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Article A New Method for a Piezoelectric Energy Harvesting System Using a Backtracking Search Algorithm-Based PI Controller

Mahidur R. Sarker *, Azah Mohamed and Ramizi Mohamed

Department of Electrical, Electronic and System Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia (UKM), Bangi 43600, Malaysia; [email protected] (A.M.); [email protected] (R.M.) * Correspondence: [email protected]; Tel.: +60-3-8911-8408

Academic Editors: Hiroshi Toshiyoshi and Chang-Hyeon Ji Received: 14 July 2016; Accepted: 1 September 2016; Published: 23 September 2016

Abstract: This paper presents a new method for a vibration-based piezoelectric energy harvesting system using a backtracking search algorithm (BSA)-based proportional-integral (PI) voltage controller. This technique eliminates the exhaustive conventional trial-and-error procedure for obtaining optimized parameter values of proportional gain (Kp), and integral gain (Ki) for PI voltage controllers. The generated estimate values of Kp and Ki are executed in the PI voltage controller that is developed through the BSA optimization technique. In this study, mean absolute error (MAE) is used as an objective function to minimize output error for a piezoelectric energy harvesting system (PEHS). The model for the PEHS is designed and analyzed using the BSA optimization technique. The BSA-based PI voltage controller of the PEHS produces a significant improvement in minimizing the output error of the converter and a robust, regulated pulse-width modulation (PWM) signal to convert a MOSFET switch, with the best response in terms of rise time and settling time under various load conditions.

Keywords: energy harvesting; optimization; micro devices; low voltage; controller

1. Introduction The energy harvesting from the ambient energy sources, such as solar, wind, thermal, sound, vibration, solid waste, etc., are commonly popular now-a-days because of rising power demand [1–4]. Along with the renewable energy generation methods, micro-level energy harvesting has become the focus of new researchers and developers to power ultra-low power devices at remote or hard-to-reach zones. There are three techniques to harvest energy from vibration, including electrostatic, electromagnetic, and piezoelectric. Among them, harvesting the micro-level energy utilizing piezoelectric vibration transducers (PVT) is now a greater concern to be researched [5–8]. The block diagram of a piezoelectric energy harvesting system (PEHS) is shown in Figure1; it can be summarized into three core components: piezoelectric devices, the power electronic interface, and electrical energy storage. One of the most popular power electronic converters for energy harvesting applications is a single-direction DC-DC converter. The DC-DC converters are called boost, buck, and buck-boost. The principle of such a converter is that the output voltage magnitude increases or decreases compared to the input voltage magnitude from ambient sources [9–13]. Operated under an open loop condition, the DC-DC converter displays poor voltage regulation and insufficient active response, and such converter is used as a closed loop feedback control system for output voltage regulation. Some researchers have proposed to switch the converter on and off (duty cycle) to achieve the optimal output

Micromachines 2016, 7, 171; doi:10.3390/mi7100171 www.mdpi.com/journal/micromachines Micromachines 2016, 7, 171 2 of 16

Micromachines 2016, 7, 171 2 of 16 voltage from the controller. Power flow is regulated through high frequency pulse width modulation frequency pulse width modulation (PWM) for switching control of the MOSFETs in the circuitry of (PWM) for switching control of the MOSFETs in the circuitry of the DC-DC converter [14–16]. the DC-DC converter [14–16]. The advantages of the single-phase DC-DC converters is the need of a The advantagessingle MOSFET of the to single-phase be switched, DC-DCsince its losses converters are small is the and need is suitable of a single for the MOSFET energy harvesting to be switched, since itsapplications. losses are small and is suitable for the energy harvesting applications.

Figure 1. Block diagram of vibration energy harvesting system. Figure 1. Block diagram of vibration energy harvesting system. Usually, the proportional-integral (PI) controller has been largely utilized in controlling various Usually,applications the proportional-integral due to its normal control, (PI) simple controller design has and been low-cost largely maintenance, utilized inrobustness, controlling and various applicationsruggedness due [17]. to its Additionally, normal control, the PI controller simple design is utilized and to low-costregulate voltage, maintenance, current, etc. robustness, Hence, and ruggednessthe advantage [17]. Additionally, is to utilize the a PI controller to is so utilizedlve different to regulate technical voltage, problems, current, such etc.as high Hence, the overshoot, high steady state error, and torque, due to changes in mechanical load [18]. In [19], a advantage is to utilize a PI controller to solve different technical problems, such as high overshoot, conventional PI controller is proposed to control a boost converter. On the other hand, the high steadydisadvantage state error, of a PI and controller torque, is the due requiremen to changest of inmathematical mechanical modeling load [18 and]. Inthe [trial-and-error19], a conventional PI controllertechnique is proposed[20,21]. The todifficult control part a is boost to find converter. the best parameter On the values, other hand,such as the the disadvantageproportional of a PI controllergain (Kp) is theand requirementintegral gain (Ki). of mathematicalGenerally, those modelingparameters andof the the controller trial-and-error need manual technique tuning to [20,21]. The difficultobtain partthe best is tovalues, find and the bestis time parameter consuming. values, There are such some as known the proportional techniques to gain find (Kp)the optimal and integral gain (Ki).PI voltage Generally, controller those values, parameters such as the Ziegle of ther–Nichols controller method, need Cohen-Coon manualtuning method, toand obtain Lambda the best tuning method, etc. However, such techniques have certain disadvantages, such as being values, and is time consuming. There are some known techniques to find the optimal PI voltage trial-and-error methods, require manual tuning, and complex mathematical models [18, 22]. Some controlleroptimization values, suchalgorithms, as the such Ziegler–Nichols as genetic algorith method,m proportional-integral Cohen-Coon method,(GA-PI) optimization and Lambda [23], tuning method,bacterial etc. However,foraging proportional-in such techniquestegral-derivative have certain (BF-PID) disadvantages, optimization [24], such and as beingparticle trial-and-error swarm methods,optimization require manualproportional-integral-derivative tuning, and complex (PSO-PID) mathematical optimization models [25], [ 18have,22 ].been Some utilized optimization to algorithms,enhance such the asperformances genetic algorithm of PI controller proportional-integral and to obtain the parameters (GA-PI) optimizationof a PI controller. [23 ],The bacterial foragingbacktracking proportional-integral-derivative search algorithm (BSA) method (BF-PID) is an optimization optimization [ 24technique], and particle that has swarm the merits optimization of stability, toughness, and the ability for global convergence, yet is simple to implement [26]. proportional-integral-derivative (PSO-PID) optimization [25], have been utilized to enhance the In this study, the BSA optimization technique is developed for tuning the parameters of a PI performancescontroller of for PI a controllerPEHS. The andresults to obtainof the proposed the parameters methods ofare acompared PI controller. with the The results backtracking of search algorithmPSO-based PI (BSA) controller. method The is proposed an optimization BSA-PI co techniquentroller obtained that has the theminimum merits objective of stability, function toughness, and the(MAE) ability faster for globalthan the convergence, other techniques yet in isterms simple of ri tose time, implement settling time, [26]. and in all aspects. The rest Inof this the study,paper is the organized BSA optimization as follows: Section technique 2 describes is developedthe design of forthe tuningPI voltage the controller parameters based of a PI controlleron BSA for afor PEHS. a PEHS; The Section results 3 presents of the proposed the proposed methods BSA-PI are voltage compared controller with for the a vibration-based results of PSO-based PEHS; Section 4 presents a simulation model PI voltage controller for the PEHS utilizing the PI controller. The proposed BSA-PI controller obtained the minimum objective function (MAE) faster proposed BSA technique; Section 5 presents the experimental set-up; Section 6 presents the results than theand other discussion; techniques and, finally, in terms the ofconclusion rise time, is settlinggiven in Section time, and 7. in all aspects. The rest of the paper is organized as follows: Section2 describes the design of the PI voltage controller based on BSA for a PEHS; Section2. Design3 presentsPI Voltage the Contro proposedller Based BSA-PI on BSA voltage for PEHS controller for a vibration-based PEHS; Section4 presents a simulationThe traditional model and PIpopular voltage PI controller, controller uses for two the PEHSloops for utilizing control. theOne proposed is the inner BSA current technique; Sectioncontrol5 presents loop theand experimentalthe other is the set-up;outer voltage Section cont6 presentsrol loop. BSA the resultsis a systematic and discussion; method to and,iterate finally, the conclusionthrough all is givenof the inpossible Section configurations7. of a search space algorithm developed by [27]. It is a

