As C1 charges beyond 12.6 V (the Z1 breakdown voltage plus the diode drop across the base-emitter junction of Q1), Q1 is forced into conduction, in turn activating Q2 and latching Q1. With Q1 on, the high side of C1 now has a current return path to ground and discharges through the Maxim MAX666 low-dropout (LDO) linear regulator U1. 

Figure 12

         The regulator is biased to provide a stable +5 V to the serial ID encoder U2 and RF transmitter U3, as long as C1 has sufficient charge to produce a valid regulator output voltage (Vout). Note that Vout exhibits some ripple when supplying the transmitter during the ID code’s On periods. When Vout swings below approximately 4.5 V (as set by R5 and R6), the low-battery in pin (LBin on U1) is pulled below its threshold, driving the low-battery out pin (LBout) to ground momentarily. This negative pulse through C3 turns Q1 Off, thus deactivating Q2 and renewing the C1 charging cycle. Note that R1, R2, and R3 bias Q1 and Q2 to show C1 a very high load impedance when the Q1-Q2 latch is deactivated. Finally, we included R4 and C2 to better match the load stage to the charging circuit and source impedance; the remaining resistors support the load stage components in other ways.

         Figure 13 is a representative graph of signals from the power-conditioning circuitry with the PZT source during a walk. The upper trace shows the voltage across C1 (in this case, 47 F), and the lower trace shows the MAX666 linear regulator’s output. Charge accumulates on the bucket capacitor, increasing with each step until the capacitor stores enough energy to power the transmitter for roughly half a second, generally after three to five steps with the current system. Substituting a high-frequency switching regulator for the MAX666 would further improve the efficiency of this circuit; this line of inquiry led to the results summarized in the following section.

Figure 13. Stored voltage (top) and regulated power output (bottom) waveforms for shoe-powered RFID transmitter while walking.