- Email: [email protected]
Average Torque Control of a Switched Reluctance Motor Drive for Light Electric Vehicle Applications*
Proceedings of the 20th World Congress Proceedings of 20th Proceedings of the the 20th World World Congress The International Federation of Congress Automatic Control Proceedings of the 20th World Congress The International Federation of Control The International Federation of Automatic Automatic Control Toulouse, France, July 9-14, 2017 Available online at www.sciencedirect.com The International Federation of Automatic Control Toulouse, Toulouse, France, France, July July 9-14, 9-14, 2017 2017 Toulouse, France, July 9-14, 2017
ScienceDirect
IFAC PapersOnLine 50-1 (2017) 11535–11540
Average Torque Control of a Switched Average Torque Control of a Switched Average Torque Control of a Average Torque Control ofLight a Switched Switched Reluctance Motor Drive for Electric Reluctance Motor Drive for Light Reluctance Motor Drive for Light Electric Electric ReluctanceVehicle Motor Applications Drive for Light Electric Vehicle Applications Vehicle Applications Vehicle Applications
Muhammad Usman Jamil ∗∗ Waree Kongprawechnon ∗∗ ∗ Muhammad Usman Jamil Jamil ∗∗ Waree Kongprawechnon ∗∗ Muhammad Waree ∗ Nattapon ∗∗ Muhammad Usman Usman JamilChayopitak Waree Kongprawechnon Kongprawechnon ∗∗ Nattapon Chayopitak Nattapon Chayopitak ∗∗ Nattapon Chayopitak ∗ ∗ School of Information, Communication and Computer Technologies ∗ School of Information, Communication and Computer Technologies Information, Communication and Computer Technologies ∗ School (ICT),of International Institute Technology (SIIT), School ofSirindhorn Information, Communication andof Computer Technologies (ICT), Sirindhorn International Institute of Technology (SIIT), (ICT), Sirindhorn International Institute of Technology (SIIT), usman [email protected], Thammasat University, Thailand (e-mail: m (ICT), Sirindhorn Institute of Technology (SIIT), Thammasat University,International Thailand (e-mail: (e-mail: m usman usman [email protected], Thammasat University, Thailand m [email protected], [email protected], [email protected]). Thammasat University, Thailand (e-mail: m usman [email protected], [email protected], [email protected]). ∗∗ [email protected], [email protected]). Electronics and Computer Technology Center (NECTEC), ∗∗ National [email protected], [email protected]). ∗∗ National Electronics and Computer Technology Center (NECTEC), and Computer Technology Center ∗∗ National Electronics 112 Thailand Science Park, Thailand (e-mail: National Electronics and Computer Technology Center (NECTEC), (NECTEC), 112 Thailand Science Park, Thailand (e-mail: 112 Science [email protected]) 112 Thailand Thailand Science Park, Park, Thailand Thailand (e-mail: (e-mail: [email protected]) [email protected]) [email protected]) Abstract: In this paper, an online average torque control (ATC) of a switched reluctance motor Abstract: In this paper, an online average torque control (ATC) of aa switched reluctance motor Abstract: In paper, an average torque (ATC) (SRM) for light electric vehicle (LEV) applications is proposed. The purpose reluctance of the ATCmotor is to Abstract: In this this paper,vehicle an online online average torque control control (ATC) of of a switched switched reluctance motor (SRM) for light electric (LEV) applications is proposed. The purpose of the ATC is to (SRM) for light electric vehicle (LEV) applications is proposed. The purpose of the ATC is to control for thelight average torque in the mostapplications inner control loop to stabilize the system dynamics. (SRM) electric vehicle (LEV) is proposed. The purpose of the ATC is to control the average torque in the most inner control loop to stabilize the system dynamics. control the average torque in the most inner control loop to stabilize the system dynamics. This is carried out by estimating the average torque at every time instant by considering the control the average torque in the most inner control loop to stabilize the system dynamics. This is carried out by estimating the average torque at every time instant by considering the This carried out the average torque at instant by the motorisprimary parameters, i.e., rotor position, speed, and phasetime currents. To achieve the desired This carried parameters, out by by estimating estimating theposition, average speed, torqueand at every every instant by considering considering the motorisprimary primary i.e., rotor rotor phasetime currents. To achieve achieve the desired desired motor parameters, i.e., position, speed, and phase currents. To averageprimary torque parameters, in wide speed range and controller efficiency forcurrents. traction To control, thethe proposed motor i.e., rotor position, speed, and phase achieve the desired average torque in wide speed range and controller efficiency for traction control, the proposed average torque speed and traction the proposed ATC algorithm is wide designed torange adjust thecontroller changingefficiency referencefor current andcontrol, switching angles to average torque in inis wide speedto range and controller efficiency for traction control, the angles proposed ATC algorithm designed adjust the changing reference current and switching to ATC algorithm is designed to adjust the changing reference current and switching angles to obtain the desired average torque at the operating speed. This paper also proposes a torque ATC algorithm is designed to adjust the changing reference current and switching angles to obtain the desired average torque at the operating speed. This paper also proposes aa torque obtain the desired average at operating speed. paper also estimation method based ontorque the Fourier Series approximation of the inductance profile to obtain obtain the method desired based average torque at the the operating speed. This This paper also proposes proposes a torque torque estimation on the Fourier Series approximation of the inductance profile to obtain estimation method based on the Fourier Series approximation of the inductance profile to obtain accurate torque estimation results. The Series simulation of a 3 kW,of6/4 SRM for LEV application is estimation method based on the Fourier approximation the inductance profile to obtain accurate torque estimation results. The simulation of a 3 kW, 6/4 SRM for LEV application is accurate torque estimation results. The simulation of a 3 kW, 6/4 SRM for LEV application is used to demonstrate the effectiveness of simulation the proposed method. accurate torque estimation results. The of a 3 kW, 6/4 SRM for LEV application is used to demonstrate the effectiveness of the proposed method. used to demonstrate the effectiveness of the proposed method. used to demonstrate the effectiveness of the proposed method. © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: average torque control, switched reluctance motor, light electric vehicle Keywords: Keywords: average average torque torque control, control, switched switched reluctance reluctance motor, motor, light light electric electric vehicle vehicle Keywords: average torque control, switched reluctance motor, light electric vehicle 1. INTRODUCTION The torque control of a SRM does not depend upon the 1. INTRODUCTION INTRODUCTION The torque control of a SRM does not depend upon the 1. The torque control of SRM the reference model control e.g., not fielddepend orientedupon control. 1. INTRODUCTION The torque control of aatheory, SRM does does not depend upon the reference model control theory, e.g., field oriented control. reference model control theory, e.g., field oriented control. However, model the torque control is e.g., attained by adjusting all control theory, field oriented control. As vehicle production has been continuously increasing reference the torque control is attained by adjusting all As vehicle vehicle production production has has been been continuously continuously increasing increasing However, However, the torque control attained by adjusting all control variables according tois precalculated or measured As However, the torque control is attained by adjusting all all over the globe, the conspicuous problems brought control variables according to precalculated or measured As vehicle production hasconspicuous been continuously increasing all over the globe, the problems brought control variables according to precalculated or measured functions (J. Zhang, 2015). In indirect instantaneous all over the globe, the conspicuous problems brought control variables according to In precalculated or measured by over vehicles have become a great concern these days. functions (J. Zhang, 2015). indirect instantaneous all the globe, the conspicuous problems brought by vehicles vehicles have have become become aa great great concern concern these these days. days. functions (J. 2015). In indirect torque control (IITC), the torque a SRMinstantaneous is a cascade by In of indirect (J. Zhang, Zhang, 2015). Thus, many have countries all over the globe, suchthese as China, torque control control (IITC), the the torque of SRMinstantaneous is a cascade by vehicles become a great concern days. functions Thus, many countries all over the globe, such as China, torque (IITC), torque of aaainstantaneous SRM is function, controlled by regulating the phase Thus, many countries all over the globe, such as China, torque control (IITC), the torque of SRM is aa cascade cascade Japan, etc., have started research on zero