Inter national J our nal of P o wer Electr onics and Dri v e System (IJPEDS) V ol. 17, No. 1, March 2026, pp. 140 ∼ 154 ISSN: 2088-8694, DOI: 10.11591/ijpeds.v17.i1.pp140-154 ❒ 140 Modied r ey-optimized PI contr oller f or BLDC motor perf ormance under New Eur opean Dri ving Cycle conditions Dibyadeep Bhattacharya 1,2 , Raja Gandhi 3 , Chandan K umar 4 , Karma Sonam Sher pa 2 , Rak esh Roy 1 1 Department of Electrical Engineering, NIT Me ghalaya, Shillong, India 2 Electrical and Electronics Engineering, Sikkim Manipal Institute of T echnology , Sikkim Manipal Uni v ersity (SMU), Majitar , India 3 Department of Electrical Engineering, SCE Supaul, Bihar , India 4 Department of Electronic and communication Engineering, SCE Supaul, Bihar , India Article Inf o Article history: Recei v ed May 23, 2025 Re vised Dec 26, 2025 Accepted Jan 23, 2026 K eyw ords: Brushless direct current Modied rey algorithm Ne w European Dri ving Cycle P article sw arm optimization PI tuning ABSTRA CT This paper presents the application of a modied rey algorithm (MF A) for tuning the proportional-inte gral (PI) speed controller of a brushless direct current (BLDC) motor dri v e, tar geting impro v ed o v erall dynamic performance of the motor dri v e system for electric v ehicle (EV) applications. The controller’ s ef fecti v eness is e v aluated under tw o v ar iants of the Ne w European Dri ving Cycle (NEDC) to replicate real-w orld dri ving scenarios. T o v alidate the ef fecti v eness of the propos ed approach, a comparati v e study is carried out with tw o widely used optimization techniques, such as the standard rey algorithm (F A) and particle sw arm optimization (PSO). Comparati v e analysis re v eals that the MF A-tuned controller deli v ers superior speed tracking accurac y , with signicantly reduced speed error , speed ripple, and copper losses, when compared to controllers optimized using the standard rey algorithm (F A) and particle sw arm optimization (PSO). These impro v ements enhance both the ener gy ef cienc y and operational stability of the motor dri v e. Furthermore, the result of the e xperiment sho ws that the proposed controller demonstrates strong adaptability under v arying load and speed conditions, posi tioning it as a rob ust solution for both electric v ehicles and industrial motor control applications. This is an open access article under the CC BY -SA license . Corresponding A uthor: Raja Gandhi Department of Electrical Engineering, SCE Supaul Bihar 852131, India Email: rajag andhi1991@gmail.com 1. INTR ODUCTION The gro wing global emphasis on reducing greenhouse g as emissions and transitioning to w ards sustainable transportation has accelerated t he adoption of electric v ehicles (EVs). At the heart of EV propulsion systems lies the electric motor , which dire ctly inuences v ehicle performance, ener gy ef cienc y , and dri ving range. Among the v arious motor technologies, brushless direct current (BLDC) motors ha v e g ained prominence due to their high ef cienc y , compact size, lo w maintenance, and f a v ourable torque-speed characteristics. These attrib utes mak e BLDC motors well-suited for a wide range of EV applications, from tw o-wheelers to passenger cars [1]-[3]. Ho we v er , the performance of a BLDC motor is hea vily dependent on the ef fecti v eness of its control strate gy . Con v entional proportional-inte gral (PI) controllers are widely emplo yed for current and speed re gulation due to their simple structure and ease of implementation. Nonetheless, x ed-g ain PI controllers J ournal homepage: http://ijpeds.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 141 often struggle under dynamic load conditions and v arying dri ving c ycles, leading to suboptimal performance, particularly in terms of ener gy consumption and transient response [4]-[7]. In the literature, v arious techniques ha v e been emplo yed to tune PI controllers, with manual or con v entional tuning methods being the most common. Ho we v er , these approaches oft en f all short when applied to comple x and dynamic systems such as electric v ehicle (EV) motor dri v es. Their inability to adapt to v arying load conditions and system nonlinearities can lead to suboptimal performance, reduced ef cienc y , and poor control accurac y [8]-[10]. F or