Ultra-Low Power Control System for Maximal Energy Harvesting From Short Duration Vibrations

252 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 18, NO. 2, MARCH 2010

Ultra-Low Power Control System for MaximalEnergy Harvesting From Short Duration Vibrations

Krishna Vijayaraghavan and Rajesh Rajamani

Abstract—With the advent of ultra-low power sensor packages,there is renewed interest in harvesting vibration energy to powerthem, thus creating a self sustaining battery-less sensor system. Theoptimal algorithms previously developed in literature to harvestvibration energy are complex and hence require controllers thatconsume a significant amount of power. The relatively high powerrequirement combined with the inherent complex design of thesealgorithms would also limit them to only applications in whichsustained vibration energy is available for harvesting. To addressthese issues, this paper presents new control systems to optimize theamount of energy harvested from short duration vibrations. Onlyalgorithms that can be implemented using simple ultra-low poweranalog electronic components are considered. The first algorithmtermed “fixed threshold switching”, has been adapted from liter-ature on harvesting energy from sustained vibration. The secondand third algorithms are new optimal control algorithms termed“maximum voltage switching” and “switched inductor”, respec-tively. The three algorithms are theoretically evaluated and com-pared for a short duration vibration application. The final sectionof this paper presents experimental results from the implementa-tion of all the three algorithms on a new battery-less wireless trafficsensor.

Index Terms—Battery-less, energy harvesting, optimal vibrationenergy harvesting, short duration vibrations, standalone sensors,traffic sensor, ultra-low power control systems, wireless.

NOMENCLATURE

Electro-mechanical coupling value.

Thickness of piezo (0.191 mm).

Strain in the Piezo, from (3).

Constant associated with the mechanicalsystem equaling .

Constant associated with the mechanicalsystem model arising due to electro-mechanicalcoupling, ,

.

Open-circuit natural frequency of themechanical system (38 Hz).

Damping ratio associated with the vibratingmechanical system (0.7).

Manuscript received May 17, 2008. Manuscript received in final form March11, 2009. First published July 21, 2009; current version published February 24,2010. Recommended by Associate Editor P. Meckl. This work was supportedin part by a research grant from the ITS Institute, University of Minnesota.

The authors are with the Department of Mechanical Engineering, Universityof Minnesota, Minneapolis, MN 55455 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCST.2009.2018135

Width of the support beam (25 mm) also thewidth of the piezo.

Strain produced per unit applied electric fieldm V .

Open circuit electric field produced for an unitapplied stress Vm N .

1 Piezo constant defined as the open circuitvoltage developed per unit applied strain

V .

Thickness of the support beam (6.25 mm).

Load current through .

Current through the Piezo.

Length scale associated with the mechanicalsystem.

Mass associated with the mechanical system.

Displacement of the mechanical system.

Magnitude of displacement of the mechanicalsystem at the point where the force is applied.

Capacitance of the Piezo.

Storage capacitor.

Modulus of elasticity of the piezo atconstant voltage (constant electric field)

.

Elastic modulus of the main beam (200 GPa).

Elastic modulus of the support beam (200GPa).

Area moment of inertia main beammm .

Area moment of inertia support beammm .

Value of inductance used in “SwitchedInductor” algorithm (Section III-B3) (10 mH).

Effective length of the main beam (1.7125 m).

Effective length of the support beam (0.2 m).

Total resistance in the circuit due to switchesand other components (not including ) (327ohms).

Load resistance (1000 ohms).

1063-6536/$26.00 © 2009 IEEE

VIJAYARAGHAVAN AND RAJAMANI: ULTRA-LOW POWER CONTROL SYSTEM FOR MAXIMAL ENERGY HARVESTING 253

Diode resistance.

Load switch.

Piezo switch.

Voltage across the storage capacitor .

Maximum voltage across the storage capacitor.

Voltage across the piezo capacitor .

Forward voltage drop across each diode (1.1V for the diode used).

On (high) threshold.

Off (low) threshold.

Voltage measured across the piezo.

Voltage open circuit voltage generated due tothe strain.

Maximum value of corresponding to themaximum value of the strain.

Extremum value of corresponding tothe th extremum of displacement “ ”.

I. INTRODUCTION

S TANDALONE wireless sensor packages have been re-placing wired sensors in many applications that require the

sensors to be either implanted in-vivo (as in the case of bio-sen-sors) or embedded in host structures (such as bridges and roadstructures). These wireless sensor packages have traditionallybeen powered from electro-chemical batteries. Advances inelectronics have achieved ultra-low power integrated circuitsand micro-controllers as well as ultra-low power transmitters.Researchers have taken advantage of these advancementsto successfully build new sensor packages [30], [31], [44].Owing to the extremely low power requirement of these sensorpackages, there has been renewed interest in vibration energyharvesting (VEH) technologies that would eliminate batteriesin wireless sensor, thus creating a self sustaining battery-lesssensor system. In addition to extending the useful life of thesensors, VEH would eliminate chemicals from in-vivo environ-ments like the human body.