emission electric function, controlled by regulating the instantaneous phase Thus, many countries all over the globe, such as China, Japan, etc., have started research on zero emission electric function, controlled by regulating the instantaneous phase currents (K. Sahoo, 2005). In direct instantaneous torque Japan, have started research on controlled by regulating theinstantaneous instantaneoustorque phase vehiclesetc., (EVs). The benefits of EVs areemission energy electric saving, function, currents (K. Sahoo, 2005). In direct Japan, etc., haveThe started research on zero zero emission electric vehicles (EVs). benefits of EVs are energy saving, currents (K. 2005). In instantaneous control (DITC), a digital hysteresis controllertorque is devehicles (EVs). The EVs saving, currents (K. Sahoo, Sahoo, 2005). In direct directtorque instantaneous environmental friendliness, safeofdriving, lowenergy maintenance, control (DITC), (DITC), digital hysteresis torque controllertorque is devehicles (EVs).friendliness, The benefits benefits EVs are arelow energy saving, control environmental safeofdriving, driving, maintenance, aaaa digital hysteresis torque controller is signed to obtain high bandwidth for the drive. However, environmental friendliness, safe low maintenance, control (DITC), digital hysteresis torque controller is dedeand low noise friendliness, pollution (Wang Yan, 2011). Moreover, signed to obtain a high bandwidth for the drive. However, environmental safe driving, low maintenance, and low low noise noise pollution pollution (Wang (Wang Yan, Yan, 2011). 2011). Moreover, Moreover, signed to obtain aa high bandwidth for the drive. However, the torque is estimated by using the terminal quantities, and signed to obtain high bandwidth for the drive. However, in the present EVs, several types of motors are being the torque torque is is estimated estimated by by using using the terminal terminal quantities, quantities, andthe lowpresent noise pollution (Wang Yan, 2011). Moreover, in EVs, several several types of motors motors are being being the i.e., torque phase isvoltages andbycurrents Inderka, 2003a). in the present EVs, types are estimated using the the(R. terminal quantities, used, such as, DC motors, induction motor, permanent i.e., phase phase voltages voltages and currents currents (R. Inderka, 2003a). in thesuch present EVs,motors, severalinduction types of of motor, motors permanent are being the used, as, DC i.e., and (R. Inderka, 2003a). Various control methods have been proposed in the last used, such as, DC motors, induction motor, permanent i.e., phase voltages and have currents Inderka, 2003a). magnetsuch motor, and motors, switchedinduction reluctancemotor, motors. The key Various control methods been (R. proposed in the the last used, as, DC permanent magnet motor, and switched reluctance motors. The key Various control methods have been proposed in few decades to control and estimate torque, and alsolast to magnet motor, and switched reluctance motors. The key Various control methods have been proposed in the last advantage of the switched reluctance motor (SRM) is few decades to control and estimate torque, and also to magnet motor, and switched reluctance motors. The key advantage of of the the switched switched reluctance reluctance motor motor (SRM) (SRM) is is few decades control and torque, and also to minimize the to torque ripples ofestimate SRMs, (D. A. Torrey, 2015); advantage few decades to control and estimate torque, and also to that, it has a simple mechanical construction, i.e., a minimize the torque ripples of SRMs, (D. A. Torrey, 2015); advantage of the switched reluctance motor (SRM) is that, it it has has aa simple simple mechanical mechanical construction, construction, i.e., i.e., aa Sezen, minimize the ripples of A. 2015); 2016; C. Salame, 2015; Salem,(D. 2014; R. In-derka, that, minimize the torque torque ripples of SRMs, SRMs, A. Torrey, Torrey, 2015); purely laminated steel structure exists without theany Sezen, 2016; C. Salame, Salame, 2015; Salem,(D.2014; 2014; R. In-derka, In-derka, that, itlaminated has a simple construction, i.e., a Sezen, purely steel mechanical structure exists exists without theany theany 2016; C. 2015; Salem, R. 2003b). In hybrid combination of direct torque control purely laminated steel structure without Sezen, 2016; C. Salame, 2015; Salem, 2014; R. In-derka, rotor windings, permanent magnets,exists or squirrel cage bars. 2003b). In hybrid combination of direct torque control purely laminated steel structure without theany rotor windings, windings, permanent permanent magnets, magnets, or or squirrel squirrel cage cage bars. bars. 2003b). combination of torque control (DTC)-sliding mode control (SMC), torque is rotor 2003b). In In hybrid hybrid combination of direct direct the torque control Hence,windings, robustness in operation, and high reliability exists (DTC)-sliding mode control (SMC), (SMC), the torque is rotor permanent magnets, or squirrel cage exists bars. (DTC)-sliding Hence, robustness in operation, and high reliability mode control the torque is estimated by taking in to account the phase flux and phase Hence, robustness in operation, and high reliability exists (DTC)-sliding mode control (SMC), the torque is in a SRM (D. A. Torrey, 2015; Shahakar, 2013). estimated by taking in to account the phase flux and phase Hence, robustness in operation, and high reliability exists in aa SRM SRM (D. A. A. Torrey, 2015; 2015; Shahakar, 2013). 2013). estimated by taking the flux phase current. of the adaptive torque controller in estimatedThe by performance taking in in to to account account the phase phase flux and and phase current. The performance of the the adaptive adaptive torque controller in a SRM (D. (D. A. Torrey, Torrey, 2015; Shahakar, Shahakar, 2013). current. The performance of torque controller is also analyzed by considering the mismatch disturbance current. The performance of the adaptive torque controller is also analyzed by considering the mismatch disturbance is also analyzed considering mismatch disturbance and uncertainties (Salem, 2014). In high is alsoparameter analyzed by by considering the the mismatch disturbance This research project is supported by Sirindhorn International and parameter uncertainties (Salem, 2014). In high and parameter uncertainties (Salem, 2014). In dynamics DTC for SRM, the reference torque is controlled This research project is supported by Sirindhorn International This research and parameter uncertainties (Salem, 2014). In high high project is supported by Sirindhorn International Institute of Technology (SIIT), Thammasat University, and the This research project is supported by Sirindhorn International dynamics DTC for SRM, the reference torque is controlled for SRM, the reference torque is controlled dynamics DTC Institute of (SIIT), University, and by using the energy ratio estimation technique and also by dynamics DTC for SRM, the reference torque is controlled Institute Electronics of Technology Technology (SIIT), Thammasat Thammasat University, and the the National and Computer Technology Center (NECTEC) by using the energy ratio estimation technique and also by Institute of Technology (SIIT), Thammasat and the National Electronics and TechnologyUniversity, Center (NECTEC) by using energy ratio technique and also changing the switching angles (R. Inderka, National Electronics and Computer Computer Center (NECTEC) of Thailand for the Excellent Foreign Technology Student (EFS) Scholarship and by using the the energy ratio estimation estimation technique and 2003b). also by by changing the switching angles (R. Inderka, 2003b). National Electronics and Computer Technology Center (NECTEC) of for Excellent Foreign Student (EFS) Scholarship and changing the angles (R. Inderka, 2003b). Feedback linearization torque (FL-DTC) of Thailand Thailand for the the Foreign Student (EFS) Scholarship and the equipments forExcellent this research. The research project is partially changing the switching switchingdirect angles (R. control Inderka, 2003b). of Thailand for the Excellent Foreign Student (EFS) Scholarship and Feedback linearization linearization direct torque control (FL-DTC) the for research. The project is Feedback direct torque control (FL-DTC) the equipments equipments for this thisResearch research.Universities The research research project is partially partially funded by the National (NRU) by the Office of based on space vector modulation is used to control the Feedback linearization direct torque control (FL-DTC) the equipments for this research. The research project is partially funded the Research Universities (NRU) Office based on on space space vector vector modulation modulation is is used used to to control control the the funded by by the National National Research(HEC), Universities (NRU) by by the the Office of of based Higher Education Commission and Thammasat University, torque and also to reduce the torque and stator flux funded by the National Research Universities (NRU) by the Office of based is used to flux control the Higher the torque and stator torque on andspace also to tovector reducemodulation Higher Education Education Commission Commission (HEC), (HEC), and and Thammasat Thammasat University, University, Thailand. torque and also reduce the torque and stator flux Higher Education Commission (HEC), and Thammasat University, torque and also to reduce the torque and stator flux Thailand. Thailand.