2. Design PI Voltage Controller Based on BSA for PEHS The traditional and popular PI controller, uses two loops for control. One is the inner current control loop and the other is the outer voltage control loop. BSA is a systematic method to iterate through all of the possible configurations of a search space algorithm developed by [27]. It is a general Micromachines 2016, 7, 171 3 of 16 technique which finds the solutions of computation problems, notably constraint satisfaction problems for each individual application.

2.1. Conventional PI Voltage Controller PI controllers are the most common single-input-single-output (SISO) feedback controllers in use in industry and others applications. The standard format of the controller is shown below in Equation (1) [28]: t Z Controller Output = Kpe + Ki edt (1) Micromachines 2016, 7, x FOR PEER 0 3 of 17 2.1. Conventional PI Voltage Controller where e is the error, Kp is the proportional gain, Ki is the integration gain factor, and t is the time. The performance ofPI-controllers a PI controller are the ismost highly common dependent single-input-s oningle-output its gains. (SISO) If feedback these gains controllers are in- chosen improperly, use in industry and others applications. The standard format of the controller is shown below in the output willEquation experience (1) [28]. overshoot, become oscillatory, or even diverge. The adjustment of these controller gains to the optimum values for a desired controlt response is called tuning of the control ControllerOutput = K e + K edt p i  (1) loop. There are different methods documented in the literature0 for the tuning of PI controllers, which may not necessarilywhere resulte is the error in the and optimumKp is the proportional gains ofgain the and controller.Ki is the integration In addition, gain factor and the t is most the effective tuning methods are thetime. use The of performance different of optimization a PI controller is highly techniques. dependent on In its this gains. study If these agains BSA are optimization-basedchosen PI improperly, the output will experience overshoot, become oscillatory, or even diverge. The voltage controlleradjustment has been of these considered. controller gains to the optimum values for a desired control response is called tuning of the control loop. There are different methods documented in the literature for the tuning of 2.2. ConventionalPI Backtracking controllers, which Search may not Algorithmnecessarily result (BSA) in the optimum gains of the controller. In addition, the most effective tuning methods are the use of different optimization techniques. In this study BSA BSA is a population-basedoptimization based PI voltage iterative controller algorithm has been considered. designed to be a global minimizer. This allows searches to be flexible2.2. Conventional and Backtracking less time Search consuming Algorithm (BSA) for attempting to recreate the initial direction [27]. Usually, BSA is usedBSA to is solvea population-based constraint iterative satisfaction to be a global problems. minimizer. This The allows BSA searches is divided to be fixable into five processes as shown in Figureand less2. time consuming for attempting to recreate the innocent direction [27]. Usually, BSA is use to solve constraint satisfaction problems. The BSA is divided into five processes as shown in Figure 2.

Figure 2. General flowchart of BSA. Figure 2. General flowchart of backtracking search algorithm (BSA). 2.3. Control Strategy 2.3. Control StrategyThe PI controller is an active controller to adjust the single-phase boost converter DC output voltage for PEHS. The block diagram of a dSPACE controlled converter describes for this study is shown in Figure 3 which includes PVT, rectifier with filter, a dSPACE DS1104 controller, boosts The PI controllerconverter and is ana load. active The feedback controller loop is utilized to adjust for connecting the single-phase output of boostconverter, converter with DC output voltage for a PEHS.the dSPACE. The The blockimplementation diagram of the MATLAB/S of a dSPACEimulink converter controlled control algorithm converter simulated described for this in real-time is accomplished using dSPACE DS1104 RTI. Besides, the dSPACE input-output library study is shownblock in is Figure required3 to, include which in the includes control algorithm a PVT, [29,30]. a rectifier with a filter, a dSPACE DS1104 controller (dSPACEThe GmbH, analog-to-digital Paderborn, converter Germany),(ADC) terminal of boost the dSPACE converter, DS1104 is and used aforload. additional The feedback loop signal handling. With standalone converter, the approach is to control the output voltage supplied to is utilized for connectingthe load. The duty output ratios of switching voltages devices of are converter, modified by the with control the signal DSPACE. which is the Thepreferred implementation of the MATLAB/Simulinknecessary frequency (Mathworks of the converter Ltd., output Cambridge, [31]. The triangular UK) converter signals of 10 kHz control to produce algorithm the simulated in real-time is accomplished using a dSPACE DS1104 RTI. Additionally, the dSPACE input-output library block is required to include in the control algorithm [29,30]. The analog-to-digital converter (ADC) terminal of the dSPACE DS1104 is used for additional signal handling. With a standalone converter, the approach is to control the output voltage supplied to the load. The duty ratios of switching devices are modified by the control signal, which is the preferred Micromachines 2016, 7, 171 4 of 16

Micromachines 2016, 7, 171 4 of 16 necessarypreferred frequency necessary of thefrequency converter of the output converter [31]. output The triangular[31]. The triangular signals of signals 10 kHz of to10 producekHz to the switchingproduce signals the switching conduct signals the MOSFET. conduct the The MOSFET. frequency The frequency of the triangular of the triangular signal findssignal thefinds converter the switchingconverter frequency switching at whichfrequency the at MOSFET which the is MOSFET switched. is switched.