instance, in [11], a nonlinear model predicti v e control (NMPC) approach is introduced for BLDC motor control in EVs, tar geting the reduction of o v er -e xcitation, which causes unnecessary ener gy loss. By incorporating a nonlinear motor -load model, the NMPC optimizes v olt age inputs to minimize current and torque errors, enhancing ef cienc y and torque response under changing loads. A BLDC motor -based EV model using real-time dri ving c ycles w as de v eloped to e v aluate PI D, intelligent, h ybrid, and adapti v e supervis ory controllers [12]. The adapti v e supervisory controller achie v es the best results in ener gy ef cienc y and dri ving range, despite its dependence on training data. Building on these adv ancements, numerous optimization techniques based on articial intell igence (AI) ha v e been implemented to further enhance controller performance. T echniques such as fuzzy logic, neural netw orks, genetic algorithms (GA), particle sw arm optimization (PSO), whale optimization, gre y w olf optimization, ant optimization, and the B A T algorithm ha v e sho wn promise in ne-tuning controller parameters and impro ving system s tability and responsi v eness [13]. Ho we v er , each of these optimization techniques ha v e their o wn pros and cons. As in [14], a comparati v e analysis of tunning proportional-inte gral (PI) controller for controlling the speed re gulation of a brushless DC (BLDC) motor using parti cle sw arm optimization (PSO) and whale optimization algorithm (W O A) has been presented. The objecti v e is to reduce transient response time and enable f aster attainment of the desired speed in a closed-loop control system. A mathematical model of the BLDC motor has been de v eloped and simulated in Simulink, with the controller parameters (Kp and Ki) optimized using MA TLAB implementations of both PSO and W O A. The results indicate that the PI controller tuned with W O A performed better than its PSO counterpart by achie ving optimal g ain v alues in a v ery fe w iterations and with reduced computation time. Though W O A is kno wn for its straightforw ard yet ef fecti v e search methods that enable f ast identication of optimal solutions, W O A, lik e man y sw arm intelligence techniques, struggles with issues such as premature con v er gence, limited population di v ersity , and the risk of getting trapped in local optima [15]. Another study [16] presents the design of a b uck-boost con v erter -fed BLDC motor dri v e and e v aluates the motor’ s beha vior under PI, fuzzy logic, h ybrid PI-fuzzy , and gre y w olf optimization (GW O)-based controllers. K e y parameters such as speed, torque, o v ershoot, settling time, rise time, and steady-state error are analyzed, along with po wer quality f actors lik e total harmonic distortion (THD), crest f actor , and po wer f actor . Simulation and modeling are done using MA TLAB/Simulink and results ha v e sho wn that GW O of fers better o v erall performance with simpler computation compared to traditional techniques. GW O has sho wn strong performance in handling free optimization problems. Ho we v er , when applied to constrained optimization problems, where the search landscape becomes more comple x and irre gular , this leader -dri v en strate gy may lead to premature con v er gence. T o counter this, introducing randomness into the search process can help maintain population di v ersity and a v oid stagnation [17]. The result in [18] has applied neural approximation, friction compensation, and eccentricity c on t rol using simple acti v ation functions in designing a no v el nonlinear PI control method for nonlinear systems with unkno wn parameters and disturbances. Unlik e traditional adapti v e control, it ensures stability by dri ving error dynamics to a root of a perturbation function. The approach handles matched uncertainties and unkno wn control directions without high-g ain feedback. Among the other e v olving optimization techniques, the rey algorithm (F A), introduced by Y ang [19] in 2008, has g ained attention for its ef fecti v eness in solving comple x optimization problems. Inspired by the natural ashing beha vior of reies, F A relies on global communication among agents to ef ciently e xplore the search space and identify both local and global optimal