Thailand. Copyright © 2017, 2017 IFAC 12027 2405-8963 © IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2017 IFAC 12027 Copyright ©under 2017 responsibility IFAC 12027 Peer review of International Federation of Automatic Control. Copyright © 2017 IFAC 12027 10.1016/j.ifacol.2017.08.1628
Proceedings of the 20th IFAC World Congress 11536 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
ripples (Y. Choi, 2016). The iterative learning control method is used to control and estimate torque of a SRM by combing the P-type feedback controller with an iterative learning controller (ILC) (K. Sahoo, 2005). However, DTCsliding mode control, feedback linearization DTC, and sliding mode control based estimation of SRM by using ILC, and IITC based field oriented schemes are all model base techniques. The exact dynamics of the motor need to be known to control and estimate the torque of SRM. Moreover, in these techniques torque is estimated by considering the primary and secondary parameters of a motor, i.e., terminal phase currents, voltages, and flux linkages. Furthermore, the literature discussed above reveals that the torque is also estimated by using the Fourier series (FS) of the inductance profile up to the 3rd or more harmonics. Hence, this increases the system complexity (C. Moron, 2012). To overcome these issues, an average torque control (ATC) of a SRM drive for LEVs is proposed. The linear estimated torque of a SRM for LEVs is obtained by accumulating the torque of each phase, and a linear magnetic model of a SRM is established to estimate an average torque. The estimated inductance and flux-linkage of a SRM with their FS is considered only for first harmonics. Consequently, in order to control the average torque in SRM traction, control/drive control is used. The purpose of this classical control is to adjust all control variables of a drive at every operating point, i.e., reference current, turning on and turning off the switching angles. These control variables are being set for the entire operating range according to the predetermined lookup tables. These lookup tables play an important role for properly selecting the control variables for each operating point and also depend upon the reference torque, and the speed of the motor for LEV applications. Hence, the key advantages of the proposed control are: a) it has the highest degree of flexibility and control level b) it provides the minimum speed to hight speed operational area c) it provides fast torque control. 2. DYNAMICS AND MODELING DESCRIPTION OF A SRM DRIVE 2.1 Mathematical Preliminaries of a SRM
into account the nonlinear magnetization saturation. The energy equation for a SRM torque production is generally expressed as: dEe = dEf + dEm
where, dEe = α i dt, and α = V − R i. dEe is called differential electrical energy. dEf , dEm are differential stored field energy (magnetic energy) and mechanical energy (co-energy), respectively. The differential stored field energy is divided into its constituent component as (A. Cheok, 2002): dEf =
dλ (θ, i) dt
∂Ef ∂Ef di |θ=constant + dθ |i=constant ∂i ∂θ
(4)
By considering the stored differential field energy as (Miller, 2001): dEe = i
∂λ (θ, i) ∂λ (θ, i) di |θ=constant + i dθ |i=constant ∂i ∂θ (5)
By substituting (4) into (5) yields, dEm = i
∂Ef ∂λ (θ, i) dθ − dθ ∂θ ∂θ
(6)
The overall instantaneous torque is defined as: Te (θ, i) =
dEm dθ
(7)
By substituting (6) into (7) returns, Te (θ, i) = i
∂λ (θ, i) ∂Ef − ∂θ ∂θ
(8)
Note that, the equation (8) is rarely used, and it is called variant of the conventional torque equation. However, it is normally written as a function of co-energy form which is used in this paper to compute torque of a SRM and it is expressed as:
The overall dynamics of a SRM consist of a set of electrical equations of every phase and the mechanical equation of the system (L. Kalaivani, 2013; Miller, 2001). The phase voltage equation of a SRM is expressed as: V = Ri +
(3)
Te (θ, i) =
∂Ecoenergy |i=constant ∂θ
(9)
(1)
where, λ (θ, i) is the phase flux linkage nonlinear function of rotor position (θ), and the phase current (i) using a magnetically linear approximation, where, λ (θ, i) = L (θ, i) i. L is the inductance. The flux linkage non-linear function is expressed as: V = Ri + L (θ, i)
di dL (θ, i) + iω dt dθ
(2)
The graphical interpretation of differential stored energy and differential co-energy is expressed in Fig. 1 by taking
Fig. 1. Graphical interpretation of stored energy and coenergy
12028
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
2.2 Modeling Description of a SRM With Finite Element Method
Fig. 2. (a) 6/4 SRM flux distribution at 19◦ (b) 6/4 SRM flux distribution at aligned position
×10-3
Inductance (H)
All the operational characteristics of a SRM for LEV applications such has flux-linkage, inductance, torque, position of rotor, and current are examined by using finite element method (FEM) software. The constructed mesh structure of the SRM model by using FEM is shown in Fig. 2.
11537
Phase Current=50A Phase Current=100A Phase Current=150A Phase Current=200A
1.5 1 0.5 0 0
10
20
30
40
50
60
70
80
90
Rotor Position (deg)
Fig. 4. Self-Inductance versus rotor position for a SRM
In a SRM the area enclosed by the flux linkage of each phase is used to directly measure the produced torque between 0◦ − 90◦ , as shown in Fig. 5. Consequently, the torque is produced when the self-inductance of any phase of a SRM rises as the position of the rotor teeth comes to aligned position with the stator teeth. So, the positive torque is produced when dL dθ > 0, and negative torque is < 0. produced when dL dθ
In the presence and absence of magnetic saturation for different values of current, the motor characteristic are examined. The SRM position of the rotor is considered from 0◦ to 90◦ . Fig. 3 depicts that from a rage of 0 A to 200 A the phase current of the SRM increases. It also depicts that, the flux linkage values depend on the position of the rotor between 0◦ to 45◦ . When the position of the rotor is at 0◦ , the rotor is at an un-aligned position and has a very small flux linkage value. When the position of the rotor is at 45◦ , the rotor is at an aligned position and has the maximum flux linkage value.
Phase Current=50A Phase Current=100A Phase Current=150A Phase Current=200A
Torque (Nm)
20 10 0 -10 -20 0
10
20
30
40
50
60
70
80
90
Rotor Angle (deg)
Flux Linkage (Wb)
Fig. 5. Torque versus rotor position for SRM 0.06 0.04 0.02
Rotor Position=1 (deg) Rotor Position=15 (deg) Rotor Position=30 (deg) Rotor Position=45 (deg)
0 -0.02 0
20
40
60
80
100
120
140
160
180
3. AVERAGE TORQUE CONTROL OF SRM
200
Current (A)
Fig. 3. Flux linkage versus current curve for SRM Fig. 4 depicts the SRM self-inductance versus position of the rotor. Mathematically, this is expressed as: L (θ, i) =
λ (θ, i) i
(10)
Fig. 4 also depicts that, the self-inductance of a SRM varies with the position of the rotor and also with the current. When the rotor is at an un-aligned position (i.e. 0◦ ), the self-inductance has a very small value, and when the position of the rotor is at an aligned position (i.e. 45◦ ), the self-inductance has a higher value. The self-inductance curve shows that from rotor position 0◦ to 45◦ the motor produces positive torque or motoring torque, and from 46◦ to 90◦ the motor produces negative torque or generating torque.
Besides the indirect instantaneous torque control (ITC) strategy, there is also another strategy called average torque control (ATC). In an ATC, a torque sharing look-up table is used. In the ATC strategy, torque sharing look-up table data is used for constant torque generation, and this data is simply divided by a torque sharing curve to obtain the torque of each phase. However, in the proposed control strategy, a torque sharing look-up torque table with Iref , θON , and θOFF is used rather than the conventional torque sharing function (TSF). According to Iref and ω, the reference torque command is equally divided into each 3 phases to provide the reference current for each phase, i.e., Iref− a , Iref− b , Iref− c . However, this look-up torque table data is obtained by experiment and comprises information of the Iref , θON and θOFF of a SRM. In order to control the torque smoothness, each phase torque is assigned to each phase current. Moreover, for smooth phase torque, the current ripple is kept as small as possible. Therefore, the frequency of hysteresis current control (HCC) or Bang-Bang control (BBC) is kept high.
12029
Proceedings of the 20th IFAC World Congress 11538 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
Hysteresis Band
ΔI=10A
Iref_a Tcmd
TorqueTo-Current Look-up Table
ΔIa Hysteresis Current Control
Iref_b Iref_c
ω θOFF θON
Sa,b,c 1
ΔIb 0 ΔI a,b,c
ΔIc
LEV-SRM
A magnetic model of a SRM is established for estimating the average torque. The inductance of a SRM with their Fourier series (FS), and instantaneous torque is expressed as:
TL
- V +
Switching Rule
Va
Gate
Vb
Signals
Vc
-1
LEVSRM
Drive
ic ib i a
θON θOFF
θ
ω Current Feedback
∞ ˆ (θ, i) 1 2 1 2 dL ˆ = i mam cos (mθ) (12) Te (θ, i) = i 2 dθ 2 m=1
1/s Speed Feedback
Fig. 6. The torque control block diagram with look-up torque table method Fig. 6, depicts the look-up torque table with Iref , θON , and θOFF . The inputs of the look-up torque table are Tcmd and ω. This look-up torque table also generates Iref , θON , and θOFF angles for a SRM at each time instant. These angles give information about the rotor and stator teeth. The θON angle gives information about the rotor teeth, when they start to overlap with the stator teeth. The θOFF angle gives information about the rotor and stator teeth when they are at the aligned position. It also gives information about the inductance of a SRM, which increases from θON to θOFF . The sloppiness of inductance also increases, which affects the motoring torque Fig.4. θON and θOFF determine the performance of a SRM. The torque speed range, efficiency of machine, torque ripple, and acoustic noise all depend upon θON and θOFF . Therefore, θON should be set near the minimum inductance position to start the positive torque, and θOFF should be set near the maximum inductance position. Moreover, the HCC or BBC is used to limit the current of each phase with high frequency. This HCC or BBC also controls each phase torque by a given current command. According to the current error of each phase and the hysteresis switching table, i.e. chopping technique (a) soft chopping and (b) hard chopping, the switching rule generates an active switching signal for asymmetric converter. This converter generates the gate signals for the LEV-SRM drive, which generates separately Va , Vb , Vc for every phase of a SRM, which are totally independent of each other.
The FS estimated inductance, estimated flux linkage and estimated torque up to infinity harmonics are defined below in equations (13), (14), (15). However, the key point of this proposed methodology is that we have considered only first harmonics and got the best torque estimation results as shown in Fig. 9.