FigureFigure 3. Block3. Block diagram diagramof of thethe dSPACE DS1104 DS1104 controller controller converter. converter. 3. Proposed BSA-PI Voltage Controller for Vibration-Based PEHS 3. Proposed BSA-PI Voltage Controller for Vibration-Based PEHS The proposed BSA-PI voltage controller has gained popularity because of its easy design, Thelow-cost proposed for maintenance, BSA-PI voltage and controller it does not has depend gained popularityon a mathematical because ofmodel. its easy However, design, low-costthe for maintenance,traditional PI andcontroller it does has not demerits, depend such on aas mathematical a required mathematical model. However, model and the need traditional for a PI controllertrial-and-error has demerits, technique such to as obtain a required the Kp mathematical and Ki values model for developing and need the for controller. a trial-and-error technique to obtain the Kp and Ki values for developing the controller. 3.1. Backtracking Search Algorithm (BSA) 3.1. BacktrackingVarious Searchoptimization Algorithm techniques (BSA) have been modified to increase the system efficiency, such as VariousPSO, GA, optimization gravitational techniquessearch algorithm have (GSA), been modified and ant colony to increase search the technique, system are efficiency, utilized suchto as PSO,solve GA, gravitationalreal-valued mathematical search algorithm optimization (GSA), andproble antms. colony Usually, search to solve technique, difficult are mathematical utilized to solve optimization problems, non-linear and non-differentiable optimization methods are utilized. BSA real-valued mathematical optimization problems. Usually, to solve difficult mathematical optimization optimization is a metamorphic computation method established by [27]. The assumption of BSA for problems,generating non-linear a sample and population non-differentiable consists of optimization two innovative methods edges areand utilized.mutation BSA operators. optimization BSA is a metamorphicgoverns the computationvalue of the find method on the established best populations by [27 and,]. The in the assumption location boundary, of BSA for conducts generating a a samplerobust population investigation consists for ofpossibilities two innovative of abuse edges [27,32–35]. and mutation Thus, operators. BSA optimization BSA governs has thebeen value of thedemonstrated find on the bestin significant populations research and, as in one the of locationthe most boundary,powerful optimization conducts a methods robust investigation[33–35]. for possibilities of abuse [27,32–35]. Thus, BSA optimization has been demonstrated in significant research as one3.2. of Optimal the most PI Voltage powerful Controllers optimization methods [33–35]. The optimization technique combines three necessary features, including input information, an 3.2. Optimalobjective PI function, Voltage Controllersand optimization limitations. All elements are working for development and Thearrangement optimization to achieve technique optimal combines PI parameter three values necessary. The optimization features, includingtechnique is input to obtain information, the best solution by minimizing the objective function though the input data and the collection of the an objective function, and optimization limitations. All elements are working for development and limitations in all generations of the iterative procedure. arrangement to achieve optimal PI parameter values. The optimization technique is to obtain the best solution3.3. Input byInformation minimizing the objective function though the input data and the collection of the limitations in all generations of the iterative procedure. The input data for the PI voltage controller of the optimization technique are a number of 3.3. Inputboundary Information PI optimal parameter values for input and output. The input matrixes build a number of columns and rows. The numbers of columns are produced by the mathematical values to the Theboundary input for data error for and the alteration PI voltage of error. controller The ou oftput the of optimizationthe optimal PI techniqueparameter values are a are number the of boundarynumber PI of optimal rows generated parameter by the values size of for populations, input and as output. shown Thein the input matrix: matrixes build a number of columns and rows. The numbers of columns are produced by the mathematical values to the boundary X ij X 1 j  for error and alteration of error. The outputB of the= optimal PI parameter values are the number(2) of rows ij X X  generated by the size of populations, as shown in thei1 matrix:ij  " # Xij X1j Bij = (2) Xi1 Xij Micromachines 2016, 7, 171 5 of 16 where B is the input data of the optimization technique, i = 1, 2, ... , A, A is the size of the population, and j = 1, 2, ... , S, where S is the problem dimension. In this study, two problem dimensions and a population of 50 have been considered to obtain the best parameter values for the PI voltage controller.

3.4. Objective Function An objective function is essential for the optimization method to achieve a minimum error. Therefore, the objective function finds the best value of the PI voltage controller output to improve the system permanence. The MAE is utilized as an objective function to find appropriate parameter values for controller for best results. The MAE function can be calculated as shown in Equation (3).

1 H MAE = ∑ |error| (3) H i=1

Here, H is the number of sample, error is PI voltage control for boost converter.

3.5. BSA for an Optimal PI Voltage Controller The BSA has been developed to choose some important parameters; for example, the number of iterations (I), the size of the population (A), and the number of problem variables (S) for the PI voltage controller. The BSA is divided into five processes, including initialization, selection-I, mutation, crossover and selection-II [32–35].

3.5.1. Initialization The initialization method is an archaic structure for the population of the mathematical values of the PI parameter (Tij) described by the following Equation (4):  Tij = arb. upj − lowj + lowj (4) where i = 1, 2, 3, ... , A and j = 1, 2, 3, ... , S, here A is the population size and S is the problem dimension, respectively. The objective function (MAE) is calculated for each population [27–31].

3.5.2. Selection-I

In the BSA’s Selection-I define the historical population (oldTij) to be utilized for calculating the find direction. The primary historical population is defined utilizing Equation (5):  oldTij = arb. upj − lowj + lowj (5)

The oldTij remembers the population arbitrarily selected from the former propagation for building the find direction matrix, holding the biased benefit of earlier contract to produce a new trial population. The comparison between two arbitrary values is shown in the following condition:

if a < b then oldTij = Tij (6)

oldTij = permuting(oldTij) (7)

3.5.3. Mutation Mutation is a method that generates the new population of the primary and history population as shown in Equation (8), in which arb. is the standard normal distribution, the E value controls the amplitude of the search-direction matrix:

Mutant = Tij + E.arb.(oldTij − Tij) (8) Micromachines 2016, 7, 171 6 of 16

BSA produces a sample population, and then accepts a partial benefit of its experiences from earlierMicromachines propagation. 2016, 7, 171 6 of 16

3.5.4.3.5.4. Crossover Crossover

In thisIn procedure,this procedure, the sample the sample of population of populationGij is created.Gij is created. The primary The primary sample ofsample the populations of the is occupiedpopulations from is mutation,occupied from as shown mutation, in Equation as shown (8). in TheEquation crossover (8). The contains crossover of two contains parts. of The two first partparts. creates The the first binary part matrixcreates calledthe binarymapij ,matrix and the called second map partij, and is procedurethe second comparisonpart is procedure between comparison between population Tij and trial population Gij. Crossover is utilized to achieve updates population Tij and trial population Gij. Crossover is utilized to achieve updates in mapij. in mapij. 3.5.5. Selection-II 3.5.5. Selection-II Here, the optimization method runs to compare the population Tij and trial population Gij to Here, the optimization method runs to compare the population Tij and trial population Gij to achieve the best population and fitness value. Figure4 shows the flow diagram explaining the achieve the best population and fitness value. Figure 4 shows the flow diagram explaining the BSA-basedBSA-based PI voltage PI voltage controller. controller.