There are several sources of sustained vibration that havebeen identified as potential power sources for battery-less wire-less sensors. Such sustained vibrations sources are found in me-chanical structures [22], [33], [35], as well as in the animal andhuman body [1], [37]. In addition to the sources of sustained vi-bration that have been examined in literature, there is a wholeclass of short duration vibration sources that is yet to be com-pletely explored. In fact, there is tremendous potential for har-vesting energy from such short duration vibrations. For instance,a traffic sensor embedded in the road experiences short durationvibration with the arrival of each automobile. VEH can be usedto power an embedded traffic sensor that would transmit the ar-rival of every automobile by harvesting energy from these vi-brations. Similarly, the short duration vibration in a sensor em-

1The constant “�” is not available for the piezo material, hence an equivalentconstant is used.

Fig. 1. Energy harvesting circuit.

bedded in an airport runway could be used to harvest sufficientenergy to power sensors that would measure friction coefficienton the runway. Yet another application would involve embed-ding sensors in artificial knee implants to harvest energy fromthe vibration that would result during walking. This energy canthen be used to power a sensor that monitors the health of theimplant.

The paper by Sodano et al. [36] provides a good review ofVEH techniques. Some of the earlier work has also focusedon developing control algorithms to optimize the amount ofenergy harvested [21], [28]. Ottoman et al. [28], [29] haveproposed an “Optimal Pulse Width Modulator Switching”algorithm and Lefeuvre et al. [22] have proposed an algorithmtermed “Synchronized Charge Extraction.” Section II brieflyreviews these algorithms and finds them to be inadequate topower a fully battery less sensor. Section III proposes two newalgorithms that can be used to optimally harvest energy fromshort duration vibrations. The performances of the algorithmsare compared to the performance of an existing algorithm fromliterature. Section IV presents a novel battery-less wirelesstraffic sensor that utilizes the algorithms developed for energyharvesting. In Section V, the developed algorithms are evalu-ated experimentally using the new battery-less wireless trafficsensor.

II. ENERGY HARVESTING ALGORITHMS

In order to replace the battery, the vibration energy needs tobe transduced to electrical energy using an electric circuit. Onesuch electric circuit is shown in Fig. 1. The energy harvestingsystem consists of a piezo-electric substrate (“Piezo Crystal”)that is used to generate an alternating electrical voltage from thevibrations. By rectifying (using the diode bridge) and storingthis voltage in a storage capacitor , energy is harvestedto drive load circuits. Since the power available from vibra-tions is rather low, all researchers have utilized switching al-gorithms to intermittently drive the load by controlling a loadswitch . In Fig. 1, all the components that are poweredby VEH, including the “actual load” and additional circuitrysuch as step-down dc-dc convertors that might be needed, arerepresented by an equivalent resistance . Sections II-A–II-Dreview three different control algorithms that have been previ-ously proposed in literature to harvest vibration energy.

A. Fixed Threshold Switching

In this algorithm, the voltage due to the vibration is rectifiedand stored in the capacitor . The switch is closed when


exceeds a fixed high threshold. is opened whensubsequently falls below a low threshold. Hence this algorithmshall be termed “fixed threshold switching” (FTS). Kymissis etal. [19] have implemented FTS using circuitry that is completelypowered from the energy that is harvested. Elvin et al. [9], haveproposed using a similar scheme to power sensors that could beembedded in structures.

Ottoman et al. [28] have shown that for an ideal circuit (withideal diodes and no resistive losses in the circuit), maximumpower is extracted from the piezo when is maintained athalf the peak open circuit voltage of the piezo (i.e.,

) during switching. Hence although FTS hasbeen implemented using self-powered circuitry, it is suboptimalin terms of the energy that is harvested. The thresholds wouldhave to change in real-time based on the magnitude of vibrationin order to maximize the energy harvested.

B. Optimal Pulse Width Modulator Switching

Ottoman et al. [28], [29] have proposed an optimal algorithmto charge a 3-V battery from sustained mechanical vibrations. Inthis algorithm, a pulse width modulator (PWM) circuit is usedto switch . In [28], Ottoman et al. have proposed an adap-tation law to determine the duty cycle of the PWM required foroptimal power extraction. In [29], the researchers have proposedan improvement to the circuit used in [28]. The new circuit con-tains additional circuitry to integrate the dc-dc converter as wellas the controller. The overall power consumed by the controlcircuitry has also been reduced.

From the analysis in the two papers, it is clear that the “Op-timal Pulse Width Modulator Switching” algorithm can improvethe amount of energy harvested. However, the authors them-selves have pointed out that a large amount of power is neededby the control circuitry. Although this algorithm could be madefeasible and self-sustaining by using a large array of piezo har-vesters, the overall efficiency is expected to be fairly low whenthe number of piezo harvesters is small. Owing to the adaptivenature of the algorithm, the optimization of the duty cycle canonly be achieved for a sustained and periodic vibration. Fur-ther, the proposed algorithms cannot be implemented withoutthe use of a storage battery. Hence this algorithm cannot be di-rectly used to power a battery-less wireless sensor. Due to thepower requirements and adaptive nature of this algorithm, thisalgorithm cannot be used to optimally extract energy from shortduration vibrations.