ˆ p (θ) = a0 − L
ˆ p (θ) = a0 − λ
∞
m=1
∞
m=1
am sin [m (θ − (p − 1)) θs ]
(13)
(14)
am sin [m (θ − (p − 1)) θs ] ip
∞ 1 mam cos [m (θ − (p − 1)) θs ] Tˆp (θ, ip ) = i2p 2 m=1
(15)
where, θs = 2pi nR , nR is number of rotor poles. p = 1, 2, 3 represents the phase A, B, C of a SRM respectively. The coefficients are chosen as a0 = 0.00016 and a1 = 0.00195. The overall proposed block diagram of DATC of a SRM for LEV for closed loop estimated torque control is shown in Fig. 7.
4. TORQUE ESTIMATION, DESIGN AND IMPLEMENTATION OF DATC WITH PI CONTROLLER OF A SRM FOR LEV
Hysteresis Band
+ V -
ΔI=10A
e Tref
-
Tavg
PI Controller
T
Tsat Tcmd Torque Saturator
Look-Up Torque Table
Iref Hysteresis
Switch Control Gate LEV-SRM Signal Drive Generator Signals
Current Control
ω θOFF θON
ic
ib
θ
ia
TL
Va Vb Vc
LEVSRM
ω
θON θOFF
1/s
The estimated torque of a SRM is obtained by accumulating torque of each phase and expressed as in equation (11).
Current Feedback Speed Feedback
Average
Tˆe ( θ, ia , ib , ic ) = Tˆa (θ, ia ) + Tˆb (θ, ib ) + Tˆc (θ, ic ) (11) ∂ Tˆa (θ, ia ) = gˆ (θ, ia ) = ∂θ
∂ Tˆb (θ, ib ) = gˆ (θ − θs , ib ) = ∂θ
∂ Tˆc (θ, ic ) = gˆ (θ − 2θs , ic ) = ∂θ
ia 0 ib 0 ic
0
^ Te
θ Torque Estimator
1/s
ia, ib, ic
Fig. 7. Block diagram of DATC of a SRM for LEV
ˆ θ, i di λ a a ˆ θ − θs , i di λ b b ˆ θ − 2θs , i di λ c c
5. SIMULATION RESULTS In this paper, an ATC of a 3-phase 3 kW 6/4 a SRM drive is implemented to control an LEV with step loading torque. The detailed specifications of SRM for an LEV is given in Table 1. 12030
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
11539
Parameters Maximum Power Maximum Speed Stator Resistance Rotor Inertia Number of Stator Poles Number of Rotor Poles Maximum Peak Current Number of Phases Maximum Torque DC Bus Voltage Un-aligned Inductance Aligned Inductance
% Error (Nm)
Table 1. Value 3 kW 8000 RPM 0.0321 Ω 5.1060E-04 kg · m2 6 4 200 A 3 8N 48 V 0.2599 m H 1.8010 m H
0 -20
10
15
20
Fig. 10. Percentage error between Tcmd and Te (avg) , and Percentage error between Te (avg) and Te (est)
Current (A)
40
Phase-1 Phase-2 Phase-3
20 0 0
0.05
0.1
0.15
0.2
Time (s)
0.2
Current (A)
0.3 Desired Torque Command Actual Average Output Torque Estimated Average Output Torque
0.1 0 0
5
10
15
20
Time (s)
Fig. 8. Desired, actual and estimated average torque of a SRM for LEV Fig. 9 depicts the simulated output torque with transient and steady state torque waveform of a SRM respectively. Output Torque (Nm)
5
Time (s)
0.4
2.5
Actual Output Instantaneous Torque Estimated Output Instantaneous Torque
2 1.5 1 0.5 0 0
0.05
0.1 Time (s)
0.15
0.2
(a) Transient waveform of an actual and estimated torque Output Torque (Nm)
Error Between T cmd and T e (avg) Error Between T e (avg) and T e (est)
-40 0
The desired, actual, and estimated average torque are shown in Fig. 8. The proposed ATC of a SRM for LEV applications is fast to converge to steady state for a desired torque command. Torque (Nm)
20
0.8 0.6
Actual Output Instantaneous Torque Estimated Output Instantaneous Torque
0.4 0.2 0 19.99
19.992
19.994 19.996 Time (s)
19.998
20
20
Phase-1 Phase-2 Phase-3
10 0 19.99
19.992
19.994
19.996
19.998
20
Time (s)
Fig. 11. a) Transient current of each phase of a SRM b) Steady state current of each phase of a SRM
Fig. 11 illustrates the transient and steady state current waveform of each phase for a SRM with a constant torque command Tcmd = 0.3Nm. Fig. 11 also elaborates about the current of each phase, and also the commutation angle between the two phases. It is also clear that each specified phase current waveform produces the largest torque of described polarity for a given current. It shows that before activating the next reference phase current, the previous phase current should linearly decline to zero, so that it is brought to zero before it produces a negative torque. Fig. 12 and Fig. 13 shows the representation of position, and tracking control Iref and switching angles (θON , θOFF ) which are being changed at every time instant. Furthermore, these switching angles play an important role in the noise reduction when they are placed near to the unaligned position.
(b) Steady state waveform of an actual and estimated torque
Fig. 9. Actual and estimated torque of a SRM for LEV Fig. 10 depicts the average %error between Tcmd and Te (avg) and also %error between Te (avg) and Te (est of a SRM at every time instant. Mathematically, % Error = Tcmd −Te (avg) T −Te (est) × 100 and % Error = e (avg) × 100 . Tcmd Te (avg) The figure depicts that, in the beginning the %error is high, and after time 3s the %error reduces and remains in a specific bound.
Position (rad)
15000 10000 5000 0 0
5
10 Time (s)
Fig. 12. Position of a SRM for LEV
12031
15
20
Proceedings of the 20th IFAC World Congress 11540 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
Iref (A)
150 100 50 0 0
5
10
15
20
θ ON , θ OFF (deg)
Time (s) 40
θ ON
30
θ OFF
20 10 0
5
10
15
20
Time (s)
Fig. 13. Iref , θON and θOFF of a SRM for LEV 6. CONCLUSION A closed loop an ATC of a SRM for LEVs is proposed, to control and estimate the average torque of the shaft of motor. The average torque of the shaft is estimated by using the Fourier series of inductance only for the first harmonics by using the primary parameters of the motor, i.e., rotor position and phase currents. Consequently, in order to control the direct average torque of a SRM, traction control is used. However, the average torque control of the shaft at the commanded torque level is attained by continuously adjusting the current reference, turning on, and turning off switching angles of the drive. Furthermore, oscillations, which occur in speed, and average torque control by performing open loop torque control, are also eliminated with the proposed ATC. Finally, precise average torque control and torque estimation are attained by using the proposed methodology for LEV applications.
Salame, C. (2015). Speed control of 8/6 switched reluctance motor with torque ripple reduction taking into account magnetic saturation effects. Energy Procedia, 74, 112 – 121. Salem, F. (2014). Performance analysis of DTC-SVM sliding mode controllers-based parameters estimator of electric motor speed drive. Mathematical Problems in Engineering, Hindawi, 2014, 1–11. Sezen, S. (2016). Finite element modeling and control of a high-power SRM for hybrid electric vehicle. Simulation Modelling Practice and Theory, 62, 49 – 67. Shahakar, A. (2013). Direct instantaneous torque control of switched reluctance motors. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Energy, Vol. 2, Issue 1. Torrey, D. (2015). Guidance in selecting advanced control techniques for switched reluctance machine drives in emerging applications. IEEE Transactions on Industry Applications, 51(6), 4505–4514. Yan, W. (2011). Applications of SR drive systems on electric vehicles. Zhang, J. (2015). Direct torque control of sensorless induction machine drives: A two-stage kalman filter approach. Mathematical Problems in Engineering, Hindawi, 2015, 1–17.
