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Speed and Rotor displacement control of Bearing Less
Switched Reluctance Motor by using Sliding Mode Control
1Nageswara Rao Pulivarthi, 2G.V.Siva Krishna Rao and 3G.V.
Nagesh Kumar 1,3Department of EEE, GITAM University, Visakhapatnam, India
2Dept. of EEE, AUCE (A), Andhra University, Visakhapatnam,
India [email protected] , [email protected] ,
[email protected] .
Abstract
In this paper sliding mode control based speed and rotor displacement control
methods are proposed, to get the desired constant speed, the rotor position and its
displacements when the Bearing less switched reluctance motor(BSRM) under
different loads and change of motor parameters. By using this proposed sliding mode
controller, the BSRM drive exhibits the robustness and the more stable position
operation and constant speed as compared with the PID controller. Before applying
suspension loads and torque loads to the rotor, the rotor has to be suspended to the
center and keeps in the stationary position. To maintain the current within a preset
band a hysteresis controller is employed in both torque phase currents and
suspension force currents. When the torque load changes, the rotor has an eccentric
displacement, but it can be pulled back quickly to its center position, due to control
action in suspension phase currents.
Key words: Bearing less, hysteresis controller, displacement, magnetic suspension, sliding mode
control.
1. Introduction:
Bearing less switched reluctance motor (BSRM) have a wide range of applications
in industry as generator starters, electric vehicle, wind turbine ventilators and so on.
Now a days the need of bearing less drive open a massive market and it sets the new
trend to electric drives and motors. The bearing less SRM has the superiorities of
both the magnetic bearing and the SRM[1], such as no friction, no lubrication, and
high speed capability.
In recent times, a number of structures of BSRM have been proposed, firstly, R.
Bosch and J. Bichsel are proposed Bearing less Electric motor concepts and
advantages and winding patterns [1-2]. After that an 8/6 BSRM model was
introduced by M Takemoto, Suzuki and Akira Chiba, in which suspending forces and
motor net torque are coupled each other, due to that, the controlling problem turn
into difficulty while operating this conventional drive [3-5]. To get the decouple
International Journal of Pure and Applied MathematicsVolume 114 No. 7 2017, 175-184ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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nature between suspending Force and motor torque, a single layer winding on a
single pole design was proposed by H. J. Wang, Dong. H. Lee and Jin-Woo Ahn. A
separate windings for suspension force and torque production purposes which are
wound on separate salient poles [6-10]. The same was applied to in this particular
10/8 and 12/14 BSRM. An attractive radial force will be built up between stator poles
and rotor due to its saliency nature between stator poles and rotor poles [11-12]. This
produced radial net force can be further distributed into two components, one is the
suspension force component in x-y direction which useful for levitating the rotor
towards the desired center position (0, 0) in an x-y coordinate system and another one
is motor torque component which is useful for the rotation of the rotor in radial
direction [13-15].
In this paper, speed and the magnetically levitated rotor position and its
displacements are controlled by using Sliding Mode controller (SMC), under different
loads and change of both electrical and mechanical type motor parameters. The
performance of the drive is tested at different load conditions in a systematic manner.
Agreeing to the suspended rotor in air at the center position by using suspension
winding magnetic forces, the control scheme of the proposed BSRM, is separated into
three stages. First one is, only suspend the rotor to the center position by applying
suspension currents to all suspension windings through asymmetric converter along
with current hysteresis controller and SMC controller Secondly, when the rotor is
levitated and kept in center position then excite the main motor torque currents to
the stator main winding to accelerate the rotor to the desired speed. After confirming
the desired speed, then apply torque loads the rotor shaft. The 12/14 BSRM winding
pattern and its structure is illustrated in Fig.1.
The drive incorporates two hysteresis control loops for the torque currents, and
four for the suspension force. To get the desired speed and rotor position a sliding
mode controller with Variable Structure System is applied to the proposed 12/14
BSRM. The drive speed performance and rotor displacements and suspension forces
in X and Y directions under Sliding mode controller (SMC) is compared with PI/PID
controller, the SMC shows the better performance for all conditions.
Is3
Is2
Is4
Is1
Fig.1. 12/14 BSRM Structure and winding pattern.
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2. The mathematical modeling of 12/14 BSRM.
Due to decoupled nature exist between torque and suspension forces the state
equations are considered separately. The state equations of motoring are given by
dt
idRiu
),( (1)
dtiL
wiDRiudi m ]
),(
),([
(2)
dRiudt
d (3),
dwwJ
K
J
TT
dt
dwm
F
m
j
Lej
m
1
(4),
dwdt
dm (5)
Therefore, the net torque T in Phase-A is explained as follows:
LiT 2
2
1 (6)
Where Ψ, R, θ, V are per phase flux linkages, per phase resistance, rotor position per
phase, phase voltage, and Te , Tl, J, KF, W are Net electromagnetic torque produced,
load torque applied, combined moment of Inertia of the rotor, damping coefficient,
Rotor speed respectively.
The rotor dynamics of Bearing Less SRM at standstill position or rest is written by
kxdt
xdmFx
2
2
; mgkydt
ydmFy
2
2
(7)
Where m, k, g are mass, spring constant and gravity in y- direction.