C. Synchronous Charge Extraction

Lefeuvre et al. [22] have proposed an algorithm termed“synchronized charge extraction”. In this algorithm, energyis extracted from the piezo only when the displacement ofthe mechanical system reaches an extremum. In other words,the charge extraction is synchronized to the extremum of themechanical displacement. In their implementation of the circuitshown inFig. 1, the researchers have eliminated the storagecapacitor. The output of the rectifier is directly connectedthrough the switch to the dc-dc converter. Under idealconditions (with ideal diodes and no dissipative losses in thecircuit), the “Synchronized Charge Extraction” algorithm hasbeen shown to theoretically harvest 400% more power than

the “Pulse Width Modulator Switching” algorithm. From theanalysis it is clear that this increase in power is a function of thedamping effect of the piezo on the mechanical vibrations. Thisdamping arises as a result of the electromechanical coupling. Itwill be evident from the discussion in Section IV-D2 that theelectromechanical coupling is direct function of the size of thepiezo in relation to the size of the mechanical system. Hence,the effectiveness of this algorithm would rely on the use ofpiezos with large thickness.

Although the “Synchronized Charge Extraction” algorithmwould significantly increase the amount of power harvested, thealgorithm has several limitations. In order to determine the oc-currence of the maximum, the displacement of the vibratingstructure is continuously monitored using an inductive pickupor an equivalent sensor. This additional displacement sensorthat is needed could consume a significant amount of power.Due to lack of information on the power requirements of thecontroller, it can be assumed that the algorithm will be imple-mented on an external controller, which would also consumeadditional power. For persistent excitation, it might be possibleto harvest sufficient energy from an array of piezos to powerthe control circuitry. However, the power consumption of thecontroller would somewhat limit the overall efficiency of thisalgorithm. When the vibrations are not sustained, it may not beviable to continuously power the inductive pickup sensor. Thus,in the case of short duration vibrations, even an array of piezoelements may not suffice. Hence, this algorithm would not beviable to harvest energy from short duration vibrations.

D. Motivation for New Algorithms

It is evident from the above brief literature review that past al-gorithms have almost exclusively focused on harvesting energyfrom sustained vibrations. VEH from short duration vibrationshas been largely ignored. Furthermore, these algorithms are ei-ther suboptimal or have high power requirements. Hence thesecontrollers would be inefficient for most VEH applications. Dueto their relatively large power requirements, the optimal algo-rithms cannot be implemented to harvest energy from short termvibrations. Hence this paper develops ultra-low power controlsystems to optimize the amount of energy harvested from shortduration vibrations. Only algorithms that can be implementedusing low power analog electronics are considered. The algo-rithms that are developed can also be easily adapted to optimallyharvest energy from sustained vibrations.

III. PROPOSED CONTROLLERS

A. System Model

The dynamics of the VEH system will be modeled as con-sisting of a mechanical sub-system and an electrical sub-system.When the piezo is open (the terminals are unconnected), the me-chanical sub-system will be modeled as a second order systemwith

(1)

However, when the electrical system is active and the piezosources current, the voltage across the capacitor , in-creases. Subsequently, the voltage across the piezo, , de-


creases by . This change in piezo voltage will induce aforce, , on the mechanical system. Hence, (1)is modified to become

(2)

The strain can be represented as

(3)

From (2) and (3), the mechanical sub-system dynamics canbe rewritten in terms of strain as

(4)

where is amount of static strain produced for a unit appliedforce and is amount of static strain produced for a unitchange in .

The most important component of the electrical sub-systemis the piezo electric substrate that transduces this strain to anelectrical voltage. At low frequencies, the piezo is modeled asa voltage source in series with a capacitance using (5)–(7) [7],[26]. A more sophisticated model can be found in Weinbert etal. [43]

(5)

(6)

(7)

In order to calculate the overall electrical dynamics, eachdiode making up the bridge is modeled by a piecewise linearmodel [34]. The piezo current can then be written as (8) andthe dynamics of the capacitor voltage can be given by (9). Seeequation (8)–(9) at the bottom of the page.

For the purpose of simulation, we consider the mechanicalsystem with parameters 38 Hz, and

.(These parameters were chosen to match the experimental

setup. See Section IV-D for details on how the parameters wereidentified from experimental data.)

The input load on the system is modeled as two short durationpulses as shown in Fig. 2 with a magnitude of 3937.5 N.

Fig. 2. Force Input used for simulation.

Algorithms

Of the total energy generated in the Piezo, only the fractiontransferred to the storage capacitor is available to drive theload. is a measure of this energy. The peak power at theload, given by , is also a function of . Hence,in Sections III-B1–III-B8, the available voltage, , is deter-mined for each of three different control algorithms.