solutions. Due to its simplicity , rob ustness, and high con v er gence spe ed, F A has been successfully applied in v arious elds such as pattern recognition, neural netw ork training, and clusteri ng [20]-[22]. In the conte xt of motor dri v e systems, F A has been emplo yed to optimize the parameters of PI controllers used in controlling induction motors, permanent magnet synchronous machines, and BLDC motors. As BLDC motors are increasingly being used in automoti v e, aerospace, and industrial applications, achie ving accurate and ef cient control under uctuating loads is essential [23], [24]. Despite its notable adv antages, the traditi o na l F A is not without limitations. One of the primary dra wbacks is its relati v ely high computational demand, as it often requires a lar ge number of iterations to achie v e con v er gence. This e xtended computation time can be particularly problematic in real-time Modied r ey-optimized PI contr oller for BLDC motor performance under ... (Dibyadeep Bhattac harya) Evaluation Warning : The document was created with Spire.PDF for Python.
142 ❒ ISSN: 2088-8694 or resource-constrained applications. Moreo v er , F A may suf fer from premature con v er gence or get trapped in local optima, especially in high-dimensional or comple x search spaces, which can limit its ef fecti v eness in nding truly optimal solutions for PI controller tuning in motor dri v e systems [25]. These challenges ha v e dri v en researchers to e xplore impro v ed v ariants of F A or entirely ne w metaheuristic algorithms that can of fer better con v er gence speed, enhanced global search capability , and reduced computational o v erhead. In response to these challenges, this paper proposes a modied v ersion of the rey algorithm aimed at reducing computation time while maintaining ef fecti v e performance. The k e y enhancement in v olv es restricting the search space of the reies within a dened range, which helps to focus the optimization process and achie v e f aster con v er gence. This modied F A is tested on a BLDC motor dri v e system, where it is used to tune the PI controller parameters more ef ciently . T o e v aluate the ef fecti v eness of the proposed approach, the motor’ s performance is tested using the Ne w European Dri ving Cycle (NEDC) [26], [27]. T w o distinct scenarios are considered to assess the algorithm under v arying operating conditions. The results are then compared ag ainst those obtained using tw o well-established optimization techniques, such as the standard rey algorithm (F A) and particle sw arm optimization (PSO), to demonstrate the superiority of the proposed method in terms of accurac y , response time, computational ef cienc y , and copper loss. The structure of the paper is di vided into se v en k e y sections. The follo wing section pro vides an o v ervie w of the BLDC motor control system. Secti on three introduces the mathem atical formulation of the modied rey algorithm. Section four outlines the algorithm o wchart in detail. Section v e e xplains the Ne w European Dri ving Cycle (NEDC), which is used to e v aluate the controller’ s performance. Section six presents the analysis of the results obtained, and the nal remarks and conclusions are also discussed in Section se v en. 2. BLDC MO T OR CONTR OL DRIVE A v ector control BLDC dri v es enables precise management of motor torque and speed by independently re gulating the ma gn e tic ux and the torque-producing currents. In this approach, a 1 kW BLDC motor is controlled using a speed controller dri v er circuit, specically emplo ying a PI-based controller as sho wn in Figure 1. This controller adjusts motor speed to match a reference command by monitoring and ne-tuning the current magnitudes. The dif ference between speed controller output and the actual current, measured via the current measurement block, is fed to the PI controller . The PI controller processes this error and generates a control signal that is then used to produce the in v erter g ate pulses required to ef fecti v ely re gulate the motor speed. The ability to achie v e such i mpro v eme nts highlights the crucial role of precise tuning of the PI parameters in ensuring ef cient and ef fecti v e BLDC motor control, thus making utilization of optimization techniques in such