Figure 4. Proposed BSA-based optimum proportional-integral (PI) voltage controller design procedure. Figure 4. Proposed BSA-based optimum proportional-integral (PI) voltage controller design procedure.

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4.4. Simulation Simulation Model Model PI PI Voltage Voltage Controller Controller for for PEHS PEHS Utilizing Utilizing the the Proposed Proposed BSA BSA Technique Technique TheThe completed completed PI PI voltage voltage controller controller simulation simulation model model for forthe thePEHS PEHS is developed is developed using using the PVT the (asPVT an (as input an inputsource), source), full-wave full-wave rectifier, rectifier, low pass low filter, pass and filter, boost and converter boost converter with temporary with temporary storage devicesstorage devicesas shown as shownin Figure in Figure 5. This5. Thisfigure figure denotes denotes the the schematic schematic diagram diagram of of the developeddeveloped MATLAB/SimulinkMATLAB/Simulink PEHS. PEHS.

FigureFigure 5. BlockBlock diagram diagram of of the the proposed proposed BSA-based BSA-based PI PI voltage voltage controller controller for for piezoelectric energy energy harvestingharvesting system system (PEHS).

TheThe functionsfunctions ofof the the integrated integrated energy energy harvesting harvesting system system circuit circuit are as follows:are as follows: the PVT performsthe PVT performsas a bending as a mechanicalbending mechanical structure structure that produces that produces an amount an of amount charge of from charge force. from The force. electrical The electricalequivalent equivalent circuit of circuit the PVT of isthe simulated PVT is simulated using Matlab/Simulink using Matlab/Simulink software. software. The role The of role the PVTof the is PVTto be is stressed to be stressed mechanically mechanically by a force by vibration,a force vibration, when one when side ofone PVT side is of flexed, PVT thenis flexed, the other then sidethe otheris free side to move.is free Whento move. the When PVT vibrates,the PVT itsvibrates, electrodes its electrodes receive an receive amount an ofamount charge of that charge tends that to tendscounteract to counteract the imposed the imposed strain.This strain. amount This amount of charge of ischarge harvested, is harvested, stored, stored, and delivered and delivered to power to powerelectrical electrical circuits. circuits. The PVT The isPVT interfaced is interfaced with awi powerth a power electronic electronic network network that extractsthat extracts power power and anddelivers delivers it to ait storage to a storage device, device, such as such a rechargeable as a rechargeable battery or battery a supercapacitor. or a supercapacitor. Since the piezoelectric Since the piezoelectriccrystal-based crystal-based PVT generates PVT low generates AC voltage low AC output voltage with output fluctuations with fluctuations and harmonics, and harmonics, it is difficult it isto difficult process to this process low level thissignal low level at various signal at magnitudes. various magnitudes. At the end, At the the AC end, power the AC that power is harvested that is harvestedfrom an energy-harvesting from an energy-harvesting PVT needs toPVT be rectifiedneeds to through be rectified a standard through diode a standard bridge before diode it bridge can be beforedelivered it can to be storage. delivered The to output storage. of theThe rectifieroutput of DC the voltage rectifier contains DC voltage ripples. contains Usually, rippl thesees. Usually, ripples theseare at ripples a maximum are at fora maximum a half-wave for rectifiera half-wave and rectifier a minimum and a for minimum a full-wave for a rectifier. full-wave For rectifier. most of For the mostapplications, of the applications, direct voltage direct from voltage a rectifier from to a the rectifier load leads to the to load poor leads operation to poor of theoperation circuit. of If the circuit.rectifier If outputthe rectifier is smooth output and is smooth steady, and then steady the overall, then the operation overall operation of the circuit of the improves circuit improves because becausethe filter the circuit filter reduces circuit thereduces ripples the and ripples produces and aproduces constant a DC constant voltage. DC However, voltage. theHowever, theoretical the theoreticalrate of power rate extractionof power extraction can be greatly can be improved greatly improved by interfacing by interfacing the harvesting the harvesting transducer transducer with a withpower a power electronic electronic switching switching converter. converter. Power electronicPower electronic converters converters are capable are capable of imposing of imposing static or staticdynamic or dynamic relationships relationships between thebetween voltages the and volt currentsages and of thecurrents PVT by of operating the PVT theby transistorsoperating likethe transistorsswitches. One like ofswitches. the most One popular of the powermost popular electronic power converters electronic for energyconverters harvesting for energy applications harvesting is applications is the single-phase DC-DC converter. This converter has become the subject of considerable interest for low-power PEHS applications.

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Micromachines 2016, 7, 171 8 of 16 Micromachines 2016, 7, 171 8 of 16 the single-phase DC-DC converter. This converter has become the subject of considerable interest for low-powerTheThe PWMPWM PEHS switchingswitching applications. techniquetechnique isis usedused forfor controcontrollinglling thethe PEHSPEHS byby thethe BSABSA method.method. TheThe PEHSPEHS modelmodelThe isis PWMsurveyedsurveyed switching dependingdepending technique onon thethe is voltage usedvoltage for feedbacfeedbac controllingkk signal.signal. the PEHS AllAll possiblepossible by the BSA casescases method. ofof voltagevoltage The drops PEHSdrops havemodelhave beenbeen is surveyed consideredconsidered depending duringduring onthethe the changechange voltage inin feedback loadsloads inin signal.thethe simulationsimulation All possible modelmodel cases byby of constructingconstructing voltage drops aa very havevery powerfulbeenpowerful considered controllercontroller during forfor thethe PEHS.PEHS. change TheThe in loads developeddeveloped in the controller simulationcontroller isis model usedused to byto obtainobtain constructing thethe bestbest a veryvaluesvalues powerful forfor thethe PIcontrollerPI voltagevoltage forcontrolcontrol the PEHS. parametersparameters The developed byby thethe BSABSA controller optimizationoptimization is used technique.technique. to obtain TheThe the PWMbestPWM values techniquetechnique for the receivesreceives PI voltage KpKp andcontroland KiKi values parametersvalues fromfrom by thethe the PIPI BSA controllercontroller optimization andand generategenerate technique.ss switchingswitching The PWM signalssignals technique forfor thethe receives boostboost Kp converterconverter and Ki valuesofof thethe MOSFETfromMOSFET the PIfor for controller gate gate drives drives and to to generatesdeliver deliver DC DC switching voltages voltages signalsto to the the PEHS. forPEHS. the However, However, boost converter the the BSA-PI BSA-PI of the voltage voltage MOSFET controller controller for gate isdrivesis usedused to toto deliver obtainobtain suitable DCsuitable voltages PIPI parameterparameter to the PEHS. values.values. However, FigureFigure 6 the6 showsshows BSA-PI flowchartflowchart voltage ofof controller thethe controlcontrol is used algorithmalgorithm to obtain forfor PEHS.suitablePEHS. PI parameter values. Figure6 shows flowchart of the control algorithm for PEHS.