1) Fixed Threshold Switching: This algorithm is an adapta-tion of FTS used for harvesting energy from sustained oscilla-tions. In this algorithm, the load is connected to , by settingthe control input to logic high (1) when the crosses a pre-determined high (on) threshold . The control is turned off(0), if falls below a low (off) threshold . The controlsignal to , can be given by the control law state transitiondiagram shown in Fig. 3.

Theorem 1 describes the maximum voltage generated andstored across the storage capacitor when this controller is used.This will be compared later with the maximum voltage gener-ated by the other two new controllers.

Theorem 1: If the displacement of the beam has a first localextremum value (with a corresponding ),and the switch is closed when , then seeequation (10) at the bottom of the page.

For a sufficiently large

(11)

(The proof of this Theorem is provided in the Appendix.)

ifotherwise

(8)

if is closed

if is open (9)

if

otherwise.(10)


Fig. 3. State transition diagram for “fixed threshold switching”.

Fig. 4. � for “fixed Threshold Switching” algorithm.

Fig. 5. Load current for 1 K load with “Fixed Threshold Switching” algorithm.

The fixed threshold switching is the simplest algorithm, andwould serve as a baseline for evaluating the performance of theother control algorithms. Simulation results obtained using thisbaseline control law are shown in Figs. 4–6. The voltage in thestorage capacitor for 2.75 V and 1.5 V is seen inFig. 4. Fig. 5 shows the current through the 1 K (1 Kohm) loadresistance and Fig. 6 shows the instantaneous power consumed

Fig. 6. Instantaneous Power consumed by 1 K Load with “Fixed ThresholdSwitching” algorithm.

Fig. 7. State transition diagram for “max voltage switching”.

by the resistor. The peak power is 7.56 mW and the total energytransferred to the load is 30 J.

2) Max Voltage Switching: In this algorithm, the load is con-nected to the capacitor , when the voltage reaches a max-imum value. The control is turned off, if falls belowthe off-threshold . The control law can be given by the statetransition diagram shown in Fig. 7.

The occurrence of maximum can be determined using analogelectronics. For instance, the max-detector can be realized usinga high pass resistance–capacitance (RC) filter given by (12). Amaximum is declared when the output of this filter falls belowa threshold. The value of this threshold is small and determineshow close to zero the derivative must become for the voltage tobe recognized as maximum

(12)

Theorem 2 describes the maximum voltage generated andstored across the storage capacitor when the max voltage con-troller is used.

Theorem 2: If the displacement of the beam has the first localextremum value (with a corresponding ),then is given by (13a) and (13b) at the bottom of the page.

if

otherwise(13a)

if

otherwise(13b)


Fig. 8. � for “Max Voltage Switching” algorithm.

Fig. 9. � for modified “Max Voltage Switching” algorithm.

Thus, for a sufficiently large strain voltage, the difference be-tween and is distributed between andin the inverse ratio of their capacitance.

(The proof of this Theorem is provided in Appendix.)It is seen from theorem 2 that when

(14)

For the current setup, is obtained to be 1 V for the firstpulse. This agrees with the simulation results shown in Fig. 8. Itshould be noted that the first pulse charges the storage capacitorto 1 V, but there is no discharge to the load because the voltageis too low 1.5 V .

Since we have a priori knowledge about the nature of theloading, it is possible to modify the to turn ON only atthe end of the second pulse. One way of achieving this wouldinvolve checking for a maximum larger than a low threshold.For the particular load acting on the sensor (consisting of twopulses and hence four extremums in the vibration signal),is approximately four times the value of obtained for thefirst pulse. From Fig. 9, is 3.9 V. Fig. 10 shows the current

Fig. 10. Load current for 1 K load with modified “Max Voltage Switching”algorithm.

Fig. 11. Instantaneous power consumed by 1 K Load with modified “MaxVoltage Switching” algorithm.

through the 1 K (1 Kohm) load resistance and Fig. 11 shows theinstantaneous power consumed by the resistor.

Since the storage capacitor is allowed to charge to a highervoltage, this algorithm will deliver a larger peak power incomparison to the “Fixed Threshold switching”. Hence, thisalgorithm is always more efficient at harvesting vibration en-ergy than the simple fixed threshold algorithm described in theprevious section. Indeed, the value of peak power (15.4 mW)and the amount total energy transferred to the load (70 J) islarger than those that were obtained for the “Fixed ThresholdSwitching” algorithm.

3) Switched Inductor: This section proposes a third algo-rithm that would further enhance . This algorithm uses acircuit shown in Fig. 14. The new circuit uses an inductorand a piezo switch in addition to the components shownin Fig. 1. The voltage drop across is given by . isturned on when reaches a maximum and is turnedon when reaches a maximum. The switches andare turned off when the respective voltages and

drop below an off-threshold . As discussed in the pre-vious section, the occurrence of maximum can be determinedusing analog electronics. The control law for is given bythe state transition diagram shown in Fig. 12 and the control


Fig. 12. State transition diagram for �� (“Switched Inductor”).