systems quiet and of fering benets lik e increased ef cienc y , rapid dynamic response, and reduced copper loss. Figure 1. Block diagram for rey algorithm-based v ector control of BLDC motor dri v e 3. MA THEMA TICAL FORMULA TION OF MODIFIED FIREFL Y OPTIMIZA TION TECHNIQ UES 3.1. Initial points calculation The direct torque control of the BLDC motor dri v e needs appropriate parameters of the PI controller for proper operation of the motor . The proportional ( K p ) and inte gral ( K i ) g ains must be within a limit for Int J Po w Elec & Dri Syst, V ol. 17, No. 1, March 2026: 140–154 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 143 running t he motor in stable conditions. The lo wer and upper bound of K p , K i g ain are termed as K p l b , K p ub , K i l b and K i ub respecti v ely . From these upper and lo wer bound the middle points are calculated as gi v en in (1). K p m = 0 . 5 ( K p ub + K p lb ) K i m = 0 . 5 ( K i ub + K i lb ) (1) Using the upper , lo wer bound, and middle point of K p , K i , eight points are chosen at the boundaries of K p and K i as gi v en i n (2) which is sho wn in Figure 2. The optimized v alue of K p and K i will be in between the re gion of these boundaries. All these eight points are considered as the pop of the rey optimization technique. Point 1 = ( K p lb , K i lb ) Point 2 = ( K p lb , K i ub ) Point 3 = ( K p ub , K i lb ) Point 4 = ( K p ub , K i ub ) Point 5 = ( K p m , K i lb ) Point 6 = ( K p m , K i ub ) Point 7 = ( K p lb , K i m ) Point 8 = ( K p ub , K i m ) (2) The upper and lo wer bounds of each particle ( K p and K i ) can be estimated using (3) and (4) [20]. K p = σ J 1 . 5 P ϕ f (3) K i = σ K p (4) Where, σ tuning coef cient, J is the rotor inertia, P is the number of poles and ϕ f is ux linkage. Figure 2. Boundaries of K p and K i 3.2. Determination of new K p and K i Initially , the objecti v e functions are calculated for rst tw o pops (point 1 and point 2). These tw o points are mark ed as P ointi [ K p ( i ) , K i ( i ) ] and P ointj [ K p ( j ) , K i ( j ) ]. By comparing these tw o objecti v e functions, the pop for higher objecti v e function is modied by follo wing (5)-(15). In the process, four parameters ( α , β 0 , θ and γ ) are considered as constant. Here α is randomness st rength which v aries from 0 to 1 randomly . it controls the de gree of randomness in rey mo v ement. Higher alpha (closer to 1) leads to more e xploration of the search space while a lo wer alpha (closer to zero) leads to more e xploitation (focusing on promising areas already disco v ered). β 0 is attracti v eness constant. it determines the inuence of a rey attracti v eness on the other reies. higher β 0 leads to stronger attraction, guiding it to a better result while lo wer β 0 leads Modied r ey-optimized PI contr oller for BLDC motor performance under ... (Dibyadeep Bhattac harya) Evaluation Warning : The document was created with Spire.PDF for Python.
144 ❒ ISSN: 2088-8694 to weak er attraction, allo wing more di v erse e xploration. γ is absorption coef cient. it controls the intensity of light absorption by other reies. Higher g amma means rey are more inuenced by other brighter reies leading to f aster con v er gence, while lo wer g am ma allo ws for more free mo v ement in the search s p a ce. θ is randomness reducti on f actor . It go v erns ho w much the randomness ( al pha ) is reduced o v er iterat ions. Higher theta leads to decrease in randomness allo wing e xploration in more promising area. Lo wer theta means higher de gree of randomness throughout, which indicates continuati on of the e xploration. The α 1 is c alculated from alpha and theta as gi v en in (5). Using the K p , K i v alue for P ointi and P o intj , the xK p and x K i are calculated using (6) and (7). The xK p and x K i are the components of ne w K p and K i . From the upper and lo wer bounds, the scal eK p and scal eK i are calculated as gi v en in (8) and (9). β is calculated from β 0 , γ and r which is gi v en in (10), where r is obtained from pointi and pointj using (11). α 1 = α θ (5) xK p = 0 . 5( K p ( i ) + K p ( j )) (6) xK i = 0 . 