START START

Read Output voltage for boost converter Read Output voltage for boost converter Compute the error (e) Compute the error (e) Duty ratio Duty ratio

Compare with triangular waveform Compare with triangular waveform

Pulse Width Modulation (PWM) Pulse Width Modulation (PWM) MOSFET MOSFET

FigureFigure 6. 6. Flowchart Flowchart of of the the control control algorithm algorithm for for the the PEHS. PEHS.

5.5. ExperimentalExperimental Experimental SetupSetup Setup TheThe hardware hardware structure structure is is the thethe depiction depictiondepiction of ofof an an electronic electronic system, system, method, method,method, and and to to regulate regulate implementationimplementationimplementation ofof of thethe the designdesign design forfor for suchsuch such aa a prototypprototyp prototypeee system.system. system. TheThe The hardwarehardware hardware implementationimplementation implementation isis oneone is one ofof theofthethe vitalvital vital partsparts parts toto verify toverify verify thethe the circuit circuit circuit functionalityfunctionality functionality isis in isin properinproper proper operation.operation. operation. TheThe PVT PVT benderbender is isis a aa pre-mounted pre-mountedpre-mounted and andand prewired prewiredprewired double doubledouble quick-mount quick-mountquick-mount bending bendingbending generator. generator.generator. The TheThe use useofuse a ofof frequency aa frequencyfrequency generator generatorgenerator with withwith a poweraa powerpower amplifier amplifieamplifier isr isis preferred preferredpreferred to toto control controlcontrol thethethe mechanicalmechanical energy energy generationgeneration by by varying varying the the frequency. frequency. The TheThe experimental experimentalexperimental test test setup setup for for data data extraction extraction from from the the PVT PVT is is shownshown in in Figure Figure 7 7.7.. ToTo conduct conductconduct thethethe PVT PVTPVT analysis, analysis,analysis, thethethe natural naturalnatural frequency frequencyfrequency hashashas been beenbeen changed changedchanged manuallymanuallymanually betweenbetween 1212 HzHz and andand 74 7474 Hz HzHz through throughthrough the thethe amplifier amplifieramplifier unit, unit,unit, investigating investigatinginvestigating the thethe resonance resonanceresonance frequency frequencyfrequency of the ofof PVT thethe PVTdetailsPVT detailsdetails as shown asas shownshown in the in in Results thethe ResultsResults and Discussionand and Discussion Discussion (Section (Section(Section6). 6).6).

Figure 7. Experimental test bench layout. Figure 7. Experimental test bench layout.

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5.1.5.1. Piezoelectric Piezoelectric Vibration Vibration TransducerTransducer AA singlesinglesingle PVT PVTPVT has hashas been beenbeen tested testedtested with withwith the energy thethe energyenergy harvesting harvestingharvesting power conversionpowerpower conversionconversion circuits. The circuits.circuits. prototype TheThe prototypeofprototype a PVT is ofof shown aa PVTPVT in isis Figure shownshown8 . inin The FigureFigure parameter 8.8. TheThe pa valuesparameterrameter of the valuesvalues PVT of areof thethe summarized PVTPVT areare summarizedsummarized as shown in asas Table shownshown1. Theinin TableTable energy 1.1. TheThe harvesting energyenergy harvestingharvesting PVT is a pre-mounted PVTPVT isis aa pre-mountedpre-mounted and prewired andand double prewiredprewired quick-mount doubledouble quick-mountquick-mount bending generator bendingbending generatordesignedgenerator to designeddesigned attach easily toto attachattach to sources easilyeasily to ofto sources mechanicalsources ofof mechanicalmechanical strain. strain.strain.

FigureFigure 8.8. PrototypePrototype ofof thethe piezoelectricpiezoelectric vibrationvibration transducerstransducers (PVT).(PVT).

TableTable 1.1. PiezoelectricPiezoelectric vibrationvibration transducertransducer parameters.parameters.

ParameterParameter PVT PVT Units Units Parameter PVT Units PiezoPiezo MaterialMaterial 5A4 5A4 E E Piezo Material 5A4 E WeightWeight 10.410.4 gramsgrams Weight 10.42 grams Stiffness 1.9 × 10 2 N/m StiffnessStiffness 1.9 × 1.910 ×2 10 N/mN/m CapacitanceCapacitanceCapacitance 232232232 nFnF nF peak Rated TipRatedRated Deflection TipTip DeflectionDeflection ±2.6 ±2.6 ±2.6 (mm (mm(mmpeak))peak) MaximumMaximumMaximum Rated Frequency RatedRated FrequencyFrequency 52 52 52 Hz Hz Hz

5.2.5.2. Experimental Experimental Setup Setup of of thethe PEHSPEHS AsAs aa partpart ofof thethe prototypeprototype developmentdevelopment ofof thethe PEHS,PEPEHS,HS, thethe performanceperformance evaluaevaluationevaluationtion isis essentialessential toto verifyverify thethe conformanceconformance withwith thethe simulation.simulation. To To verifyveverifyrify thethe simulatedsimulated model,model, anan integratedintegrated prototypeprototype forfor thethethe PEHSPEHSPEHS was waswas constructed, constructed,constructed, tested, tested,tested, and andand evaluated evaluateevaluate indd in thein thethe laboratory, laboratory,laboratory, which whichwhich is shown isis shownshown in Figure inin FigureFigure9a,b. This9a,b.9a,b. equipment ThisThis equipmentequipment is considered isis consideredconsidered to build toto build abuild prototype aa prototprotot systemypeype systemsystem for the forfor PEHS thethe PEHSPEHS as shown asas shownshown in Table inin2 Table.Table To verify 2.2. ToTo verifytheverify simulation thethe simulationsimulation results, results,results, a hardware aa hardwarehardware prototype prototypeprototype for the for PEHSfor thethe was PEHSPEHS fabricated waswas fabricatedfabricated in the laboratory. inin thethe laboratory.laboratory.

((aa))

Figure 9. Cont.

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(b)

Figure 9. (a) dSPACE-based PEHS prototype implementation block diagram; and ( b) in-lab PEHS prototype experimental setup.

