High-precision speed control of four-phase switched reluctance motor fed from asymmetric power converter

+Model JESIT 203 1–12

ARTICLE IN PRESS Available online at www.sciencedirect.com

ScienceDirect Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

High-precision speed control of four-phase switched reluctance motor fed from asymmetric power converter

1

2

3

Q1

4

Q2

Ghada A. Abdel Aziz a,∗ , Mahmoud Amin a,b a b

5

Power Electronics and Energy Conversion Department, Electronic Research Institute, Cairo, Egypt Electrical and Computer Engineering Department, Manhattan College, Riverdale, NY 10471, USA Received 25 December 2017; accepted 12 March 2018

6

Abstract

7

18

Switched reluctance motors (SRMs) are used in the industry due to their simple motor design construction, the susceptibility of running at wide speed range, high torque to inertia ratio, low cost, and high reliability. In this paper, the SRM drive system is fed from asymmetric four-phase power converter (APC) using soft switching technique. This paper presents a proposed precise speed controller (PSC) for a four-phase 75 KW 8/6 SRM. The performance of the PSC is evaluated and compared with PI and fuzzy logic (FLC) speed controllers. This comparison is based on the values of the rise time, settling time, overshoot, undershoot, speed error in the steady state, and torque ripples percentage of the three speed controllers. The robustness of the proposed PSC is validated in such cases e.g. mechanical parameter disparities, and external load disturbances. The four-phase SRM responses of motor speed versus speed command, speed error, four-phase currents, SRM reference current, and electromagnetic torque are investigated using MATLAB/SIMULINK. © 2018 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

19

Keywords: Switched reluctance motor (SRM); Precise speed controller (PSC); Asymmetric power converter (APC); Fuzzy logic controller (FLC)

8 9 10 11 12 13 14 15 16 17

20

1. Introduction

21

Switched reluctance motor (SRM) is an electrical machine which issues torque as a result of the magnetic attraction between salient stator poles and the salient poles placed on the rotor. This rotor is fabricated by a ferromagnetic material. According to the SRM structure, the stator has only the windings whilst the rotor does not have any windings hence, power losses are less and a high torque is produced (Miller, 1993; Wang et al., 2017). The inductances of the SRM are non-linear which make the electromagnetic torque high, non-linear, and laborious to control. Broadly, a simple

22 23 24 25 26

Q3

∗

Corresponding author. E-mail address: aghada [email protected] (G.A. Abdel Aziz). Peer review under the responsibility of Electronics Research Institute (ERI).

https://doi.org/10.1016/j.jesit.2018.03.006 2314-7172/© 2018 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 2

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Nomenclature I The phase current The reference current of the SRM iref L The phase inductance of the SRM R The phase resistance of the SRM Upper switch status SxH SxL Lower switch status Te The electromagnetic torque Maximum torque Tmax Tmin Minimum torque Tav The average electromagnetic torque The terminal voltage V Vdc The DC-link voltage ωr The rotor angular speed θr The rotor position angle θ on /θ off The turn-on and turn-off position angles θ A , θ B , θ C , θ D The rotor position angles of the 4-phases ψ The flux linkage by the winding