5( K i ( i ) + K i ( j )) (7) scal eK p = | K p ub − K p l b | (8) scal eK i = | K i ub − K i l b | (9) β = β 0 e − γ r 2 (10) r = q [ K p ( i ) − K p ( j )] 2 + [ K i ( i ) − K i ( j )] 2 (11) Finally , the ne w K p and K i are calculated using (14) and (15). K p ( new ) = K p ( i ) + β [ K p ( j ) − K p ( i )] + stepsK p (12) K i ( new ) = K i ( i ) + β [ K i ( j ) − K i ( i )] + stepsK i (13) Here the stepsK p and stepsK i of (12) and (13) are calculated using (14) and (15), where r andK p and r andK i are v ery important parameters. In con v entional rey algorithm, the r andK p and r andK i are considered an y random v alues. So the selection of the ne w K p and K i has no selecti v e area. stepsK p = α 1( r andK p − xK p ) scal eK p (14) stepsK i = α 1( r andK i − xK i ) scal eK i (15) Figure 3. Illustration of the proposed tuning process for the PI controller parameters: (a) determination of the upper and lo wer limits of ne w of K p and K i (b) selecti v e search re gion in the K p and K i plane In the modied rey algorithm, the r andK p and r andK i are chosen within a range so that the ne w K p and k i must be within a selecti v e area . F or that limits of r andK p and r andK i are obtained by substituting Int J Po w Elec & Dri Syst, V ol. 17, No. 1, March 2026: 140–154 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 145 K p ( new ) = K p ( i ) , K p ( new ) = K p ( j ) and K i ( new ) = K i ( i ) , K i ( new ) = K i ( j ) into the update equations (12) and (13) respecti v ely . The v alues obtained from these substitutions are then compared with (14) and (15), which pro vide the lo wer and upper limits of the g ains. As a result, the bounds of r andK p re obtained in (16) and (17), while the bounds of r andK i are gi v en in equations (18) and (19) as illustrated in Figure 3(a). The shaded re gion i n the illustrati v e diagram Figure 3(b) represents the selecti v e search space where the ne w parameters are chosen, ensuring a focused and ef cient e xploration in modied rey algorithm (MF A). r andK p l = β [ K p ( i ) − K p ( j )] α 1 scal eK p + [ K p ( i ) + K p ( j )] 2 (16) r andK p u = [1 − β ][ K p ( j ) − K p ( i )] α 1 S cal eK p + [ K p ( i ) + K p ( j )] 2 (17) r andK i l = [1 − β ][ K i ( j ) − K i ( i )] α 1 S cal eK p + [ K i ( i ) + K i ( j )] 2 (18) r andK i u = [1 − β ][ K i ( j ) − K i ( i )] α 1 S cal eK i + [ K i ( i ) + K i ( j )] 2 (19) In con v entional methods, r andK p and r andK i are chosen an y random v alues. Ho we v er by choosi ng the random v alues in a suitable manner will gi v e the more optimized v alues. The random choosing of these v alues will search in the area of K p and K i randomly . Ho we v er , by shrinking the searching area to w ards the best optimized v alue will gi v e the better results in the performance of the motor dri v e. 4. FLO WCHAR T OF THE MODIFIED FIREFL Y OPTIMIZA TION TECHNIQ UE The o wchart of the modied rey optimization technique is sho wn in Figure 4 and is e xplained belo w in step wise. - Step 1 : All the parameters are initialized in rst step. Here the α , β , θ and γ are selected as some constant v alues within their range. Eight bounce points are calcul ated from the upper and lo wer bound of K p and K i using (2). i, j and number of iteration (iter) are also initialized as 1. - Step 2 : In this step, objecti v e functions are calculated for point i and point j and the y are termed as F x ( p ) and F x ( q ) respecti v ely . - Step 3 : Here F x ( p ) and F x ( q ) are compared. If F x ( p ) v alue is higher than F x ( q ) , point i will be modied in step 4. If F x ( q ) v alue is higher than F x ( p ) , no modication will tak e place and it will jump to step 6. - Step 4 : This step gi v es the calc u l ation of ne w K p , K i using (5) to (19) and the ne w objecti v e function F x ( r ) is determined. - Step 5 : The ne w objecti v e function F x ( r ) is compared with F x ( p ) in this step. If F x ( r ) is less than F x ( p ) , F x ( p ) is upgraded to F x ( r ) and the po p i is upgraded with ne w K p and K i . In case F x ( p ) is less than F x ( r ) , no modication will be done in popi and it will go to step 6. - Step 6 : In this step, j is upgraded to ne xt v alue if it is not reached to maximum numbe r of operands ( M AX P O P ) and it will go to step 2 ag ain. If j reaches to maximum v alue, it will go to step 7. - Step 7 : Here, i is upgraded to ne xt v alue if it is not reached to maximum number of operands ( M AX P O P ). j is also initialized to 1 and ag ain jump to step 2. In case i reaches to maximum v alue, it will go to step 8. - Step 8 : Here number of iteration is check ed whether it has reached to maximum v alue or not. If it does not reaches the maximum v alue, it will be increased to ne xt number and jump to step 2. When it reaches the maximum v alue it will go to step 9. - Step 9 : When all the iterations are completed, the best v alue (lo west objecti v e function) is stored and the corresponding K p and K i are considered as optimized K p and K i . In the rst step initializati on of the required parameters for the modied rey algorithm i s done, which is customized specically for the objecti v e of speed control in the BLDC motors. The problem dimensions of the problem search space which is denoted as D is set to 2, it reects that tw o control parameters are essential for the speed re gulation, which are proportional g ain (Kp) and the inte gral g ain (Ki). These parameters are chosen based on the BLDC motor characteristics to ensure that the problem objecti v e are met. Nop denotes the number of population of the reies which is set to 8. This helps to create a balance between Modied r ey-optimized PI contr oller for BLDC motor performance under ... (Dibyadeep Bhattac harya) Evaluation Warning : The document was created with Spire.PDF for Python.
146 ❒ ISSN: 2088-8694 computational comple xity and e xploration capability . The upper bounds (ub) and the lo wer bounds (lb) for the Kp and Ki are determined according to the motor parameters. This bounds helps the algorithm to nd optimal v alue in which the motor can operate with ef fecti v e speed control. T o terminate the algorithm and nd a suitable con v er gence point the maximum number of iteration (maxIter) is set to 2. There are some control parameters such as alpha, which are randomness strength which v aries from 0 to 1 and it is highly random, beta0 which is attracti v eness coef cient, g amma which is absorpti on coef cient and theta which is randomness reduction f actor , these parameters are congured to inuence the beha vior of the reies, there v alues are selected s uch that the e xploration and e xploitation capabilities increases. Furthermore, the initial position of the rey particles which is denoted as pop are such that it is under a dened bound, with 8 or 4 v alues at e v ery corner such that all the points in a search space is co v ered, so that the algorithm does not al w ays search in one place. The iteration count (iter) be gins from 1 with loop indices as i and a counter j both their v alues starts at 1. W ith these the iterati v e process be gins for optimizing the control parameters which is Kp and Ki. Figure 4. Flo wchart of modied rey optimization technique 4.1. Attracti v eness and mo v ement The ne xt step calculates the attracti v eness and the mo v ement of the rey . It in v olv es e v aluating the objecti v e function of the tw o positions of the reies at Fx(p) and Fx(q) for the generated population pop(i) and pop(j) respecti v ely . The objecti v e function Fx performs an inte gral time square error (ITSE) operation on each of the position of the rey . The attracti v eness of the rey depends on the objecti v e function v alues, the lo wer the ITSE v alue the higher will be the attracti v eness. The rey shifts its position to the more attracti v e rey , this attracti v e get inuenced by the randomness f actor which is alpha. This step helps the rey get attracted to the most promising v alue for ef fecti v e speed control in BLDC motor . 4.2. Comparison between Fx(r) and Fx(p) This step compares the tness function of Fx(p) and Fx(q) for the current iteration (p) with the tness function for the pre vious iteration (q). If the current t ness function is greater it means the rey position Int J Po w Elec & Dri Syst, V ol. 17, No. 1, March 2026: 140–154 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 147 is good for speed performance of the BLDC motor , therefore the algorithm proceeds to step number 4. If the current tness function is not greater (NO), it indicated the rey position will not impro v e the speed performance therefore the algorithm mo v es to step 6. 4.3. Determination of new Kp and Ki In this s tep, the ne w v alues of Kp and Ki are calculated based on the (5) to (19) and the ne w obj ecti v e function F x ( r ) is determined. 