REFERENCES Cheok, A. (2002). A new torque and flux control method for switched reluctance motor drives. IEEE Transactions on Power Electronics, 17(4), 543–557. Choi, Y. (2016). Feedback linearization direct torque control with reduced torque and flux ripples for IPMSM drives. IEEE Transactions on Power Electronics, 31(5), 3728–3737. Inderka, R. (2003a). DITC-direct instantaneous torque control of switched reluctance drives. IEEE Transactions on Industry Applications, 39(4), 1046–1051. Inderka, R. (2003b). High-dynamic direct average torque control for switched reluctance drives. IEEE Transactions on Industry Applications, 39(4), 1040–1045. Kalaivani, L. (2013). Speed control of switched reluctance motor with torque ripple reduction using non-dominated sorting genetic algorithm (NSGA-II). International Journal of Electrical Power & Energy Systems, 53, 69 – 77. Miller, T. (2001). Electronic Control of Switched Reluctance Machines. Newnes Power Engineering Series. Elsevier Science. Moron, C. (2012). Torque control of switched reluctance motors. IEEE Transactions on Magnetics, 48(4), 1661– 1664. Sahoo, K. (2005). Indirect torque control of switched reluctance motors using iterative learning control. IEEE Transactions on Power Electronics, 20(1), 200–208. 12032
ScienceDirect
IFAC PapersOnLine 50-1 (2017) 11535–11540
Average Torque Control of a Switched Average Torque Control of a Switched Average Torque Control of a Average Torque Control ofLight a Switched Switched Reluctance Motor Drive for Electric Reluctance Motor Drive for Light Reluctance Motor Drive for Light Electric Electric ReluctanceVehicle Motor Applications Drive for Light Electric Vehicle Applications Vehicle Applications Vehicle Applications
Muhammad Usman Jamil ∗∗ Waree Kongprawechnon ∗∗ ∗ Muhammad Usman Jamil Jamil ∗∗ Waree Kongprawechnon ∗∗ Muhammad Waree ∗ Nattapon ∗∗ Muhammad Usman Usman JamilChayopitak Waree Kongprawechnon Kongprawechnon ∗∗ Nattapon Chayopitak Nattapon Chayopitak ∗∗ Nattapon Chayopitak ∗ ∗ School of Information, Communication and Computer Technologies ∗ School of Information, Communication and Computer Technologies Information, Communication and Computer Technologies ∗ School (ICT),of International Institute Technology (SIIT), School ofSirindhorn Information, Communication andof Computer Technologies (ICT), Sirindhorn International Institute of Technology (SIIT), (ICT), Sirindhorn International Institute of Technology (SIIT), usman [email protected], Thammasat University, Thailand (e-mail: m (ICT), Sirindhorn Institute of Technology (SIIT), Thammasat University,International Thailand (e-mail: (e-mail: m usman usman [email protected], Thammasat University, Thailand m [email protected], [email protected], [email protected]). Thammasat University, Thailand (e-mail: m usman [email protected], [email protected], [email protected]). ∗∗ [email protected], [email protected]). Electronics and Computer Technology Center (NECTEC), ∗∗ National [email protected], [email protected]). ∗∗ National Electronics and Computer Technology Center (NECTEC), and Computer Technology Center ∗∗ National Electronics 112 Thailand Science Park, Thailand (e-mail: National Electronics and Computer Technology Center (NECTEC), (NECTEC), 112 Thailand Science Park, Thailand (e-mail: 112 Science [email protected]) 112 Thailand Thailand Science Park, Park, Thailand Thailand (e-mail: (e-mail: [email protected]) [email protected]) [email protected]) Abstract: In this paper, an online average torque control (ATC) of a switched reluctance motor Abstract: In this paper, an online average torque control (ATC) of aa switched reluctance motor Abstract: In paper, an average torque (ATC) (SRM) for light electric vehicle (LEV) applications is proposed. The purpose reluctance of the ATCmotor is to Abstract: In this this paper,vehicle an online online average torque control control (ATC) of of a switched switched reluctance motor (SRM) for light electric (LEV) applications is proposed. The purpose of the ATC is to (SRM) for light electric vehicle (LEV) applications is proposed. The purpose of the ATC is to control for thelight average torque in the mostapplications inner control loop to stabilize the system dynamics. (SRM) electric vehicle (LEV) is proposed. The purpose of the ATC is to control the average torque in the most inner control loop to stabilize the system dynamics. control the average torque in the most inner control loop to stabilize the system dynamics. This is carried out by estimating the average torque at every time instant by considering the control the average torque in the most inner control loop to stabilize the system dynamics. This is carried out by estimating the average torque at every time instant by considering the This carried out the average torque at instant by the motorisprimary parameters, i.e., rotor position, speed, and phasetime currents. To achieve the desired This carried parameters, out by by estimating estimating theposition, average speed, torqueand at every every instant by considering considering the motorisprimary primary i.e., rotor rotor phasetime currents. To achieve achieve the desired desired motor parameters, i.e., position, speed, and phase currents. To averageprimary torque parameters, in wide speed range and controller efficiency forcurrents. traction To control, thethe proposed motor i.e., rotor position, speed, and phase achieve the desired average torque in wide speed range and controller efficiency for traction control, the proposed average torque speed and traction the proposed ATC algorithm is wide designed torange adjust thecontroller changingefficiency referencefor current andcontrol, switching angles to average torque in inis wide speedto range and controller efficiency for traction control, the angles proposed ATC algorithm designed adjust the changing reference current and switching to ATC algorithm is designed to adjust the changing reference current and switching angles to obtain the desired average torque at the operating speed. This paper also proposes a torque ATC algorithm is designed to adjust the changing reference current and switching angles to obtain the desired average torque at the operating speed. This paper also proposes aa torque obtain the desired average at operating speed. paper also estimation method based ontorque the Fourier Series approximation of the inductance profile to obtain obtain the method desired based average torque at the the operating speed. This This paper also proposes proposes a torque torque estimation on the Fourier Series approximation of the inductance profile to obtain estimation method based on the Fourier Series approximation of the inductance profile to obtain accurate torque estimation results. The Series simulation of a 3 kW,of6/4 SRM for LEV application is estimation method based on the Fourier approximation the inductance profile to obtain accurate torque estimation results. The simulation of a 3 kW, 6/4 SRM for LEV application is accurate torque estimation results. The simulation of a 3 kW, 6/4 SRM for LEV application is used to demonstrate the effectiveness of simulation the proposed method. accurate torque estimation results. The of a 3 kW, 6/4 SRM for LEV application is used to demonstrate the effectiveness of the proposed method. used to demonstrate the effectiveness of the proposed method. used to demonstrate the effectiveness of the proposed method. © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: average torque control, switched reluctance motor, light electric vehicle Keywords: Keywords: average average torque torque control, control, switched switched reluctance reluctance motor, motor, light light electric electric vehicle vehicle Keywords: average torque control, switched reluctance motor, light electric vehicle 1. INTRODUCTION The torque control of a SRM does not depend upon the 1. INTRODUCTION INTRODUCTION The torque control of a SRM does not depend upon the 1. The torque control of SRM the reference model control e.g., not fielddepend orientedupon control. 1. INTRODUCTION The torque control of aatheory, SRM does does not depend upon the reference model control theory, e.g., field oriented control. reference model control theory, e.g., field oriented control. However, model the torque control is e.g., attained by adjusting all control theory, field oriented control. As vehicle production has been continuously increasing reference the torque control is attained by adjusting all As vehicle vehicle production production has has been been continuously continuously increasing increasing However, However, the torque control attained by adjusting all control variables according tois precalculated or measured As However, the torque control is attained by adjusting all all over the globe, the conspicuous problems brought control variables according to precalculated or measured As vehicle production hasconspicuous been continuously increasing all over the globe, the problems brought control variables according to precalculated or measured functions (J. Zhang, 2015). In indirect instantaneous all over the globe, the conspicuous problems brought control variables according to In precalculated or measured by over vehicles have become a great concern these days. functions (J. Zhang, 2015). indirect instantaneous all the globe, the conspicuous problems brought by vehicles vehicles have have become become aa great great concern concern these these days. days. functions (J. 2015). In indirect torque control (IITC), the torque a SRMinstantaneous is a cascade by In of indirect (J. Zhang, Zhang, 2015). Thus, many have countries all over the globe, suchthese as China, torque control control (IITC), the the torque of SRMinstantaneous is a cascade by vehicles become a great concern days. functions Thus, many