Table 2. Equipment list for the experimental setup. Equipment Name Equipment Model Equipment Quantity EquipmentPVT Name EH220-A4-503YB Equipment Model Equipment 1 Quantity AmplifierPVT Module Smart EH220-A4-503YB material 1 1 AmplifierVibration Module Shaker Smart - material 1 1 Vibration Shaker - 1 DigitalDigital Voltmeter Voltmeter 72-7130A 72-7130A 1 1 Copper-BoardCopper-Board - - 2 2 DigitalDigital Oscilloscope Oscilloscope DSO DSO ×× 2074A2074A 1 1 dSPACEdSPACE Controller Controller DS1104 DS1104 1 1 Voltage Probe - 2 Voltage Probe - 2 Switch - 5 Resistive loadSwitch LED - - 5 5 ResistiveInductor Lload LED 3500 - µH 5 1 Filter CapacitorInductor C L 3500 300 μµHF 1 2 FilterMOSFETs Capacitor C SI9926CDY 300 μF 2 1 Schottky Diodes IN5819 5 MOSFETs SI9926CDY 1 Schottky Diodes IN5819 5 6. Results and Discussion 6. ResultsThis sectionand Discussion describes the results of the PVT and optimal results of the BSA-PI and the PSO-PI voltageThis controller section describes algorithms the of results the PEHS. of the PVT and optimal results of the BSA-PI and the PSO-PI 6.1.voltage Extracting controller Data algorithms from the PVT of the PEHS.

6.1. ExtractingThis experiment Data from was the conducted PVT to obtain the behavior of the PVT by using energy harvesting kits, an amplifier module, and shaker. The amplifier module is set to vary of the input frequency This experiment was conducted to obtain the behavior of the PVT by using energy harvesting manually to generate the vibration signal at different levels and different frequency ranges to obtain kits, an amplifier module, and shaker. The amplifier module is set to vary of the input frequency the response of the PVT. The analytical output of the PVT is shown in Table3. Figure 10 shows that the manually to generate the vibration signal at different levels and different frequency ranges to obtain PVT produces maximum output at 65 Hz. The input of 65 Hz is used to develop the simulation and the response of the PVT. The analytical output of the PVT is shown in Table 3. Figure 10 shows that experimental models of the PEHS. the PVT produces maximum output at 65 Hz. The input of 65 Hz is used to develop the simulation and experimental models of the PEHS.Table 3. Analytical data from the PVT.

Frequency (Hz) 12 16 19 21Table 24 3. Analytical 28 30 34data 36from 40the PVT. 44 48 50 54 60 65 70 74 FrequencyVrms (Hz) 0.312 0.516 0.819 0.921 124 28 1.2 30 1.7 34 2 361.26 40 1.17 1.2 44 1.2748 1 50 1.3 54 260 652.75 0.5 70 0.274 Vrms 0.3 0.5 0.8 0.9 1 1.2 1.7 2 1.26 1.17 1.2 1.27 1 1.3 2 2.75 0.5 0.2

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3 Maximum Peak 2.5

2

1.5

1 Amplitude (V) 1 Amplitude (V)

0.5

0 10 20 30 40 50 60 70 80 Frequency (Hz)

Figure 10. Frequency spectrum of the PVT.

6.2. Simulation and Analysis This section describes the outcome of the improvement results of the BSABSA optimization-basedoptimization-based PI voltage controller for the PEHS. The simulation results have been compared with the hardware results to verify the functionality of the developeddeveloped PEHS. The PI voltage controller parameters were effectively tuned by the BSA optimization technique to obtain the optimal (Kp, Ki) parameter values for the the PI. PI. This This process process has has also also been been led led through through PSO PSO optimization optimization techniques techniques to tofind find the the optimal optimal PI parameter.PI parameter. Population-based Population-based optimization optimization techniques techniques can find can optimal find optimal solutions solutions for almost for almost all types all oftypes problems. of problems. However However the mathematical the mathematical optimization optimization technique technique cannot cannot find findany anysolution solution when when the problemthe problem dimension dimension is high. is high. This Thiscomparison comparison is used is used to estimate to estimate and anddefine define the robustness the robustness of the of BSAthe BSA optimization. optimization. Figure Figure 11 represents 11 represents the opti the optimizationmization performance performance of the of BSA the BSA and andPSO PSO using using the objectivethe objective function function of MAE of MAE for for 100 100 iterations. iterations. Th Thee BSA BSA optimization optimization technique technique has has obtained obtained the minimum objective function MAE MAE values. values. Table Table 44 showsshows thethe valuesvalues ofof thethe outputoutput errorerror byby differentdifferent techniques. ItIt is is observed observed in Tablein Table4 that 4 thethat BSA th techniquee BSA technique produces produces the minimum the minimum error in optimizing error in optimizingthe parameter the valuesparameter of the values PI voltage of the controllerPI voltage and controller regulates and the regulates PWM signal the PWM so that signal the dutyso that of thePWM duty output of PWM of the output controller of the exhibitscontroller robustness, exhibits robustness, ruggedness, ruggedness, and efficiency. and efficiency. To ensure To that ensure the thatcomparisons the comparisons are fair, thearesame fair, the population same population size and maximum size and maximum number of number iterations of thatiterations was applied that was in appliedboth techniques in both techniques are shown are in Table shown5. in Table 5.

0.08 BSA PSO 0.07

0.06

0.05

0.04 Objective function function Objective Objective function function Objective 0.03

0.02 0 20 40 60 80 100 Iteration Figure 11. Performance comparison based on BSA and particle swarm optimization (PSO).

Table 4. Values of output error by different techniques.

Trial-and-Error PSO BSA MAE 0.153716127 0.032125084 0.021602106

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Table 4. Values of output error by different techniques.

Trial-and-Error PSO BSA MAE 0.153716127 0.032125084 0.021602106 Micromachines 2016, 7, 171 12 of 16

TableTable 5. Parameter 5. Parameter settings settings of ofBSA-PI BSA-PI and and PSO-PI. PSO-PI.

