21.07.2017  Original Paper  Ausgabe 2/2018 Open Access
Designing driving and control circuits of fourphase variable reluctance stepper motor using fuzzy logic control
 Zeitschrift:
 Electrical Engineering > Ausgabe 2/2018
1 Introduction
2 Mathematical model of a VR stepper motor
Parameter  Definition  Value  Unit 

V
 Applied phase voltage  5  V 
J
 Moment of inertia 
\(3.677\times 10^{6}\)
 N ms\(^2\)

\(r_\mathrm{a}\)
 Motor phase resistance  6 
\(\Omega \)

B
 Viscous friction constant 
\(3.5\times 10^{3}\)
 N ms 
\(K_{w}\)
 Load torque constant 
\(7\times 10^{5}\)
 N ms 
3 Design an openloop driving logic circuit
State  Inputs of control  Present state of counter  Next state of counter  Outputs of decoding part  Description of each state  

RI\(_2\)

D

\(Q_3\)

\(Q_2\)

\(Q_1\)

\(Q_3{+}\)

\(Q_2{+}\)

\(Q_1{+}\)

\(D_3\)

\(D_2\)

\(D_1\)
 
Singlephase excitation  0  0  0  0  0  0  1  0  0  1  0  A to B 15\(^{\circ }\) CW 
0  0  0  1  0  1  0  0  1  0  0  B–C 15\(^{\circ }\) CW  
0  0  1  0  0  1  1  0  1  1  0  C–D 15\(^{\circ }\) CW  
0  0  1  1  0  0  0  0  0  0  0  D–A 15\(^{\circ }\) CW  
0  1  0  0  0  1  1  0  1  1  0  A–D 15\(^{\circ }\) CCW  
0  1  1  1  0  1  0  0  1  0  0  D–C 15\(^{\circ }\) CCW  
0  1  1  0  0  0  1  0  0  1  0  C–B 15\(^{\circ }\) CCW  
0  1  0  1  0  0  0  0  0  0  0  B–A 15\(^{\circ }\) CCW  
Singlephasedoublephase excitation  1  0  0  0  0  0  0  1  0  0  1  A–AB 7.5\(^{\circ }\) CW 
1  0  0  0  1  0  1  0  0  1  0  AB–B 7.5\(^{\circ }\) CW  
1  0  0  1  0  0  1  1  0  1  1  B–BC 7.5\(^{\circ }\) CW  
1  0  0  1  1  1  0  0  1  0  0  BC–C 7.5\(^{\circ }\) CW  
1  0  1  0  0  1  0  1  1  0  1  C–CD 7.5\(^{\circ }\) CW  
1  0  1  0  1  1  1  0  1  1  0  CD–D 7.5\(^{\circ }\) CW  
1  0  1  1  0  1  1  1  1  1  1  D–DA 7.5\(^{\circ }\) CW  
1  0  1  1  1  0  0  0  0  0  0  DA–A 7.5\(^{\circ }\) CW  
1  1  0  0  0  1  1  1  1  1  1  A–AD 7.5\(^{\circ }\) CCW  
1  1  1  1  1  1  1  0  1  1  0  AD–D 7.5\(^{\circ }\) CCW  
1  1  1  1  0  1  0  1  1  0  1  D–DC 7.5\(^{\circ }\) CCW  
1  1  1  0  1  1  0  0  1  0  0  DC–C 7.5\(^{\circ }\) CCW  
1  1  1  0  0  0  1  1  0  1  1  C–CB 7.5\(^{\circ }\) CCW  
1  1  0  1  1  0  1  0  0  1  0  CB–B 7.5\(^{\circ }\) CCW  
1  1  0  1  0  0  0  1  0  0  1  B–BA 7.5\(^{\circ }\) CCW  
1  1  0  0  1  0  0  0  0  0  0  BA–A 7.5\(^{\circ }\) CCW  
Doublephase excitation  0  0  0  0  1  0  1  1  0  1  1  AB–BC 15\(^{\circ }\) CW 
0  0  0  1  1  1  0  1  1  0  1  BC–CD 15\(^{\circ }\) CW  
0  0  1  0  1  1  1  1  1  1  1  CD–DA 15\(^{\circ }\) CW  
0  0  1  1  1  0  0  1  0  0  1  DA–AB 15\(^{\circ }\) CW  
0  1  1  1  1  1  0  1  1  0  1  AD–DC 15\(^{\circ }\) CCW  
0  1  1  0  1  0  1  1  0  1  1  DC–CB 15\(^{\circ }\) CCW  
0  1  0  1  1  0  0  1  0  0  1  CB–BA 15\(^{\circ }\) CCW  
0  1  0  0  1  1  1  1  1  1  1  BA–AD 15\(^{\circ }\) CCW 
Case no.  The inputs of encoding part  The outputs of encoding part  

Clock 
\(Q_3\)

\(Q_2\)

\(Q_1\)

A

B

C

D
 
1  1  0  0  0  1  0  0  0 
2  1  0  0  1  1  1  0  0 
3  1  0  1  0  0  1  0  0 
4  1  0  1  1  0  1  1  0 
5  1  1  0  0  0  0  1  0 
6  1  1  0  1  0  0  1  1 
7  1  1  1  0  0  0  0  1 
8  1  1  1  1  1  0  0  1 
9  0  x  x  x  0  0  0  0 
10  1  x  x  x  0  0  0  0 
11  0  x  x  x  0  0  0  0 
4 Design closedloop proportional derivative (PD) fuzzy logic control
5 Simulation results
5.1 Case study I
Error e(t)  Load torque constant \((K_{w})\)
 

High (H)  Medium (M)  Low (L)  
Positive high 1 (PH1)  One  –  – 
Positive high 2 (PH2)  One  –  – 
Positive high 3 (PH3)  One  –  – 
Positive high 4 (PH4)  One  –  – 
Positive high 5 (PH5)  One  –  – 
Positive high 6 (PH6)  One  –  – 
Positive medium 1 (PM1)  –  One  – 
Positive medium 2 (PM2)  –  One  – 
Positive medium 3 (PM3)  –  One  – 
Positive medium 4 (PM4)  –  One  – 
Positive medium 5 (PM5)  –  One  – 
Positive medium 6 (PM6)  –  One  – 
Positive low 1 (PL1)  –  –  One 
Positive low 2 (PL2)  –  –  One 
Positive low 3 (PL3)  –  –  One 
Positive low 3 (PL3)  –  –  One 
Positive low 3 (PL3)  –  –  One 
Positive low 3 (PL3)  –  –  One 
Error e(t)  Change in error \(\Delta e(t)\)
 

Positive  Negative  
Positive (P)  One  Zero 
Zero (Z)  One  One 
Negative (N)  Zero  One 
5.2 Case study II
Parameter  No load  Half load  Full load  

Open loop without FLC  Closed loop using FLC  Open loop without FLC  Closed loop using FLC  Open loop without FLC  Closed loop using FLC  
Overshoot (%)  66.6  6  53.3  4.6  40  3.3 
Settling time (ms)  10  8  7  6  5  4 