Fig. 13. State transition diagram for �� (“Switched Inductor”).

Fig. 14. Energy harvesting with Inductor.

law for is given by the state transition diagram shown inFig. 13.

Theorem 3 describes the maximum voltage generated andstored across the storage capacitor when the Switched Inductoralgorithm is used.

Theorem 3: If switch is closed at first local extremumof the displacement of the beam, the voltages across capacitors

and at the end of first half-LC oscillation ( and, respectively) are given by see equation (15a) and (15b)

at the bottom of the page. (The proof of this Theorem is providedin the Appendix.)

Note: The load switch is closed when the reaches amaximum. This will prevent from increasing much further.However by using a low pass filter it is possible to filter out thepeaks occurring in due to LC oscillation. This will enableus to collect energy from multiple LC oscillation.

It is seen from theorem 3, that when

(16)

where

(17a)

(17b)

(17c)

By comparing (16) with (14), we notice that has in-creased by a factor of at least , which equals the peakovershoot of the LCR circuit. The “Switched Inductor” algo-rithm yields a higher due to the presence of the inductor.In the absence of the diode bridge rectifier, the second order dy-namics of the LCR circuit will exhibit an oscillatory behaviorfor a small time period and the dynamics would eventually con-verge to its steady-state value. The bridge rectifier in the circuitwould however clamp to the overshoot peak voltage, re-sulting in higher available voltage.

Using (this is the estimated total resistance inthe circuit) in (15), we get and .Now . Hence, the piezo woulddrive the circuit in the reverse direction. and

. Hence, . The esti-mated value for is seen to be in close agreement with thesimulation result from Fig. 15.

As mentioned in the earlier section, owing to the a prioriknowledge about the nature of the loading, it is possible tomodify the to turn ON only at the end of the second loadpulse. For the particular load acting on the sensor (consistingof four extremums in vibration), is approximately fourtimes the for first extremum (6.04 V). When comparedto the modified “max voltage switch” controller, it is seen fromFigs. 9 and 16 that the available voltage has increased by afactor of over 1.5. Subsequently from Fig. 18, the peak poweris obtained to be 36.3 mW (an increase of 136%) and the totalenergy transferred to the load equals 188 J (an increase of169%).

An intuitive explanation of the performance of the switchedinductor system can be provided as follows. When the piezois charged to , and is completely discharged through a loadresistance, the total amount of energy passing through the loadcan be calculated to be . When a storage capacitoris connected to the piezo, the capacitor is charged to a voltage

. If the storage

if

otherwise(15a)

if

otherwise(15b)


Fig. 15. � for “Switched Inductor” algorithm.

Fig. 16. � for modified “Switched Inductor” algorithm.

Fig. 17. Load current for 1 K load with modified “Switched Inductor”algorithm.

capacitor is discharged through a load, the amount of energyis .Hence, the transfer from the piezo to the storage capacitor re-sults in the loss of energy (through the resistance in the circuit).

Fig. 18. Instantaneous Power consumed by 1 K Load with modified “SwitchedInductor”.

By adding an inductor in the circuit, some of this lost energy isrecovered. This happens because the inductor causes a transientincrease in current by creating a second-order under-dampedsystem instead of a first order system. The voltage transfer tothe storage capacitor is made at the transient peak of the voltageby closing the switch at this peak. Thus, the inductor does notreplicate impedance matching that has been traditionally usedto optimize energy transfer.

4) Comparison of the Three Algorithms: It must be notedthat for the “Fixed Threshold Switching” algorithm to work re-liably, cannot be arbitrarily large. must necessarilybe chosen a volt or two lower than the lowest that canbe expected corresponding to the set of all possible .Hence, for “Fixed Threshold Switching” algorithm isnecessarily smaller than for the modified Max VoltageSwitching. From (17a) it is clear that . Thus,for “Fixed Threshold Switching” for modified “MaxVoltage Switching” for modified “Switched Inductor”.

5) Fraction of Energy Harvested: For the system that hasbeen modeled, the deflection of the point of application of forcecan be written as

(18)

The total energy supplied to the mechanical system can beestimated using

Input Energy (19)

Using this calculation for the load shown in Fig. 2, the inputenergy is found to be

Input Energy 17.037 J (20)

The fraction of available energy harvested is shown in Table I.The fraction of energy harvested can be increased by using a

larger amount of active piezo material. It must however be notedthat the primary objective of this paper is to harvest sufficientenergy for powering the sensor electronics by using the minimalamount of piezo material. Hence the use of a larger amount ofpiezo material has not been explored.


TABLE ICOMPARISON OF THE THREE ALGORITHMS

IV. TRAFFIC SENSOR

A. Introduction

Currently, traffic agencies all around the country use induc-tive loop detectors (ILDs) to monitor traffic. The Minnesota De-partment of Transportation (MnDOT) for example, monitors theflow rates at over 6000 points in the Minneapolis/St. Paul metroarea using such ILDs. An ILD consists of a big loop of metalliccoil (usually a square of side 6 ft/1.8 m or larger) buried in thelane. This loop is connected to a station which powers the loopand processes the information obtained from the loop to deter-mine if a vehicle passes over the sensor.