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

traditional control method like proportional-integral (PI) speed control in Song and Qu (2016), Nanda et al. (2016) and Milasi and Moallem (2014) is sometimes used for SRM control drives. This traditional control scheme is powerless when a detailed system model is inaccessible or the controlled system is intricate for mathematical modeling. Although conventional PI control is the most widely used method in industry applications, its gain parameters must be tuned by trial and error method to accomplish satisfactorily when a modification is made to, or a change occurs in the controlled system. In Tseng et al. (2012) a new adaptive Takagi–Sugeno–Kang (TSK)-fuzzy controller (ATSKFC) was proposed to control the SRM speed drive system. This controller has two portions: a TSK-fuzzy controller and a compensated regulator. The TSK-fuzzy controller is the foremost controller, which is used to approximate an optimal control law. The compensated controller is used to adapt the error signal between the TSK-fuzzy controller and the optimal control law. A new SRM speed controller based on Elitist-Mutated Multi-Objective Particle Swarm Optimization (EM-MOPSO) with good exactitudes and performances has been introduced in Mansouri Borujeni et al. (2015). This control technique comprises a conventional PI speed regulator and a hysteresis current controller (HCC). As a consequence of the SRM non-linearity characteristics, EM-MOPSO was used to tune the controller gains parameters of PI speed controller, turn-on/turn-off position angles along with the peak value of the phase winding current by using a multi-objective function, comprising both Integrals Squared Error (ISE) of SRM torque ripple and speed. In Silva et al. (2013), a robust SRM speed control technique based on a Generalized Predictive Controller (GPC) relating to the Model Predictive Controller (MPC) has been proposed. This controller scheme is based on designing a filter to permit a fast acting response, disturbance elimination, noise lessening and robustness with a minimum computational cost for the SRM. A balanced soft-chopping and reformed PI controller for high speed 4/2 SRM using 16 pulses per revolution resolver was presented in Lee and Ahn (2011). To minimize the ripples of the current, a balanced soft-chopping circuit was used to supply twofold switching frequency in the fixed switching frequency of the power switches. In Ishikawa et al. (2009), a new SRM speed control technique besides a flat torque control has been developed. The flat torque controller structure seems like current controller not only grasps the SRM phase currents waveforms for persistent torque production, but also compensates non-linear torque-current attitude of the SRM drive system. This paper proposes a precise speed controller (PSC) based on a three-layer feed-forward neural network for a four-phase 75 KW 8/6 SRM. The performance of the proposed PSC is evaluated and compared with PI and FLC speed controllers. The comparative analysis is based on the values of the rise time, settling time, overshoot, undershoot, speed Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

3

Fig. 1. The geometry of four-phase, 8 stator poles/6 rotor poles of SRM.

58

error in the steady state, and torque ripples percentage of the three controllers. The robustness of the proposed PSC is validated in such cases e.g. mechanical parameter variations, and external load disturbances.

59

2. The electromagnetic equations of SRM

57

60 61 62 63 Q4

64

65 66 67

68

69 70 71

72

73

74

75 76

77

Fig. 1 shows the geometry structure of a four-phase, 8 stator poles and 6 rotor poles of the SRM used in this study. Although the SRM operation seems simple, a precision investigation of the motor’s performance seeks a proper and somewhat sophisticated mathematical modeling approach. The SRM instantaneous voltage through a single-phase winding terminal is correlated to the flux linked in the winding via Faraday’s law in (1) (Rahman et al., 2001): dψ (1) dt As a consequence of both the stator and the rotor of the SRM have salient poles structure, and the magnetic saturation impacts, the flux linked in the SRM phase changes as a function of both motor phase winding current and rotor position angle. Therefore, (1) can be expanded as: V = IR +

V = IR +

∂ψ dI ∂ψ dθr + ∂I dt ∂θr dt

(2)

where the term ∂ψ/∂I in (2) is defined as L(θ r ,I), the instantaneous inductance relying on the rotor position angle θ r and instantaneous phase winding current I, the term ∂ψ/∂θ r is Kb (θ r ,I), the instantaneous back-EMF coefficient. The instantaneous electric powers of an individual phase e.g. phase winding (A), is described as: PA = VA IA = RA IA 2 + LA (θr , IA )IA

dIA dLA (θr , IA ) + IA 2 ωr dt dθr

(3)

The instantaneous torque of phase (A) is given by (4): TA =

1 2 dLA (θr , IA ) IA 2 dθr

(4)

The electromagnetic torque of a four-phase SRM is therefore given by the summation of torques developed by individual motor four-phase (A–D): Te = TA (θA , IA ) + TB (θB , IB ) + TC (θC , IC ) + TD (θD , ID )

(5)

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 4

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Fig. 2. The drive system of the four-phase SRM.

Fig. 3. The APC structure for the four-phase SRM drive system.