4.4. Comparison between Fx(r) and Fx(p) This step compares the tness function of the ne w iteration (r) for the ne w v alues of Kp and Ki with the tness function of the pre vious iteration (p). As the algorithm is dened to perform a minimization operation therefore if the ne w tness function v alue is lo wer (YES) then the pre vious tness function v alue it means the ne w Kp and Ki did impro v e the performance of the motor therefore it will assign the ne w v alue of kp and ki to the tness function of Fx(p). If the ne w tness function is higher , it indicates that the ne w v alues did not impro v e the performance so the algorithm shift to step 6. 4.5. Check whether the counter j r eached the max pop v alue If the inde x j reaches its maximum v alue of pop it then checks goes to the ne xt step to check the inde x i. if j is not equal to the maximum v alue of pop the algori thm increments the inde x j. If j is equal to maximum pop it indicates that all the possible v alues of Ki for the current Ki ha v e been e v aluated and e xplored, so the algorithm mo v es to step 7. 4.6. Check whether the counter i r eached the max pop v alue If the inde x i reaches its maximum v alue of pop it then checks goes to the ne xt step to check the inde x i. if i is not equal to the maximum v alue of pop the algori thm increments the inde x i. If i is equal to maximum pop it indicates that all the possible v alues of Kp for the current Kp ha v e been e v aluated and e xplored, so the algorithm mo v es to step 8. 4.7. Checking of algorithm stopping criteria Check if the iteration counter has reached its maximum v alue i.e whether iter = Maxiter . If the iterati on is equal to maximum iteration (YES) that means the algorithm has reached its limit so the algorithm mo v es to step 9 to stop the algorithm. If iteration is not equal to maximum iteration the algorithm increments the iteration and ag ain starts the process from step 2. 4.8. End This process ends the algorithm sho wing us the best v alues stored in pop, which will be the opti mized Kp and ki v alues. At the end of the algorithm, the algorithm displays the con v er gence graph and also the cost function v alues. 5. NEW EUR OPEAN DRIVING CYCLE (NEDC) FOR CONTR OLLER PERFORMANCE EV ALU A TION The Ne w European Dri ving Cycle is a widely accepted standardized dri ving pattern de v eloped to e v aluate the ener gy ef cienc y and performance of v ehicles under simulated conditions. It is designed to replicate real-w orld dri ving beha vior , including both city traf c and highw ay scenarios. This c ycle is particularly suitable for assessing electric v ehicle (EV) performance, making it an ideal benchmark for v alidating motor controllers such as those used in BLDC motor dri v e systems. The NEDC consists of tw o distinct parts: an urban dri ving se gment and an e xtra-urban se gment. The urban phase, kno wn as the urban dri ving c ycle (UDC), simulates lo w-speed city dri ving with frequent stops, starts, and idle periods. Co v ers a distance of approximately 4.052 kilometers o v er a duration of 195 seconds. This phase includes multiple acceleration and decelerati on patterns to mimic congested traf c conditions, as sho wn in Figure 5(a). The e xtra-urban phase, called the Extra-Urban Dri ving Cycle (EUDC), represents high-speed dri ving typically seen on highw ays or open roads. It co v ers around 6.955 kilometers in 400 seconds, with speeds ranging up to 120 kilometers per hour which is nearly 2000 rpm as sho wn in Figure 5(b). The NEDC is used as a dynamic input to e v aluate the performance of an optimized BLDC motor controller . The controller parameters are tuned usi ng the rey algorithm to enhance the motor’ s ef cienc y , dynamic response, and minimize the copper losses. Applying the NEDC as the speed reference prole in Modied r ey-optimized PI contr oller for BLDC motor performance under ... (Dibyadeep Bhattac harya) Evaluation Warning : The document was created with Spire.PDF for Python.