It is possible to develop a battery-less wireless traffic sensorthat can be embedded in the roadway. When a vehicle wouldpass over that sensor, short duration oscillations would be in-duced in the sensor. The proposed sensor would detect these vi-brations and wirelessly transmit a pulse announcing the arrivalof the vehicle to a station. Such a sensor could be powered bythose same mechanical vibrations. By eliminating data cablesand power cables, the new smaller traffic sensor would greatlyimprove the ease of installation and decrease maintenance re-quirements as well as decrease the installation time and the as-sociated traffic congestion.

B. Overview of New Sensor

The researchers in this paper have developed a novel bat-tery-less wireless traffic sensor to measure the traffic flow at apoint on the highway. The sensor is completely autonomous andcan be embedded in the highway lane without the need for con-trol/data cables. In the absence of any automobile, the sensor iscompletely turned off, consuming no power. Thus, the sensorhas ZERO idle power loss and is extremely energy efficient.When an automobile passes over the sensor, the sensor is turnedon by the vibrations and a RF pulse is transmitted wirelessly tothe station. The sensor requires no external power source as it ispowered by harvesting all its energy from vibrations that resultwhen a vehicle passes over it. Further this sensor has smallerdimensions and can be installed with much lower traffic disrup-tions. This is especially true because the sensor does not need apower source and power lines do not need to be run to the sensor.This new sensor, like the ILD, does not use complex image pro-cessing or audio processing techniques and would hence pro-vide the same level of high reliability. Owing to the battery-lessand wireless nature of the sensor, low maintenance can also be

Fig. 19. Sensor.

expected. Further it is likely that the sensor can measure thenumber of axles and weight of passing vehicle in addition tothe flow rate. It is also possible to configure several sensorsto transmit to a single station by using different transmissionfrequencies. In order to power the sensor, the three algorithmsproposed in Section III-B have been implemented using analogelectronic components. All the switches used in the algorithmscan be realized using MOSFET devices.

C. Hardware

The proposed sensor consists of a beam structure with a mainbeam (6 or 1.8 m long) and two support beams ( long or 250mm) at the ends as shown in Fig. 19. A total of eight Piezo ele-ments (four piezos for each of the support beams) are bonded atthe locations shown in Fig. 19 and connected electrically in par-allel. Ansys simulations revealed that the average of the strainover the area of all the piezos depended only on the total loadacting on the main beam. This piezo configuration would en-sure that the effective voltage generated by the piezo would notdepend on the location of the load along the beam. It shouldbe noted further that the speed of the passing vehicle can bemeasured by measuring the time difference in the loading be-tween two consecutive sensors placed a short longitudinal dis-tance apart.

D. System Parameters

1) Mechanical Parameters: By considering only the first vi-bration mode, the sensor dynamics can be represented using (4).When a static force acts on the system (4), the re-sulting static strain is given by

(21)

The same load , acting at the center of the main beam,results in an average load of being transmitted to eachsupport beam. It can be inferred from Ketchum et al. [14] thatthe resulting moment at the location of the piezo is givenby

(22)

For the support beam, 0.2 m, 0.01875 m,0.025 m, 0.00625 m and 200 GPa. Hence,

mm and

(23)

Thus

(24)


Fig. 20. Bode magnitude plot of impulse response of the sensor.

The natural frequency was obtained by observing the im-pulse response of the sensor. This impulse response was gener-ated by striking the sensor with a hammer. Fig. 20 shows the re-sulting bode plot. From the figure, rad s–38 Hz.The impulse response could not be directly used to find thedamping ratio, since the tire passing over the sensor would dampout the mechanical vibrations in the sensor. Instead a value of

was found to be appropriate.A finite-element model of the sensor structure was con-

structed (using , , and for the main beam and ,, and for the support beam) structure. From this model,

it was determined that when a unit static load is applied at themid point of the main beam, the mid point deflects by . Hence,the transfer function for the deflection of the mid point of themain beam can be written as

(25)

This relation can be used to determine the total energy sup-plied to the beam structure.