78

79

80

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

The torque ripple percentage formula can be calculated by (6):   T max − Tmin × 100 Tripple % = Tav

(6)

3. The SRM drive system The four-phase SRM drive system is illustrated in Fig. 2. This drive system comprises of a 8/6 four-phase SRM, a four-phase asymmetric power converter (APC) fed the motor, the speed controller, and the commutator. In this paper, the SRM speed is controlled by different types of speed controllers such as a precise speed controller (PSC), FLC, and conventional proportional-integral (PI) controllers. The SRM speed command is compared with actual motor speed and the error between them is adapted by a speed regulator to issue the reference motor current component iref . This reference current is subsequently multiplied by the switching signals Sabcd issued from the commutator and then the reference four-phase currents of the SRM are acquired. The reference four-phase SRM currents are compared with the actual motor four-phase currents in the feedback loop and producing the error signals. These error signals are adapted by a hysteresis current control (HCC) then the switched signals of the APC are generated. Fig. 3 depicts the asymmetric four-phase power converter (APC) circuit structure for the four-phase SRM. A softchopping (on–off) mode is used to abate the switching power losses provided that the upper-switch SXH of the APC chops and the lower switch SXL stays closed in the phase turn-on region. The drive signals of the upper/lower power switches S1, S5 of phase winding (A) are the pulse width modulated (PWM) chopping signal and position control signal corresponding to the working region of phase winding (A), respectively (Hu et al., 2016). The operating status of the APC switches in the active area for the SRM four-phases (A–D) is abridged in Table 1. There are three active modes of operation for the converter plus the inert mode in which phase winding current is zero as depicted in Fig. 4. In case of both switches S1 and S5 are on in the phase turn-on region, the current will flow in phase winding (A) promptly, and the phase leg will operate in the fluxing or excitation mode operation as shown in Fig. 4(a). Meanwhile S1 is off and S5 is on, the phase winding (A) will be in a zero-voltage loop (ZVL) and the phase Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

5

Table 1 The four-phase power converter active switching status. Switching element

SxH SxL

Switching status per phase Phase-A

Phase-B

Phase-C

Phase-D

Chopping Constant on

Chopping Constant on

Chopping Constant on

Chopping Constant on

Fig. 4. Operation modes of the converter for one-phase. (a) Excitation mode. (b) Free-wheeling mode (ZVL). (c) Demagnetization mode.

109

leg will operate in the free-wheeling mode as shown in Fig. 4(b). In case of both switches S1 and S5 are off in the phase turn-off region, the current will flow back to the source through free-wheeling diodes D1 and D5 and the phase leg will operate in the de-fluxing or demagnetization mode as illustrated in Fig. 4(c) (Zhang et al., 2016). In the soft switching state, free-wheeling and the excitation states are usually adopted. These two states operate alternatively when a definite phase winding is energized. If the upper switch SXH of the APC works as a chopping switch, the lower switch SXL will be constantly turned-on. Thereafter, the voltage difference +Vdc is applied to the motor phase winding. Furthermore, in case of hard chopping technique based on demagnetization and the excitation states, the voltage difference is almost twofold greater than that in the soft switching states. Thus, the torque ripples in the hard switching state will be higher than the soft switching state (Ro et al., 2015).

110

4. SRM speed controllers designs

111

4.1. The PSC design for SRM drives

101 102 103 104 105 106 107 108

112 113 114 115

The PSC network structure is adopted to border the uncertainty problem of the SRM control system and the SRM parameter disparities during different modes of operations. The PSC structure is depicted in Fig. 5. This controller involves a three-layer feed-forward neural network. The first layer is the input layer which has two inputs; the SRM speed error and the change in the SRM speed error. The second

Fig. 5. The PSC structure.

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 6 116 117 118

119

120

121

122 123 124

125

126 127 128 129

130

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

layer is the hidden layer with three-neurons. The third layer is the output layer with only single-neuron which issues the SRM reference current iref . The electromagnetic equation of the SRM can be expressed as: dωr Te ∗ F T = − ωr − L dt J J J From (7), the SRM electromagnetic equation can be rewritten as:

(7)

dωr (8) = C 1 T e ∗ + C 2 ω r + C3 T L dt where C1 , C2 , and C3 are nominal parameters of the SRM in the healthy mode operation. The values of C1 , C2 , and C3 are 1/J, -F/J, and -1/J. respectively. These parameters may vary during the SRM operation. Thus, (8) can be rewritten as in (9) to express the change in these parameters. dωr (9) = (C1 + C1 )Te ∗ + (C2 + C2 )ωr + (C3 + C3 )TL = C1 Te ∗ + C2 ωr + C4 dt where C1 , C2 , and C3 are the change in the SRM parameters C1 , C2 , and C3 , respectively and the value of C4 is C4 = C1 Te ∗ + C2 ωr + C3 TL + C3 TL which refers to the uncertainty of the obscure dynamic behavior of the SRM drive system. The PSC has two inputs, the SRM speed error and the change in the SRM speed error. The SRM speed error e and the change in the SRM speed error de/dt can be expressed in (10) and (11): e = ωr ∗ − ωr

(10)

∗

131

132

133

134

135

136

137

138 139 140

141

142

143

144

145

146 147

de dωr dωr = − dt dt dt By substituting (11) into (9), yields: de dωr ∗ = − C1 Te ∗ − C2 ωr − C4 dt dt From (12), the reference electromagnetic torque can be obtained as:   ∗ −C2 ωr − C4 + dωdtr − de ∗ dt Te = C1

(11)

(12)

(13)

The change of the SRM speed error can be expressed as: de = −C5 e (14) dt where C5 is the design parameters. Referring to (14), the actual speed of the SRM can track the speed command smoothly and the SRM drive system stability is guaranteed. From (14), the reference electromagnetic torque can be rewritten as:   ∗ −C2 ωr − C4 + dωdtr + C5 e ∗ (15) Te = C1 From (4) and (15), the reference SRM four-phase currents can be obtained as:  2Te ∗ I ∗ abcd = dL/dθr

(16)

The input vectors X of the PSC network can be expressed as: de T (17) ] dt The main target of the PSC is to look for a control law assuring the error signal “e” between the SRM speed command and the actual SRM speed tends asymptotically to be zero. To achieve that, the Lyapunov function V = 0.5e2 X = [X1 , X2 ]T = [e,

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

148 149

150

151 152 153 154 155

156

157 158 159 160 161 162 163

164

165

166

7

is used. In case of the derivative of the function V is negative; therefore, the error signal dynamics is stable in the sense of Lyapunov (Butler, 1992). The derivative of V can be calculated as follows: dV de dωr ∗ = e = e( − C1 Te ∗ − C2 ωr − C4 ) = −C5 e2 dt dt dt

(18)

The function V decreases when the error signal, e, is not zero. Therefore, the error signal will be zero. The neuron is an adaptive element whose weights are adaptable according to the input signal besides the output response. The adapline or (adaptive linear element) is a simple adaptive process. The Widrow–Hoff delta rule is applied for learning the adapline’s weight vector. This delta rule reduces the mean square error (MSE) and is expressed as follows (Butler, 1992): WK+1 = WK +

μeK X ε + XT X

(19)

where WK + 1 is the new weight vectors, WK is the old weight vectors of the output layer of the PSC, eK is the error signal, μ and ε are positive gain parameters. The (ek ) which is the error signal between the target output and the adapline output (Yk ) whose weights are regulated via the delta rule, converges steadily to be zero iff ε > 0.&0 < μ < 2 In (15), the adapline issue is accomplished by training weights/inputs of the PSC, and is normalized via the threshold function. The numerous functions, e.g sign, sigmoid, and saturation can be utilized as the threshold functions. The input vectors X of the adapline is supplanted with the function sgn (X), yields:  T sgn(X) = sgn(X1 ), sgn(X2 )

(20)

The delta rule of (19) in this case will be rewritten as in (21): WK+1 = WK +

μeK sgn(X) C6

(21)

168

where C6 is a positive gain parameter and the error signal eK converges to zero. This algorithm is convenient to construct simple and fast computations.

169

4.2. The fuzzy logic speed controller

167

170 171 172

Speed fuzzy logic controller (FLC) has two inputs; the first input is the speed error e(K) of the SRM and the second input is the change of SRM speed error Ce(K) as expressed in (22) and (23). The output of the speed FLC is the reference SRM current iref (K) (Hu et al., 2016).