ParameterParameter BSA-PI BSA-PI PSO-PI PSO-PI PopulationPopulation Size Size 50 50 50 50 MaximumMaximum Iteration Iteration 100 100 100 100 c1 andc1 and c2 c2 - - 2 2 E E2 2 - -

6.3. Simulation and Experimental Results in Terms ofof RiseRise andand SettlingSettling TimeTime forfor thethe PEHSPEHS The objective function, as shown in Equation (3), is optimized by BSA-PI while satisfying the constraints in Equations (4)–(8). To To validate the optimization results, the outcomes of BSA-PI are compared withwith PSO-PI.PSO-PI. The The responses responses of of the the PEHS PEHS simulation simulation results results using using PSO-PI PSO-PI controllers controllers and and the BSA-PIthe BSA-PI controller controller are shownare shown in Figure in Figure 12. From12. From Figure Figure 12 it 12 can it becan seen be seen that that BSA-PI BSA-PI can findcan find the best the optimalbest optimal result result with respectwith respect to the to rise the time rise value time ofva thelue BSA-PIof the BSA-PI controller controller is less timeis less than time the than PSO-PI the controller,PSO-PI controller, and settling and timesettling is comparatively time is comparatively large for large PSO-PI, for butPSO-PI, less for but BSA-PI. less for The BSA-PI. hardware The resultshardware agree results well agree with thewell simulated with the resultssimulated shown resu inlts Figure shown 13 in. Table Figure6 represents 13. Table the6 represents comparison the ofcomparison the optimized of the output optimized using output these techniques. using these The techniques. BSA-PI has The successfully BSA-PI has reached successfully the best reached result comparedthe best result with compared the other PSO-PIwith the controller other PSO-PI in terms cont ofroller the in rise terms time of and the settling rise time time. and settling time.

Figure 12. Simulation results BSA-PI and PSO-PI controller with respec respectt to rise time (a) and settling time (b).

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FigureFigure 13. 13. ExperimentalExperimental results results PSO-PI PSO-PI and and BSA-PI BSA-PI contro controllerller with respect to rise and settling time.

TableTable 6. Comparison results obtained usin usingg BSA-PI and PSO-PI controllers.

Rise Time Settling Time Peak over Shoot Rise Time Settling Time Peak over Shoot Steady State AlgorithmsAlgorithms Kp Kp Ki Ki Steady State Error (Tr)(Tr) (Ts)(Ts) (Po)(Po) Error BSA-PIBSA-PI 0.7 0.7 0.030.03 0.240.24 s s 0.28 0.28 s s 0% 0% 0.1 PSO-PIPSO-PI 1 1 1.5 1.5 1.4 1.4 s s 2.1 2.1 s s 0% 0% 0.1

6.4. Simulation Simulation and and Experimental Experimental Results of a Fully-Integrated PEHS This studystudy alsoalso analyzes analyzes the the simulation simulation and and experimental experimental results results of a fully-integratedof a fully-integrated PEHS PEHS input inputand output and output voltage voltage using theusing proposed the proposed new technique. new technique. The results The results using theusing BSA-PI the BSA-PI and PSO-PI and PSO-PItechniques techniques are shown are in shown Figure in14 a,b.Figure From 14a,b. Figure Fr om14a Figure it can be 14a seen it thatcan thebe inputseen that sinusoidal the input AC sinusoidalVrms 0.3 V AC generated Vrms 0.3 from V generated the PVT from and the boost PVT harvested and boost an harvested optimal outputan optimal voltage output of 6.06voltage V DC of 6.06utilizing V DC the utilizing proposed the BSA-PI proposed technique BSA-PI of technique the PEHS. of Initially the PEHS. the curve Initially bends, the butcurve after bends, 0.2 s, thebut curveafter 0.2becomes s, the steady.curve becomes On the other steady. hand, On from the Figureother hand14b, it, from is shown Figure that 14b, the voltageit is shown output that characteristics the voltage outputof the PSO-PIcharacteristics technique of arethe similarPSO-PI withouttechnique any ar significante similar without difference any for sign a changingificant difference load. Initially for a changingthe curve bends,load. Initially but after the 2.1 curve s, the bends, curve becomesbut after steady. 2.1 s, Thethe peakcurve overshoot becomes valuesteady. is similarThe peak for overshootthe two algorithms. value is similar Thus, itfor can the be two concluded algorithms. that theThus, controller it can be parameter concluded values that obtainedthe controller from parameterBSA-PI are values best suited obtained for feedback from BSA-PI PI voltage are best controller suited for design feedback in all PI aspects. voltage The controller hardware design results in allare aspects. shown inThe Figure hardware 15a,b. results Table are7 shows shown the in outcomes Figure 15a,b. of the Table PEHS 7 shows utilizing the outcomes the BSA-PI of controller, the PEHS utilizingwhich are the compared BSA-PI controller, with current which and otherare compared existing workwith current in terms and of voltage other existing and switching work in frequency. terms of voltageFew authors and switching have developed frequency. a boost Few converter authors for have PEHS, developed but no onea boost utilized converter optimization for PEHS, algorithms. but no oneThe utilized authors inoptimization [36–38] designed algorithms. a boost The converter authors to in increase [36–38] thedesigned output a voltage boost converter for PEHS to by increase varying thethe PIoutput controller, voltage power for PEHS management by varying circuit, the andPI controller, voltage regulator power management circuit, etc., without circuit, utilizingand voltage any regulatoroptimization circuit, algorithm. etc., without In [36 ],utilizing the author any designed optimization a closed algorithm. loop system, In [36], bridgeless the author boost designed rectifier a closedutilizing loop a conventional system, bridgeless PI controller boost with rectifier a 50 kHzutilizing switching a conventional frequency toPI increase controller the with output a 50 voltage, kHz switchingand the model frequency boosts to 3.3increase V DC the with output an input voltage, of 0.4 and V the AC. model The author boosts in3.3 [ 37V ]DC designed with an a input DC-DC of 0.4converter V AC. The with author a power in management[37] designed circuit a DC-DC with converter a 3 MHz with switching a power frequency management to increase circuit the with output a 3 MHzvoltage, switching and the frequency model boosts to increase 1.2 V DC the withoutput an vo inputltage, of and 0.12 the V AC.model The boosts author 1.2 in V [38 DC] designed with an inputa boost of converter0.12 V AC. from The micro-energyauthor in [38] sourcesdesigned with a boost a 170 converter kHz switching from micro-energy frequency to sources maximize with the a 170output kHz voltage, switching and frequency the model to boostsmaximize 3.3 Vthe DC output with voltage, an input and of 0.25–0.4the model V AC.boosts Therefore, 3.3 V DC in with this anstudy, input a BSA-PIof 0.25–0.4 controller V AC. isTherefore, utilized toin increasethis study, the a outputBSA-PI voltage controller of theis utilized PEHS. Theto increase advantage the outputof the BSA-basedvoltage of PIthe voltage PEHS. controllerThe advantage of the of PEHS the showsBSA-based a great PI improvement,voltage controller compared of the PEHS to the showsothers techniques,a great improvement, with stability, compared boost maximum to the othe voltage,rs techniques, and faster with response stability, in termsboost ofmaximum rise time voltage,and settling and time,faster with response changing in loads,terms inof simulationrise time and experimentalsettling time, results. with changing On the other loads, hand, in simulationthe disadvantage and experimental of the other results. methods On is the the othe requiredr hand, mathematical the disadvantage modeling of the and other trial-and-error methods is thetechnique. required Experimental mathematical results modeling show and that trial-and-er the outputror voltage technique. is 6.06 VExperimental DC with an results input of show 0.3 V that AC thewith output a 10 kHZ voltage switching is 6.06 frequency. V DC with From an input this table of 0.3 it V is AC obvious with thata 10the kHZ proposed switching approach frequency. can obtainFrom thisa higher table optimal it is obvious output that voltage the comparedproposed toapproach the others. can obtain a higher optimal output voltage compared to the others.