2) Electro-mechanical Coupling Parameters: The VEHsystem consists of piezo electric elements bonded to the sup-port beams as shown in Fig. 19. The piezos are bonded to thetop and bottom surfaces of the support beam. When a vehiclepasses over the sensor, the piezo experiences a strain from theloading and thus generates a voltage. When the piezo sourcescurrent to the circuit, increases and decreases.Since the piezo is bonded to the mechanical system, this de-crease in piezo voltage translates to a static stress

(26)

The force developed by the piezo as a result of this stress isgiven by

(27)

The pair of piezo that were considered, bonded to the top andbottom of the support beam, are separated by the height of thesupport beam . The moment developed by them is

(28)

This moment acting on the mechanical system would resultin a static strain

(29)

Noting that we get

(30)

From (4) we can deduce that for a static

(31)

Hence

(32)

Thus, the coupling coefficient

(33)

3) Electrical Parameters: The piezos are A4E sheets 0.191mm thick and of side 37.5 mm 25 mm. (They were made bycutting T107-A4E-602 sheets that were purchased from PiezoSystems, Inc). The piezo will be subject to strain in the “1” di-rection of the piezo. Hence, the “31” parameters of the piezo areused in the calculation. For A4E piezo, the modulus of elasticityat constant electric field is N m and thickness

m. Hence, open circuit voltage per unit strain is

V (34)

From the measurement of the capacitance of the sensorsystem, the equivalent capacitance is found to be

F.

V. EXPERIMENTAL RESULTS WITH TRAFFIC SENSOR

The three algorithms presented in Section III-B were im-plemented on a self-contained electronic circuit. The switches

and were implemented using MOSFETs. The ex-tremely small amount of power required by the control systemwas derived entirely from the charge energy stored in the capac-itor. Sets of experiments were carried out with each of the threecircuits connected to the piezo. Each experiment consisted ofdriving a compact car over the sensor at 20 Km/h as shown inFig. 21. This resulted in separate loading from the two axles,first by the front tires and then by the rear tires.


Fig. 21. “Schematic of test setup” (figure not drawn to scale).

Fig. 22. “Fixed Threshold” algorithms with a threshold of 2.75 V.

Fig. 23. Modified “Max Switching” algorithm.

Fig. 22 show the results from the testing of the “FixedThreshold” algorithm. The on-threshold for the algorithm waschosen at 2.75 V so that the sensor would detect light vehiclesuch as motorcycles. The MOSFET used in the switching circuitconstrains the off-threshold voltage to 1.75 V. As a result,turns on when the capacitor voltage reaches 2.75 V andturns off when falls below 1.75 V.

Fig. 24. Modified “ Switched Inductor” algorithm.

TABLE IIFRACTION OF AVAILABLE VIBRATION ENERGY UTILIZED

TABLE IIITHEORETICAL AND EXPERIMENTAL MAXIMUM VOLTAGE

The electronic circuits were then modified so that turnson when reaches a maximum. In order to detect a globalmaximum, and to collect energy from both axles, wasmodified to turn on when does not increase for a period of100 ms. The off-threshold was once again chosen to be 1.75 V.Fig. 23 show the results from modified “Max Switching” al-gorithm. It is seen that the two axles would generate a com-bined voltage of 3.95 V. This agrees well with the simulationsin Section III-B2.

Fig. 24 show the results from the modified “Switched In-ductor” algorithm experiments and the capacitor voltage isfound to be 6 V. This agrees well with the simulations inSection III-B3.

The theoretical and experimental capacitor voltages are sum-marized in Tables II and III.


It is apparent that if is controlled as prescribed, the“switched inductor” offers significant improvement over boththe fixed threshold and the maximum voltage algorithms.

VI. CONCLUSION

Past research on VEH has almost exclusively focused onharvesting energy from sustained vibrations. When it comesto short-duration vibrations, the optimal control algorithmsproposed in literature cannot be implemented due to the rela-tively large power requirements of associated microprocessorsor computers used to implement the controller. Hence, thispaper develops ultra-low power control systems to optimizethe amount of energy harvested from short duration vibrations.It has been shown via both simulations and experiments thatthe modified “Max Voltage Switching”, the first algorithm thathas been proposed in the paper, would outperform the baseline FTS algorithm previously developed in literature. It hasfurther been shown that the modified “Switched Inductor”, thesecond algorithm that has been proposed in the paper, wouldoutperform both the modified “Max Voltage Switching” andthe FTS algorithms.

The developed control algorithms have also been used in thepaper to implement a new battery-less wireless traffic sensor.The developed sensor can be embedded in a highway lane andcan measure traffic flow at that point. Due to battery-less wire-less operation and its small size, the new sensor has significantadvantages over existing inductive loop traffic sensors in termsof easy installation, low cost, low maintenance and zero powerconsumption.

APPENDIX

PROOFS OF THEOREM 1, 2 AND 3:Proof of Theorem 1: The proof will proceed by deter-

mining for the following cases:(i) when is open;

(ii) when is closed;(iii) when transitions from open to closed when

.Case (i): When is open, it is clear that

(refer Fig. 1). Thus, if, the bridge circuit

rectifies the piezo current and charges the storagecapacitor. When , thediodes block the flow of current thus preventing storagecapacitor from discharging. If does not change signsand , the effective voltage

driving the current thought the resistive element in thecircuit is given by

(35)

In modeling overall dynamics, the first-order nonlinearelectrical dynamic (5)–(9) are dominated by the muchslower dynamics of the mechanical system. The systemexhibits a two time scale property and the faster electricaldynamics needs to be modeled by its quasi-steady statevalue [15], [18] which corresponds to or