173

e (K) = ωr ∗ (K) − ωr (K)

(22)

174

Ce (K) = e (K) − e (K − 1)

(23)

175 176 177 178 179 180 181 182 183

In the fuzzification juncture, the crisp inputs variables e(K) and Ce(K) are transformed to fuzzy variables E(K) and CE(K) via the triangular shape membership functions (MFs) illustrated in Fig. 6. The universes of the discourse of the two inputs E(K) and CE(K) are (−150, 133) rad/s and (−46, 65) rad/s, respectively. The universe of discourse of the output component iref (K) is (−5, 6) A. Every universe of discourse is splited into seven fuzzy sets named as: Positive Small (PS), Positive Medium (PM), Positive Big (PB), Negative Big (NB), Negative Medium (NM), Negative Small (NS), and Zero (Z). In the rule base stage, the speed FLC implements the 49 control rules illustrated in Table 2. The output quantity iref (K) is handled in the defuzzification unit to issue the reference SRM current iref (K). In the defuzzification stage, the centroid defuzzification algorithm is applied as the crisp value is deemed as the center of gravity of the MF of iref (K) as in (24): Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 8

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Fig. 6. Membership functions. (a) Input 1: error membership function. (b) Input 2: change of error membership function. (c) Output membership function. Table 2 Fuzzy rules for the SRM speed controller. Error “e”

Change of Error “ce”

NB NM NS Z PS PM PB



184

185

186

iref (K) =

NB

NM

NS

Z

PS

PM

PB

NB NB NB NB NM NS Z

NB NB NB NM NS Z PS

NB NB NM NS Z PS PM

NB NM NS Z PS PM PB

NM NS Z PS PM PB PB

NS Z PS PM PB PB PB

Z PS PM PB PB PB PB

 

 iref i μ iref i    μ iref i

(24)

The reference electromagnetic torque iref (K) is acquired by integrating (24) as in (25): iref (K) = iref (K − 1) + iref (K)

(25)

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

9

Table 3 SRM parameters.

187

Parameter

Specification

Rated power Maximum current Number of stator poles Number of rotor poles Stator resistance Aligned inductance Unaligned inductance Saturated aligned inductance Maximum flux linkage Inertia of the SRM Friction coefficient

75 KW 25 A 8 6 0.05  23.6 e−3 H 0.67 e−3 H 0.15 e−3 H 0.486 Wb 0.01 kg m2 0.005 N m/rad/s

5. Simulation results

195

The speed control of the four-phase 8/6 SRM (Table 3) has been carried out using the Matlab/Simulink environment. The SRM is fed from a four-phase asymmetrical power converter (APC) using soft switching technique with 100 Vdc . The PSC performance is evaluated and compared with the PI and FLC speed controllers according to the rise time, settling time, overshoot, undershoot, speed error, and the percentage torque ripples. The PI speed controller gains are obtained by using pole placement technique with symmetrical optimum criterion with gains values Kp and Ki , 7000 and 0.8, respectively. The turn-on and turn-off position angles of the SRM are 37.5◦ and 52.5◦ , respectively. The speed controller robustness is appraised under different cases; without parameter variations, mechanical parameter variation in a moment of inertia with 100% increment, and load torque disturbances.

196

5.1. SRM without parameter variation

188 189 190 191 192 193 194

197 198 199 200

Fig. 7 depicts the SRM speed versus speed command, speed error between actual and speed command, the output SRM reference current from the speed controller, the actual SRM four-phase currents, and the electromagnetic torque versus the torque command in case of without parameter variations and speed command 1500 rpm condition. The SRM performance under the three speed controllers is summarized in Table 4.

Fig. 7. The SRM performance without parameter variations. (a) Proposed PSC. (b) FLC. (c) PI.

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 10

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Table 4 SRM performance without parameter variations. Response

PSC

FLC

PI

Rise time (s) Settling time (s) Overshoot Undershoot Speed error in steady state (rpm) Torque ripples (%)

0.8080 1.0571 0.0195 0.2691 1 14.03

0.8050 1.0607 0.0201 0.4063 1 15.08

0.8059 1.0605 0.0235 0.2746 1.5 15.43

Fig. 8. The SRM performance under mechanical parameter variation in moment of inertia with 100% increment. (a) Proposed PSC. (b) FLC. (c) PI.