countries all over the globe, such as China, torque (IITC), torque of aaainstantaneous SRM is function, controlled by regulating the phase Thus, many countries all over the globe, such as China, torque control (IITC), the torque of SRM is aa cascade cascade Japan, etc., have started research on zero emission electric function, controlled by regulating the instantaneous phase Thus, many countries all over the globe, such as China, Japan, etc., have started research on zero emission electric function, controlled by regulating the instantaneous phase currents (K. Sahoo, 2005). In direct instantaneous torque Japan, have started research on controlled by regulating theinstantaneous instantaneoustorque phase vehiclesetc., (EVs). The benefits of EVs areemission energy electric saving, function, currents (K. Sahoo, 2005). In direct Japan, etc., haveThe started research on zero zero emission electric vehicles (EVs). benefits of EVs are energy saving, currents (K. 2005). In instantaneous control (DITC), a digital hysteresis controllertorque is devehicles (EVs). The EVs saving, currents (K. Sahoo, Sahoo, 2005). In direct directtorque instantaneous environmental friendliness, safeofdriving, lowenergy maintenance, control (DITC), (DITC), digital hysteresis torque controllertorque is devehicles (EVs).friendliness, The benefits benefits EVs are arelow energy saving, control environmental safeofdriving, driving, maintenance, aaaa digital hysteresis torque controller is signed to obtain high bandwidth for the drive. However, environmental friendliness, safe low maintenance, control (DITC), digital hysteresis torque controller is dedeand low noise friendliness, pollution (Wang Yan, 2011). Moreover, signed to obtain a high bandwidth for the drive. However, environmental safe driving, low maintenance, and low low noise noise pollution pollution (Wang (Wang Yan, Yan, 2011). 2011). Moreover, Moreover, signed to obtain aa high bandwidth for the drive. However, the torque is estimated by using the terminal quantities, and signed to obtain high bandwidth for the drive. However, in the present EVs, several types of motors are being the torque torque is is estimated estimated by by using using the terminal terminal quantities, quantities, andthe lowpresent noise pollution (Wang Yan, 2011). Moreover, in EVs, several several types of motors motors are being being the i.e., torque phase isvoltages andbycurrents Inderka, 2003a). in the present EVs, types are estimated using the the(R. terminal quantities, used, such as, DC motors, induction motor, permanent i.e., phase phase voltages voltages and currents currents (R. Inderka, 2003a). in thesuch present EVs,motors, severalinduction types of of motor, motors permanent are being the used, as, DC i.e., and (R. Inderka, 2003a). Various control methods have been proposed in the last used, such as, DC motors, induction motor, permanent i.e., phase voltages and have currents Inderka, 2003a). magnetsuch motor, and motors, switchedinduction reluctancemotor, motors. The key Various control methods been (R. proposed in the the last used, as, DC permanent magnet motor, and switched reluctance motors. The key Various control methods have been proposed in few decades to control and estimate torque, and alsolast to magnet motor, and switched reluctance motors. The key Various control methods have been proposed in the last advantage of the switched reluctance motor (SRM) is few decades to control and estimate torque, and also to magnet motor, and switched reluctance motors. The key advantage of of the the switched switched reluctance reluctance motor motor (SRM) (SRM) is is few decades control and torque, and also to minimize the to torque ripples ofestimate SRMs, (D. A. Torrey, 2015); advantage few decades to control and estimate torque, and also to that, it has a simple mechanical construction, i.e., a minimize the torque ripples of SRMs, (D. A. Torrey, 2015); advantage of the switched reluctance motor (SRM) is that, it it has has aa simple simple mechanical mechanical construction, construction, i.e., i.e., aa Sezen, minimize the ripples of A. 2015); 2016; C. Salame, 2015; Salem,(D. 2014; R. In-derka, that, minimize the torque torque ripples of SRMs, SRMs, A. Torrey, Torrey, 2015); purely laminated steel structure exists without theany Sezen, 2016; C. Salame, Salame, 2015; Salem,(D.2014; 2014; R. In-derka, In-derka, that, itlaminated has a simple construction, i.e., a Sezen, purely steel mechanical structure exists exists without theany theany 2016; C. 2015; Salem, R. 2003b). In hybrid combination of direct torque control purely laminated steel structure without Sezen, 2016; C. Salame, 2015; Salem, 2014; R. In-derka, rotor windings, permanent magnets,exists or squirrel cage bars. 2003b). In hybrid combination of direct torque control purely laminated steel structure without theany rotor windings, windings, permanent permanent magnets, magnets, or or squirrel squirrel cage cage bars. bars. 2003b). combination of torque control (DTC)-sliding mode control (SMC), torque is rotor 2003b). In In hybrid hybrid combination of direct direct the torque control Hence,windings, robustness in operation, and high reliability exists (DTC)-sliding mode control (SMC), (SMC), the torque is rotor permanent magnets, or squirrel cage exists bars. (DTC)-sliding Hence, robustness in operation, and high reliability mode control the torque is estimated by taking in to account the phase flux and phase Hence, robustness in operation, and high reliability exists (DTC)-sliding mode control (SMC), the torque is in a SRM (D. A. Torrey, 2015; Shahakar, 2013). estimated by taking in to account the phase flux and phase Hence, robustness in operation, and high reliability exists in aa SRM SRM (D. A. A. Torrey, 2015; 2015; Shahakar, 2013). 2013). estimated by taking the flux phase current. of the adaptive torque controller in estimatedThe by performance taking in in to to account account the phase phase flux and and phase current. The performance of the the adaptive adaptive torque controller in a SRM (D. (D. A. Torrey, Torrey, 2015; Shahakar, Shahakar, 2013). current. The performance of torque controller is also analyzed by considering the mismatch disturbance current. The performance of the adaptive torque controller is also analyzed by considering the mismatch disturbance is also analyzed considering mismatch disturbance and uncertainties (Salem, 2014). In high is alsoparameter analyzed by by considering the the mismatch disturbance This research project is supported by Sirindhorn International and parameter uncertainties (Salem, 2014). In high and parameter uncertainties (Salem, 2014). In dynamics DTC for SRM, the reference torque is controlled This research project is supported by Sirindhorn International This research and parameter uncertainties (Salem, 2014). In high high project is supported by Sirindhorn International Institute of Technology (SIIT), Thammasat University, and the This research project is supported by Sirindhorn International dynamics DTC for SRM, the reference torque is controlled for SRM, the reference torque is controlled dynamics DTC Institute of (SIIT), University, and by using the energy ratio estimation technique and also by dynamics DTC for SRM, the reference torque is controlled Institute Electronics of Technology Technology (SIIT), Thammasat Thammasat University, and the the National and Computer Technology Center (NECTEC) by using the energy ratio estimation technique and also by Institute of Technology (SIIT), Thammasat and the National Electronics and TechnologyUniversity, Center (NECTEC) by using energy ratio technique and also changing the switching angles (R. Inderka, National Electronics and Computer Computer Center (NECTEC) of Thailand for the Excellent Foreign Technology Student (EFS) Scholarship and by using the the energy ratio estimation estimation technique and 2003b). also by by changing the switching angles (R. Inderka, 2003b). National Electronics and Computer Technology Center (NECTEC) of for Excellent Foreign Student (EFS) Scholarship and changing the angles (R. Inderka, 2003b). Feedback linearization torque (FL-DTC) of Thailand Thailand for the the Foreign Student (EFS) Scholarship and the equipments forExcellent this research. The research project is partially changing the switching switchingdirect angles (R. control Inderka, 2003b). of Thailand for the Excellent Foreign Student (EFS) Scholarship and Feedback linearization linearization direct torque control (FL-DTC) the for research. The project is Feedback direct torque control (FL-DTC) the equipments equipments for this thisResearch research.Universities The research research project is partially partially funded by the National (NRU) by the Office of based on space vector modulation is used to control the Feedback linearization direct torque control (FL-DTC) the equipments for this research. The research project is partially funded the Research Universities (NRU) Office based on on space space vector vector modulation modulation is is used used to to control control the the funded by by the National National Research(HEC), Universities (NRU) by by the the Office of of based Higher Education Commission and Thammasat University, torque and also to reduce the torque and stator flux funded by the National Research Universities (NRU) by the Office of based is used to flux control the Higher the torque and stator torque on andspace also to tovector reducemodulation Higher Education Education Commission Commission (HEC), (HEC), and and Thammasat Thammasat University, University, Thailand. torque and also reduce the torque and stator flux Higher Education Commission (HEC), and Thammasat University, torque and also to reduce the torque and stator flux Thailand. Thailand.