(36)

and are two capacitor connected in series. Ifdoes not change signs

(37)

Thus, see (38) at the bottom of the page.Case (ii): When is closed, once again the faster elec-trical dynamics is modeled by its quasi-steady state valuecorresponding to and . Hence, in additionto we have . Since the diodesonly conduct up to , when

is closed we have

(39)

Case (iii): When is initially open and is closed at time, for an extremely small duration of time (cor-

responding to the time scale of the electrical system), theelectrical dynamics is dominant. Since is much smallerthan the time scale of the mechanical system, the mechan-ical system can be considered to be frozen [15], [18]. Sincethe electrical dynamics is a first order system, there is noover shoot in any voltage value. Thus .At the end of , the system approaches the quasi-steadystate value and the equation is case (ii) can be used.In summary, if , the diodes do not conductand . If , is closed onlywhen . Hence, if

(40)

If is sufficiently large, .

if

otherwise

if

otherwise(38)


APPENDIX:

Lemma 1: (stated without proof)If and , (10) is mod-

ified to (41) and (42) shown at the bottom of the page.(The proof would be a direct extension of the theorem above)

see the equation at bottom of page.Proof of Theorem 2: Equation (38) derived in Case (i) of

theorem 1, holds as long as does not change signs. Since hasonly one unique local extremum, cannot change signs and (38)is valid. If , then . If ,it is evident that when . Hence,(13) follows.

Lemma 2: (stated without proof)If and , (13) is modified

to (43a) and (43b), shown at the bottom of the page.(The proof would be a direct extension of the theorem above.)

Proof of Theorem 3: When is closed in the LCRcircuit shown in Section III-B3 Fig. 14, the effective voltagedriving the resistive and inductive components of the circuit isgiven by

(44)

In the absence of , the overall dynamics is dominated bythe mechanical system and would be given by (13). Therewould be no gain in . If is closed at some

, it would be result in a step input to the electrical circuit.

If , the diode bridge will begin to conductwhen is closed

(45)

When is unidirectional, the electrical dynamics can bewritten in terms of and . Hence

(46)

(47)

Now . When and are ini-tially not charged

(48)

The piece-wise linear dynamics of the LCR system can bewritten as

(49)

Now and is unidirectional up to the first maximumof at the end of the first half-oscillation. Since (49) is validwhen is unidirectional, it can be used to determine this firstmaximum . For this second-order system

(50)

ifotherwise

(41)

(42)

if

otherwise

ifotherwise

(43a)

ifotherwise

(43b)


if

otherwise(51)

if

otherwise(52)

ifotherwise

(53a)

ifotherwise

(53b)

Hence, (51) and (52) shown at the top of the page.Note: If piezo is charged sufficiently in the reverse direction

such that , the system wouldcontinue to oscillate. When the piezo current flow in the reversedirection, and at the end of the second half oscil-lation ( and ) can be obtained by replacingwith and calculating the changes in

and .Lemma 3: (stated without proof)

If and (15) gets modi-fied to (53a) and (53b) shown at the top of the page.

(The proof would be a direct extension of the theorem above.)

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Krishna Vijayaraghavan received the M.S. degreefrom University of Minnesota, Minneapolis, in 2005and the B.Tech. degree from the Indian Institute ofTechnology, Madras, India, in 2003. He is currentlyworking towards the Ph.D. degree from the Univer-sity of Minnesota.

His research interests include fault-tolerant con-trol, battery-less wireless sensors, signal processingand real-time software.

Mr. Vijayaraghavan was a recipient of manyawards, including the ITS MN Graduate Student

Award (2008) in recognition of outstanding research contributions to IntelligentTransportation Systems (ITS) technology and the Sivasailam Merit Prize forBest Individual B.Tech. Project in Mechanical Engineering in IIT Madras(2003).

Rajesh Rajamani received the M.S. and Ph.D. de-grees from the University of California at Berkeley,in 1991 and 1993, respectively, and the B.Tech. de-gree from the Indian Institute of Technology, Madras,India, in 1989.

He is currently Professor of Mechanical Engi-neering at the University of Minnesota, Minneapolis.His research interests include sensors and controlsystems for automotive and biomedical applications.He has authored over a 100 refereed publicationsand received 4 patents. He is the author of Vehicle

Dynamics and Control (Springer Verlag, 2005).Dr. Rajamani was a recipient of several honors, including the CAREER

Award from the National Science Foundation, the 2001 Outstanding PaperAward from the IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY,and the 2007 O. Hugo Schuck Award from the American Automatic ControlCouncil. He has served as Chair of the IEEE Technical Committee on Auto-motive Control and on the editorial boards of the IEEE TRANSACTIONS ON

CONTROL SYSTEMS TECHNOLOGY and the IEEE/ASME TRANSACTIONS ON

MECHATRONICS.

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Ultra-Low Power Control System for Maximal Energy Harvesting From Short Duration Vibrations

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