203

From Fig. 7 and Table 4, the PSC has a better characteristic performance due to its small rise time, small settling time, small overshoot, small undershoot, small speed error of 1 rpm at steady state, and small torque ripples percentage compared with the FLC and PI speed controllers’ responses.

204

5.2. SRM under mechanical parameter variation in moment of inertia (J) with 100% increment

201 202

205 206 207 208 209

Fig. 8 shows the SRM speed versus speed command, speed error between actual and speed command, the output SRM reference current from the speed controller, the actual SRM four-phase currents, and the electromagnetic torque versus the torque command in case of mechanical parameter variation in moment of inertia (J) with 100% increment and speed command 1500 rpm condition. The SRM performance under the three speed controllers is summarized in Table 4. From Fig. 8 and Table 5, the PSC has a better characteristic performance due to its small rise time, small Table 5 SRM performance under mechanical parameter variation in a moment of inertia with 100% increment. Response Rise time (s) Settling time (s) Overshoot Undershoot Speed error in steady state (rpm) Torque ripples (%)

PSC

FLC

PI

0.8214 1.2487 0.0079 0.1340 1 16.1

0.8289 1.2534 0.0227 0.1346 1.5 16.27

0.8329 1.2250 0.0193 0.1373 1.5 24.52

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

11

Fig. 9. The SRM performance under load torque disturbances. (a) Proposed PSC. (b) FLC. (c) PI. Table 6 SRM performance under load torque disturbances. Response

PSC

FLC

PI

Rise time (s) Settling time (s) Overshoot Undershoot

0.8010 0.9760 0.0457 0

0.8012 0.9802 0.3389 0

0.8015 0.9797 0.1888 0

212

overshoot, small undershoot, small speed error of 1 rpm at steady state, and small torque ripples percentage compared with the FLC and PI speed controllers responses. These responses proved the robustness of the proposed PSC against the mechanical parameter variation in the moment of inertia.

213

5.3. SRM under Load Torque Disturbances

210 211

214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229

Fig. 9 shows the SRM speed versus speed command, speed error between actual and speed command, the output SRM reference current from the speed controller, the actual SRM four-phase currents and the electromagnetic torque versus the torque command in case of load torque disturbances and speed command 1500 rpm condition. The SRM started at no load till t = 1.2 s, then from t = 1.2 s to t = 1.35 s the SRM is loaded with half of the rated torque of 5 N.m, and from t = 1.35 s to t = 1.5 s the SRM is loaded with the full load of 10 N.m, and from t = 1.5 s to t = 1.7 s, the full load torque is suddenly removed. The SRM performance under the three speed controllers of PSC, FLC, and PI is summarized in Table 6. From Fig. 9 at t = 1.2 s, the speed error between the speed command and the actual speed of the SRM using the PSC, FLC, and PI controllers are 0.5 rpm, 5 rpm, 0.5 rpm, respectively. The torque ripples percentage at t = 1.2 s for the PSC, FLC, and PI controllers are 20%, 25%, and 30%, respectively. At t = 1.35 s the speed error of the PSC, FLC, PI controllers is 1 rpm, 10 rpm, and 0.5 rpm, respectively. The torque ripples percentage at t = 1.35 s for the PSC, FLC, and PI controllers are 30%, 20%, and 45%, respectively. At t = 1.55 s, the speed error of the PSC, FLC, and PI controllers are 0.5 rpm, 1 rpm, 0.5 rpm, respectively. The torque ripples percentage at t = 1.55 s for the PSC, FLC, and PI controllers are 20%, 25%, and 30%, respectively. According to Fig. 9 and Table 6, the PSC has a better characteristic performance due to its small rise time, small overshoot, small undershoot, small speed error at steady state, and small torque ripples percentage compared with the Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006

+Model JESIT 203 1–12 12

ARTICLE IN PRESS G.A. Abdel Aziz, M. Amin / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

231

FLC and PI speed controllers responses. These responses proved the robustness of the proposed PSC against the load torque disturbances.