Thailand. Copyright © 2017, 2017 IFAC 12027 2405-8963 © IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2017 IFAC 12027 Copyright ©under 2017 responsibility IFAC 12027 Peer review of International Federation of Automatic Control. Copyright © 2017 IFAC 12027 10.1016/j.ifacol.2017.08.1628
Proceedings of the 20th IFAC World Congress 11536 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
ripples (Y. Choi, 2016). The iterative learning control method is used to control and estimate torque of a SRM by combing the P-type feedback controller with an iterative learning controller (ILC) (K. Sahoo, 2005). However, DTCsliding mode control, feedback linearization DTC, and sliding mode control based estimation of SRM by using ILC, and IITC based field oriented schemes are all model base techniques. The exact dynamics of the motor need to be known to control and estimate the torque of SRM. Moreover, in these techniques torque is estimated by considering the primary and secondary parameters of a motor, i.e., terminal phase currents, voltages, and flux linkages. Furthermore, the literature discussed above reveals that the torque is also estimated by using the Fourier series (FS) of the inductance profile up to the 3rd or more harmonics. Hence, this increases the system complexity (C. Moron, 2012). To overcome these issues, an average torque control (ATC) of a SRM drive for LEVs is proposed. The linear estimated torque of a SRM for LEVs is obtained by accumulating the torque of each phase, and a linear magnetic model of a SRM is established to estimate an average torque. The estimated inductance and flux-linkage of a SRM with their FS is considered only for first harmonics. Consequently, in order to control the average torque in SRM traction, control/drive control is used. The purpose of this classical control is to adjust all control variables of a drive at every operating point, i.e., reference current, turning on and turning off the switching angles. These control variables are being set for the entire operating range according to the predetermined lookup tables. These lookup tables play an important role for properly selecting the control variables for each operating point and also depend upon the reference torque, and the speed of the motor for LEV applications. Hence, the key advantages of the proposed control are: a) it has the highest degree of flexibility and control level b) it provides the minimum speed to hight speed operational area c) it provides fast torque control. 2. DYNAMICS AND MODELING DESCRIPTION OF A SRM DRIVE 2.1 Mathematical Preliminaries of a SRM
into account the nonlinear magnetization saturation. The energy equation for a SRM torque production is generally expressed as: dEe = dEf + dEm
where, dEe = α i dt, and α = V − R i. dEe is called differential electrical energy. dEf , dEm are differential stored field energy (magnetic energy) and mechanical energy (co-energy), respectively. The differential stored field energy is divided into its constituent component as (A. Cheok, 2002): dEf =
dλ (θ, i) dt
∂Ef ∂Ef di |θ=constant + dθ |i=constant ∂i ∂θ
(4)
By considering the stored differential field energy as (Miller, 2001): dEe = i
∂λ (θ, i) ∂λ (θ, i) di |θ=constant + i dθ |i=constant ∂i ∂θ (5)
By substituting (4) into (5) yields, dEm = i
∂Ef ∂λ (θ, i) dθ − dθ ∂θ ∂θ
(6)
The overall instantaneous torque is defined as: Te (θ, i) =
dEm dθ
(7)
By substituting (6) into (7) returns, Te (θ, i) = i
∂λ (θ, i) ∂Ef − ∂θ ∂θ
(8)
Note that, the equation (8) is rarely used, and it is called variant of the conventional torque equation. However, it is normally written as a function of co-energy form which is used in this paper to compute torque of a SRM and it is expressed as:
The overall dynamics of a SRM consist of a set of electrical equations of every phase and the mechanical equation of the system (L. Kalaivani, 2013; Miller, 2001). The phase voltage equation of a SRM is expressed as: V = Ri +
(3)
Te (θ, i) =
∂Ecoenergy |i=constant ∂θ
(9)
(1)
where, λ (θ, i) is the phase flux linkage nonlinear function of rotor position (θ), and the phase current (i) using a magnetically linear approximation, where, λ (θ, i) = L (θ, i) i. L is the inductance. The flux linkage non-linear function is expressed as: V = Ri + L (θ, i)
di dL (θ, i) + iω dt dθ
(2)
The graphical interpretation of differential stored energy and differential co-energy is expressed in Fig. 1 by taking
Fig. 1. Graphical interpretation of stored energy and coenergy
12028
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
2.2 Modeling Description of a SRM With Finite Element Method
Fig. 2. (a) 6/4 SRM flux distribution at 19◦ (b) 6/4 SRM flux distribution at aligned position
×10-3
Inductance (H)
All the operational characteristics of a SRM for LEV applications such has flux-linkage, inductance, torque, position of rotor, and current are examined by using finite element method (FEM) software. The constructed mesh structure of the SRM model by using FEM is shown in Fig. 2.
11537
Phase Current=50A Phase Current=100A Phase Current=150A Phase Current=200A
1.5 1 0.5 0 0
10
20
30
40
50
60
70
80
90
Rotor Position (deg)
Fig. 4. Self-Inductance versus rotor position for a SRM
In a SRM the area enclosed by the flux linkage of each phase is used to directly measure the produced torque between 0◦ − 90◦ , as shown in Fig. 5. Consequently, the torque is produced when the self-inductance of any phase of a SRM rises as the position of the rotor teeth comes to aligned position with the stator teeth. So, the positive torque is produced when dL dθ > 0, and negative torque is < 0. produced when dL dθ
In the presence and absence of magnetic saturation for different values of current, the motor characteristic are examined. The SRM position of the rotor is considered from 0◦ to 90◦ . Fig. 3 depicts that from a rage of 0 A to 200 A the phase current of the SRM increases. It also depicts that, the flux linkage values depend on the position of the rotor between 0◦ to 45◦ . When the position of the rotor is at 0◦ , the rotor is at an un-aligned position and has a very small flux linkage value. When the position of the rotor is at 45◦ , the rotor is at an aligned position and has the maximum flux linkage value.
Phase Current=50A Phase Current=100A Phase Current=150A Phase Current=200A
Torque (Nm)
20 10 0 -10 -20 0
10
20
30
40
50
60
70
80
90
Rotor Angle (deg)
Flux Linkage (Wb)
Fig. 5. Torque versus rotor position for SRM 0.06 0.04 0.02
Rotor Position=1 (deg) Rotor Position=15 (deg) Rotor Position=30 (deg) Rotor Position=45 (deg)
0 -0.02 0
20
40
60
80
100
120
140
160
180
3. AVERAGE TORQUE CONTROL OF SRM
200
Current (A)
Fig. 3. Flux linkage versus current curve for SRM Fig. 4 depicts the SRM self-inductance versus position of the rotor. Mathematically, this is expressed as: L (θ, i) =
λ (θ, i) i
(10)
Fig. 4 also depicts that, the self-inductance of a SRM varies with the position of the rotor and also with the current. When the rotor is at an un-aligned position (i.e. 0◦ ), the self-inductance has a very small value, and when the position of the rotor is at an aligned position (i.e. 45◦ ), the self-inductance has a higher value. The self-inductance curve shows that from rotor position 0◦ to 45◦ the motor produces positive torque or motoring torque, and from 46◦ to 90◦ the motor produces negative torque or generating torque.
Besides the indirect instantaneous torque control (ITC) strategy, there is also another strategy called average torque control (ATC). In an ATC, a torque sharing look-up table is used. In the ATC strategy, torque sharing look-up table data is used for constant torque generation, and this data is simply divided by a torque sharing curve to obtain the torque of each phase. However, in the proposed control strategy, a torque sharing look-up torque table with Iref , θON , and θOFF is used rather than the conventional torque sharing function (TSF). According to Iref and ω, the reference torque command is equally divided into each 3 phases to provide the reference current for each phase, i.e., Iref− a , Iref− b , Iref− c . However, this look-up torque table data is obtained by experiment and comprises information of the Iref , θON and θOFF of a SRM. In order to control the torque smoothness, each phase torque is assigned to each phase current. Moreover, for smooth phase torque, the current ripple is kept as small as possible. Therefore, the frequency of hysteresis current control (HCC) or Bang-Bang control (BBC) is kept high.
12029
Proceedings of the 20th IFAC World Congress 11538 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
Hysteresis Band
ΔI=10A
Iref_a Tcmd
TorqueTo-Current Look-up Table
ΔIa Hysteresis Current Control
Iref_b Iref_c
ω θOFF θON
Sa,b,c 1
ΔIb 0 ΔI a,b,c
ΔIc
LEV-SRM
A magnetic model of a SRM is established for estimating the average torque. The inductance of a SRM with their Fourier series (FS), and instantaneous torque is expressed as:
TL
- V +
Switching Rule
Va
Gate
Vb
Signals
Vc
-1
LEVSRM
Drive
ic ib i a
θON θOFF
θ
ω Current Feedback
∞ ˆ (θ, i) 1 2 1 2 dL ˆ = i mam cos (mθ) (12) Te (θ, i) = i 2 dθ 2 m=1
1/s Speed Feedback
Fig. 6. The torque control block diagram with look-up torque table method Fig. 6, depicts the look-up torque table with Iref , θON , and θOFF . The inputs of the look-up torque table are Tcmd and ω. This look-up torque table also generates Iref , θON , and θOFF angles for a SRM at each time instant. These angles give information about the rotor and stator teeth. The θON angle gives information about the rotor teeth, when they start to overlap with the stator teeth. The θOFF angle gives information about the rotor and stator teeth when they are at the aligned position. It also gives information about the inductance of a SRM, which increases from θON to θOFF . The sloppiness of inductance also increases, which affects the motoring torque Fig.4. θON and θOFF determine the performance of a SRM. The torque speed range, efficiency of machine, torque ripple, and acoustic noise all depend upon θON and θOFF . Therefore, θON should be set near the minimum inductance position to start the positive torque, and θOFF should be set near the maximum inductance position. Moreover, the HCC or BBC is used to limit the current of each phase with high frequency. This HCC or BBC also controls each phase torque by a given current command. According to the current error of each phase and the hysteresis switching table, i.e. chopping technique (a) soft chopping and (b) hard chopping, the switching rule generates an active switching signal for asymmetric converter. This converter generates the gate signals for the LEV-SRM drive, which generates separately Va , Vb , Vc for every phase of a SRM, which are totally independent of each other.
The FS estimated inductance, estimated flux linkage and estimated torque up to infinity harmonics are defined below in equations (13), (14), (15). However, the key point of this proposed methodology is that we have considered only first harmonics and got the best torque estimation results as shown in Fig. 9.