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7 7 7 7 6 6 6 6 5 5 5 5 4 4 (V) 4 4 Input voltage

(V) Input voltage Input voltage 3 3 PSO-PI output voltage InputBSA-PI voltage output voltage PSO-PI output voltage tage

l 3 3 BSA-PI output voltage o tage l 2 2 V Voltage (V) o 2 2 V Voltage (V) 1 1 1 1 0 0 0 0 -1 -1 -10 5 10 15 20 -10 5 10 15 20 0 5 Time10 (s) 15 20 0 5 Time10 (s) 15 20 Time (s) Time (s) (a) (b) (a) (b) Figure 14. Simulation results of a complete PEHS utilizing a BSA-PI (a) and a PSO-PI (b) controller. Figure 14. SimulationSimulation results of a complete PEHS utilizing a BSA-PI ( a) and a PSO-PI (b) controller.

(a) (b) (a) (b) Figure 15. Experimental results of a complete PEHS utilizing a BSA-PI (a) and a PSO-PI (b) controller. FigureFigure 15. Experimental 15. Experimental results results of a complete of a complete PEHS PEHS utilizing utilizing a BSA-PI a BSA-PI (a) and (a) a and PSO-PI a PSO-PI (b) controller. (b) controller. Table 7. Comparison of the output voltage. Table 7. Comparison of the output voltage. Component [36] [37] [38] This Work Component [36] [37] [38] This Work Algorithm N/A N/A N/A BSA-PI AlgorithmComponent N/A [36][ N/A37][ N/A38] This BSA-PI Work Vin (Input voltage) 0.4 V 0.12 V (0.25–0.4) V 0.3 V Vin (InputAlgorithm voltage) 0.4 N/A V 0.12 N/A V (0.25–0.4) N/A V BSA-PI 0.3 V Vo (Output voltage) 3.3 V 1.2 V 3.3 V 6.06 V Vo (Output voltage) 3.3 V 1.2 V 3.3 V 6.06 V SwitchingVin (Input Frequency voltage) 50 0.4 kHz V 3 0.12 MHz V (0.25–0.4) 170 kHz V 100.3 kHz V Switching Frequency 50 kHz 3 MHz 170 kHz 10 kHz Vo (OutputLoad voltage)200 3.3 VΩ 10 1.2 k VΩ 30 3.3 k VΩ 1.5 MΩ, 1 MΩ, 1000 6.06 VkΩ, 500 kΩ, 300 kΩ Load 200 Ω 10 kΩ 30 kΩ 1.5 MΩ, 1 MΩ, 1000 kΩ, 500 kΩ, 300 kΩ SwitchingApplication Frequency Energy 50 harvesting kHz Energy 3 MHzharvesting Low 170 power kHz Micro-devices 10 kHz Application Energy harvesting Energy harvesting Low power Micro-devices Load 200 Ω 10 kΩ 30 kΩ 1.5 MΩ, 1 MΩ, 1000 kΩ, 500 kΩ, 300 kΩ 7. Conclusions 7. ConclusionsApplication Energy harvesting Energy harvesting Low power Micro-devices This paper presented an optimization approach to find the optimal parameter values of a PI This paper presented an optimization approach to find the optimal parameter values of a PI 7.voltage Conclusions controller for a PEHS considering a specific vibration of a PVT for micro-energy harvesting. voltage controller for a PEHS considering a specific vibration of a PVT for micro-energy harvesting. The proposed BSA-PI optimization technique is used to assist in avoiding the traditional The Thisproposed paper BSA-PI presented optimization an optimization technique approach is used to find to theassist optimal in avoiding parameter the values traditional of a PI trial-and-error procedure for finding the best values of Kp and Ki. To solve the optimization voltagetrial-and-error controller procedure for a PEHS for consideringfinding the abest specific values vibration of Kp of and a PVT Ki.for To micro-energy solve the optimization harvesting. objective problem MAE, BSA was used, and the simulation and experimental results of this Theobjective proposed problem BSA-PI MAE, optimization BSA was technique used, and is used the to si assistmulation in avoiding and experiment the traditionalal results trial-and-error of this technique are compared with the results of the PSO to validate the outcomes. The obtained results proceduretechnique forare findingcompared the with best valuesthe results of Kp of and the Ki. PSO To to solve validate the optimization the outcomes. objective The obtained problem results MAE, clearly show that the BSA-PI controller outperforms the PSO-PI controller in terms of rise time, BSAclearly was show used, that and the the BSA-PI simulation controller and experimentaloutperforms resultsthe PSO-PI of this controller technique in areterms compared of rise time, with settling time. Finally, this prototype successfully boost the 0.3 V, with 65 Hz AC to 6.06 V DC. The thesettling results time. of theFinally, PSO this to validate prototype the successfully outcomes. Theboost obtained the 0.3 V, results with clearly65 Hz AC show to that6.06 theV DC. BSA-PI The output voltage is strongly regulated at 6.06 V through a closed-loop using a BSA-PI voltage controlleroutput voltage outperforms is strongly the PSO-PI regulated controller at 6.06 in termsV through of rise time,a closed-loop settling time. using Finally, a BSA-PI this prototype voltage controller that is suitable for micro-device applications. Naturally, vibration sources produce successfullycontroller that boost is thesuitable 0.3 V, for with micro-device 65 Hz AC to a 6.06pplications. V DC. The Naturally, output voltage vibration is strongly sources regulatedproduce unstable excitation conditions (varying frequency and amplitude). In this regard the work might be atunstable 6.06 V excitation through a conditions closed-loop (varying using afrequency BSA-PI voltage and amplitude). controller In that this is regard suitable the for work micro-device might be extended for further experimentation in the future. applications.extended for further Naturally, experimentation vibration sources in the produce future. unstable excitation conditions (varying frequency and amplitude). In this regard the work might be extended for further experimentation in the future.

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Acknowledgments: This work was carried out with the financial support from the Ministry of Higher Education of Malaysia under the research grant DIP-2014-028. Author Contributions: Mahidur R. Sarker and Ramizi Mohamed conceived and designed the experiments; Mahidur R. Sarker performed the experiments; Mahidur R. Sarker, Ramizi Mohamed and Azah Mohamed analyzed the data; Ramizi Mohamed and Azah Mohamed contributed reagents/materials/analysis tools; Mahidur R. Sarker, Ramizi Mohamed and Azah Mohamed wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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