232

6. Conclusion

230

241

A precise speed controller (PSC) for a four-phase 75 KW 8/6 SRM has presented. The PSC was accomplished by Lyapunov stability theory which reinforces the SRM drive system stability. Based on this theory, the adaptation updating laws of the PSC has been designed to withstand the SRM parameters disparities and external loading disturbances. The control performance of the proposed PSC scheme has been corroborated via the Matlab simulation results. These results indicate that the proposed PSC approach has superior robustness for exterior load disturbances, the SRM parameters disparities, and better precision in speed regulation. The static and dynamic performances of the SRM drive have been promoted. The PSC also has a robust capability of online self-learning which approximate the non-linear function with any precision, and has a rapid convergence rate. The PSC has much better performance than the other two conventional PI and fuzzy logic speed controllers’ schemes.

242

Acknowledgment

233 234 235 236 237 238 239 240

244

The authors are indebted to Electronics Research Institute in Egypt for providing all the facilities required to complete this research.

245

References

243

246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274

Butler, H., 1992. Model Reference Adaptive Control from Theory to Practice, Prentice Hall Series in Systems and Control Engineering. Hu, Y., Gan, C., Cao, W., Finney, S.J., 2016. Flexible fault-tolerant topology for switched reluctance motor drives. IEEE Trans. Power Electron. 31 (June (6)), 4654–4668. Ishikawa, H., Rishab, P., Naitoh, H., 2009. Novel speed control system with flat torque control for switched reluctance motor drives. In: 2009 International Conference on Electrical Machines and Systems, Tokyo, pp. 1–6. Lee, D.H., Ahn, J.W., 2011. Speed control scheme of the high speed 4/2 switched reluctance motor. In: 2011 IEEE International Symposium on Industrial Electronics, Gdansk, pp. 750––755. Mansouri Borujeni, M., Rashidi, A., Saghaeian Nejad, S.M., 2015. Optimal four quadrant speed control of switched reluctance motor with torque ripple reduction based on EM-MOPSO. In: The 6th Power Electronics, Drive Systems & Technologies Conference (PEDSTC2015), Tehran, pp. 310–315. Milasi, R.M., Moallem, M., 2014. A novel multi-loop self-tuning adaptive PI control scheme for switched reluctance motors. In: IECON 2014 — 40th Annual Conference of the IEEE Industrial Electronics Society, Dallas, TX, pp. 337–342. Miller, T.J.E., 1993. Switched Reluctance Motors and their Control. Oxford Science, Oxford, U.K. Nanda, A.B., Pati, S., Rani, N., 2016. Performance comparison of a SRM drive with conventional PI, fuzzy PD and fuzzy PID controllers. In: 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT), Nagercoil, pp. 1––7. Rahman, K.M., Velayutham Rajarathnam, A., Ehsani, M., 2001. Optimized torque control of switched reluctance motor at all operational regimes using neural network. IEEE Trans. Ind. Appl. 37 (May/June (3)), 904––913. Ro, H.S., Kim, D.H., Jeong, H.G., Lee, K.B., 2015. Tolerant control for power transistor faults in switched reluctance motor drives. IEEE Trans. Ind. Appl. 51 (July–August (4)), 3187–3197. Silva, W.A., dos Reis, L.L.N., Torrrico, B.C., de C. Almeida, R.N., 2013. Speed control in switched reluctance motor based on generalized predictive control. In: 2013 Brazilian Power Electronics Conference, Gramado, pp. 903––908. Song, J., Qu, B., 2016. Application of an adaptive PI controller for a switched reluctance motor drive. In: 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), Auckland, pp. 1–5. Tseng, C.L., Wang, S.Y., Chien, S.C., Chang, C.Y., 2012. Development of a self-tuning TSK-fuzzy speed control strategy for switched reluctance motor. IEEE Trans. Power Electron. 27 (April (4)), 2141––2152. Wang, D., Wang, X., Du, X.F., 2017. Design and comparison of a high force density dual-side linear switched reluctance motor for long rail propulsion application with low cost. IEEE Trans. Magn. 53 (June (6)), 1––4. Zhang, C., Wang, K., Zhang, S., Zhu, X., Quan, L., 2016. Analysis of variable voltage gain power converter for switched reluctance motor. IEEE Trans. Appl. Supercond. 26 (October (7)), 1–5.

Please cite this article in press as: Abdel Aziz, G.A., Amin, M., High-precision speed control of fourphase switched reluctance motor fed from asymmetric power converter. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.03.006