ˆ p (θ) = a0 − L
ˆ p (θ) = a0 − λ
∞
m=1
∞
m=1
am sin [m (θ − (p − 1)) θs ]
(13)
(14)
am sin [m (θ − (p − 1)) θs ] ip
∞ 1 mam cos [m (θ − (p − 1)) θs ] Tˆp (θ, ip ) = i2p 2 m=1
(15)
where, θs = 2pi nR , nR is number of rotor poles. p = 1, 2, 3 represents the phase A, B, C of a SRM respectively. The coefficients are chosen as a0 = 0.00016 and a1 = 0.00195. The overall proposed block diagram of DATC of a SRM for LEV for closed loop estimated torque control is shown in Fig. 7.
4. TORQUE ESTIMATION, DESIGN AND IMPLEMENTATION OF DATC WITH PI CONTROLLER OF A SRM FOR LEV
Hysteresis Band
+ V -
ΔI=10A
e Tref
-
Tavg
PI Controller
T
Tsat Tcmd Torque Saturator
Look-Up Torque Table
Iref Hysteresis
Switch Control Gate LEV-SRM Signal Drive Generator Signals
Current Control
ω θOFF θON
ic
ib
θ
ia
TL
Va Vb Vc
LEVSRM
ω
θON θOFF
1/s
The estimated torque of a SRM is obtained by accumulating torque of each phase and expressed as in equation (11).
Current Feedback Speed Feedback
Average
Tˆe ( θ, ia , ib , ic ) = Tˆa (θ, ia ) + Tˆb (θ, ib ) + Tˆc (θ, ic ) (11) ∂ Tˆa (θ, ia ) = gˆ (θ, ia ) = ∂θ
∂ Tˆb (θ, ib ) = gˆ (θ − θs , ib ) = ∂θ
∂ Tˆc (θ, ic ) = gˆ (θ − 2θs , ic ) = ∂θ
ia 0 ib 0 ic
0
^ Te
θ Torque Estimator
1/s
ia, ib, ic
Fig. 7. Block diagram of DATC of a SRM for LEV
ˆ θ, i di λ a a ˆ θ − θs , i di λ b b ˆ θ − 2θs , i di λ c c
5. SIMULATION RESULTS In this paper, an ATC of a 3-phase 3 kW 6/4 a SRM drive is implemented to control an LEV with step loading torque. The detailed specifications of SRM for an LEV is given in Table 1. 12030
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
11539
Parameters Maximum Power Maximum Speed Stator Resistance Rotor Inertia Number of Stator Poles Number of Rotor Poles Maximum Peak Current Number of Phases Maximum Torque DC Bus Voltage Un-aligned Inductance Aligned Inductance
% Error (Nm)
Table 1. Value 3 kW 8000 RPM 0.0321 Ω 5.1060E-04 kg · m2 6 4 200 A 3 8N 48 V 0.2599 m H 1.8010 m H
0 -20
10
15
20
Fig. 10. Percentage error between Tcmd and Te (avg) , and Percentage error between Te (avg) and Te (est)
Current (A)
40
Phase-1 Phase-2 Phase-3
20 0 0
0.05
0.1
0.15
0.2
Time (s)
0.2
Current (A)
0.3 Desired Torque Command Actual Average Output Torque Estimated Average Output Torque
0.1 0 0
5
10
15
20
Time (s)
Fig. 8. Desired, actual and estimated average torque of a SRM for LEV Fig. 9 depicts the simulated output torque with transient and steady state torque waveform of a SRM respectively. Output Torque (Nm)
5
Time (s)
0.4
2.5
Actual Output Instantaneous Torque Estimated Output Instantaneous Torque
2 1.5 1 0.5 0 0
0.05
0.1 Time (s)
0.15
0.2
(a) Transient waveform of an actual and estimated torque Output Torque (Nm)
Error Between T cmd and T e (avg) Error Between T e (avg) and T e (est)
-40 0
The desired, actual, and estimated average torque are shown in Fig. 8. The proposed ATC of a SRM for LEV applications is fast to converge to steady state for a desired torque command. Torque (Nm)
20
0.8 0.6
Actual Output Instantaneous Torque Estimated Output Instantaneous Torque
0.4 0.2 0 19.99
19.992
19.994 19.996 Time (s)
19.998
20
20
Phase-1 Phase-2 Phase-3
10 0 19.99
19.992
19.994
19.996
19.998
20
Time (s)
Fig. 11. a) Transient current of each phase of a SRM b) Steady state current of each phase of a SRM
Fig. 11 illustrates the transient and steady state current waveform of each phase for a SRM with a constant torque command Tcmd = 0.3Nm. Fig. 11 also elaborates about the current of each phase, and also the commutation angle between the two phases. It is also clear that each specified phase current waveform produces the largest torque of described polarity for a given current. It shows that before activating the next reference phase current, the previous phase current should linearly decline to zero, so that it is brought to zero before it produces a negative torque. Fig. 12 and Fig. 13 shows the representation of position, and tracking control Iref and switching angles (θON , θOFF ) which are being changed at every time instant. Furthermore, these switching angles play an important role in the noise reduction when they are placed near to the unaligned position.
(b) Steady state waveform of an actual and estimated torque
Fig. 9. Actual and estimated torque of a SRM for LEV Fig. 10 depicts the average %error between Tcmd and Te (avg) and also %error between Te (avg) and Te (est of a SRM at every time instant. Mathematically, % Error = Tcmd −Te (avg) T −Te (est) × 100 and % Error = e (avg) × 100 . Tcmd Te (avg) The figure depicts that, in the beginning the %error is high, and after time 3s the %error reduces and remains in a specific bound.
Position (rad)
15000 10000 5000 0 0
5
10 Time (s)
Fig. 12. Position of a SRM for LEV
12031
15
20
Proceedings of the 20th IFAC World Congress 11540 Toulouse, France, July 9-14, 2017 Muhammad Usman Jamil et al. / IFAC PapersOnLine 50-1 (2017) 11535–11540
Iref (A)
150 100 50 0 0
5
10
15
20
θ ON , θ OFF (deg)
Time (s) 40
θ ON
30
θ OFF
20 10 0
5
10
15
20
Time (s)
Fig. 13. Iref , θON and θOFF of a SRM for LEV 6. CONCLUSION A closed loop an ATC of a SRM for LEVs is proposed, to control and estimate the average torque of the shaft of motor. The average torque of the shaft is estimated by using the Fourier series of inductance only for the first harmonics by using the primary parameters of the motor, i.e., rotor position and phase currents. Consequently, in order to control the direct average torque of a SRM, traction control is used. However, the average torque control of the shaft at the commanded torque level is attained by continuously adjusting the current reference, turning on, and turning off switching angles of the drive. Furthermore, oscillations, which occur in speed, and average torque control by performing open loop torque control, are also eliminated with the proposed ATC. Finally, precise average torque control and torque estimation are attained by using the proposed methodology for LEV applications.
Salame, C. (2015). Speed control of 8/6 switched reluctance motor with torque ripple reduction taking into account magnetic saturation effects. Energy Procedia, 74, 112 – 121. Salem, F. (2014). Performance analysis of DTC-SVM sliding mode controllers-based parameters estimator of electric motor speed drive. Mathematical Problems in Engineering, Hindawi, 2014, 1–11. Sezen, S. (2016). Finite element modeling and control of a high-power SRM for hybrid electric vehicle. Simulation Modelling Practice and Theory, 62, 49 – 67. Shahakar, A. (2013). Direct instantaneous torque control of switched reluctance motors. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Energy, Vol. 2, Issue 1. Torrey, D. (2015). Guidance in selecting advanced control techniques for switched reluctance machine drives in emerging applications. IEEE Transactions on Industry Applications, 51(6), 4505–4514. Yan, W. (2011). Applications of SR drive systems on electric vehicles. Zhang, J. (2015). Direct torque control of sensorless induction machine drives: A two-stage kalman filter approach. Mathematical Problems in Engineering, Hindawi, 2015, 1–17.
REFERENCES Cheok, A. (2002). A new torque and flux control method for switched reluctance motor drives. IEEE Transactions on Power Electronics, 17(4), 543–557. Choi, Y. (2016). Feedback linearization direct torque control with reduced torque and flux ripples for IPMSM drives. IEEE Transactions on Power Electronics, 31(5), 3728–3737. Inderka, R. (2003a). DITC-direct instantaneous torque control of switched reluctance drives. IEEE Transactions on Industry Applications, 39(4), 1046–1051. Inderka, R. (2003b). High-dynamic direct average torque control for switched reluctance drives. IEEE Transactions on Industry Applications, 39(4), 1040–1045. Kalaivani, L. (2013). Speed control of switched reluctance motor with torque ripple reduction using non-dominated sorting genetic algorithm (NSGA-II). International Journal of Electrical Power & Energy Systems, 53, 69 – 77. Miller, T. (2001). Electronic Control of Switched Reluctance Machines. Newnes Power Engineering Series. Elsevier Science. Moron, C. (2012). Torque control of switched reluctance motors. IEEE Transactions on Magnetics, 48(4), 1661– 1664. Sahoo, K. (2005). Indirect torque control of switched reluctance motors using iterative learning control. IEEE Transactions on Power Electronics, 20(1), 200–208. 12032