148 ❒ ISSN: 2088-8694 simulations enabl es the testing of the controller under v arying operational conditions. This includes assessing its beha vior during acceleration, deceleration, and steady-state phases, which are all inte gral parts of the NEDC. Figure 5. V ehicle speed proles under Ne w European Dri ving Cycle (NEDC): (a) lo w-speed urban dri ving se gment and (b) high-speed highw ay se gment 6. RESUL TS AND DISCUSSION The modied rey algorithm (MF A) is implemented in MA TLAB/Simulink as sho wn in Figure 6 with optimize PI speed control parameters for BLDC dri v e. The motor specications used for the e xperiments are listed in T able 1. T o e v aluate the ef fecti v eness of the MF A-based PI controller , its performance w as compared with tw o other commonly used tuning methods such as standard rey algorithm and particle sw arm optimization (PSO) technique. T o e v aluate the performance of these optimize controlle r , the tw o k e y scenarios of Ne w European Dri ving Cycle are considered and tested such as lo w-speed operation with frequent start-stop and high-speed dri ving with acceleration. In each case, the motor’ s speed response and copper loss are closely monitored and analyzed. In motor response the k e y parameter are speed ripple and speed error were measured to assess controller performance. The specications and parameter settings of all the algorithms used in this study are summarized in T able 2. Figure 6. Simulation model of BLDC motor dri v e with optimized PI controller in MA TLAB/Simulink Int J Po w Elec & Dri Syst, V ol. 17, No. 1, March 2026: 140–154 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 149 T able 1. BLDC motor specication P arameters V alue Unit Rated po wer 1 kW Rated v oltage 48 V olt Rated current 3 Amp Rated speed 3000 rpm Inductance 0.309 mH T orque constant 0.33 Nm/A Resistance 0.75 Ω T able 2. Initial and additional parameters Initial P arameters Additional P arameters F A, PSO & MF A V alue MF A V al ue PSO V alue P article size ( n max ) 15 γ 0.1–1 ω max 0.9 Iteration ( m max ) 25 β 0 0.5–1 ω min 0.4 K p range 0–10 α 0–1 c 1 , c 2 1.5 K i range 0–8 6.1. Case 1: Lo w-speed urban dri ving (stop-and-go conditions) During the initial phase of the NEDC c ycle (0–200 seconds), the v ehicle operates at lo w speeds with frequent accelerations and decelerations, resembling typical city traf c conditions with v ariable input load as sho wn in Figures 7 and 8. This se gment is critical for assessing ho w ef fecti v ely the controller manages abrupt changes in speed and load. Three optimization techniques are applied to tune the speed controller i n the NEDC c ycle: PSO-based PI tuning, the rey algorithm, and modied rey algorithm-based PI tuning. The results of these three tuning methods, that is, speed and current response, are depicted in Figures 8(a)-8(c), respecti v ely . Figure 7. V ariable load torque applied to lo w-speed urban dri v e All three controllers track the reference speed accurately . Ho we v er , from the observ ations, it is e vident that the modied rey algorithm pro vides superior performance compared to the other tw o con v entional optimization techniques. The modied rey-optimized BLDC controller e xhibits quick responsi v eness to frequent accelerations and braking, ensuring precise speed control throughout. Ev en with constant stops and starts, the motor runs smoothly without an y noticeable jerks or delays. This demonstrates that the controller is highly suited for urban dri ving, of fering enhanced control and a more comfortable dri ving e xperience in hea vy traf c compared to the other tw o tuning methods. T able 3 presents additional parameters for comparison, where performance is e v aluated based on speed ripple, speed error , and copper loss. These losses are calculated using (20)-(22). The results indicate that the modied rey algorithm deli v ers the best o v erall performance. Speed Error = | ω r ef − ω act | ω r ef ∗ 100 (20) Speed Ripple = | ω max − ω min | ω av g ∗ 100 (21) Copper Loss = ( I 2 a + I 2 b + I 2 c ) ∗ R ∗ T ime (22) Where, ω max and ω min are maximum and minimum speed v alue during steady state speed. T able 3. Comparison of parameters at stop-and-go conditions P arameter Experimental Result PSO F A MF A Speed error (%) 0.018 0.038 0.012 Speed ripple (%) 12.2 16.63 10.1 Copper loss (kWh) 0.281 0.273 0.265 Modied r ey-optimized PI contr oller for BLDC motor performance under ... (Dibyadeep Bhattac harya) Evaluation Warning : The document was created with Spire.PDF for Python.