The net suspending force produced by proposed BSRM is given by
2
2
2
2
xn
xn
yp
xp
yynyxnyypyxp
xynxypxxp
y
x
i
i
i
i
KKKK
KKKK
F
Fxxn (8)
By combining above two equations, we get
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xXx IKkxdt
xdmF
2
, YY IKmgkydt
ydmFy
2
(9)
Where kxynKxxnKxypKxxpdiagK X KyynKyxnKyypKyxpdiagKY
2
2
xn
xpx
I
II ,
2
2
yn
yp
YI
II
3. Proposed Sliding Mode control (SMC) method.
The objective of continuous SMC is to place the system states on a pre-determined
sliding surface, which is designed in the state space. The new derived sliding mode
control input is given by )]sgn()[()( 1 xSkxqSASBSu (10)
Where S is switching function, q and k are constants, A and B are system matrix and
Input matrix respectively. The new state equation with control input is given by
)sgn()()]()([ 11 xSkBSxqSASxSBAx (11)
The derived speed state equation is given by
)sgn()()]()([ 11 xSkBSxqSASxSBAw
(12)
+
-x* SMC
x
Mathematical
formulae
θr
Δx Fx*
x
+
-SMC
y
Mathematical
formulae
iy*
θr
Δyy*
y
Fy*
ix*
Fig.2.Rotor Displacement Control Diagram. Fig .3.Suspension winding Asymmetric converter.
Table.1: Switching rules for the suspension winding currents.
Desired force Suspending force poles selection
If oFF yx ,0 21 & ss II
If oFF yx ,0 41 & ss II
If oFF yx ,0 43 & ss II
If oFF yx ,0 23 & ss II
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Fig.4.Over all control diagram of Proposed BSRM
4. Simulation results.
Healthy conditions of Motor:
When the rotor is at the center position, the torque currents are injected to the
main phases through asymmetric converter to accelerate the rotor to the desired
speed with initial torque load of 0.01 N.mt. From Fig.5.It can be seen that the process
of the proposed BLSRM is same with that of general SRM. When the motor rotates
steadily at rated rpm, and steadily suspended at center position, the phase currents
and output torque are stable and the torque current has almost no effect on the
suspending force.
Fig.5. (a) Y-directional rotor Displacement. Fig.5. (b) X-directional rotor Displacement
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Fig.5. (c) Y-directional suspension Force. Fig.5. (d) X-directional suspension Force.
Fig.5. (e) Rotor Positions. Fig.5. (f) suspension currents
Fig.5. (g) suspension Controlled voltages Fig.5. (h). Main Phase Currents
Fig.5. (i) No-load speed Fig.5. (j) Controlled Main Phase Voltages
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Speed and displacement control of BSRM:
In order to investigate the proposed control strategies, the BSRM drive has been
simulated under different working conditions.
Fig.6. when the reference speed is doubled at t=0.5sec. Fig.7. when load torque changed at 0.05 sec.
Fig.6. Illustrates the simulated speed response with the reference speeds of 3000
and 6000 rpm, at load torque of 0.01, the speed graphs are compared with PI
controller and SMC, it can be seen that the speed response is quite good under Sliding
mode controller. Fig.7. shows the operation of the drive under load torque
disturbance. The load torque is changed from 0.2Nm to 0.4 Nm at t=0.05 sec. when
the load torque is increased there is a slight dip in the motor speed. As compare with
PI controller, the SMC gives good speed track which is very close to reference speed.
Fig.8. when the rotor Inertia J is doubled. Fig.9. when the phase resistance is increased by 25%.
Figure.8&9. Shows the speed response when the drive is subjected to uncertainties
in the electrical and mechanical parameters i.e. phase resistance and rotor inertia is
changed. Here the rotor inertia is doubled and the phase resistance is increased by
25%. Inspection of these two figures (8) & (9), indicates that there is no major changes
in speed response with the help of SMC.
0
5000
10000
0 0.05 0.1
SPEE
D IN
RP
M
TIME IN SEC
S P E E D W H E N R E F E R E N C E S P E E D C H A N G E S
speed with pi
speed withSMC
0
5000
0 0.02 0.04 0.06 0.08 0.1
spee
d in
rp
m
time in sec
speed when load changed 0.2 to 0.4 at 0..5 sec
speed with PI
speed with SMC
0
5000
10000
0 0.05 0.1
spee
d in
rp
m
time in sec
speed when Stator Phase resistance chaged by 1.25 times
speedwith PIspeedwith SMCref speed
0
5000
10000
0 0.05 0.1
spee
d in
rp
m
time in sec
speed when Moment of Inertia doubled
speed withPIspeedwithSMCref speed
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For this drive, the maximum conduction angle for each phase is 12.85 mechanical
degrees. From figure.10. It shows that the speed response with SMC is settled quickly
i.e. less than 0.02 sec when conduction angle is reduced by 2 mechanical degrees. By
using this method even improvement in speed profile, but there is a more ripples in
torque profile. The main advantage of SMC is giving robustness to the drive. This is
achieved in all aspects of speed profiles.
Fig.10. when the switching angle is decreased by 2 deg. Fig. (11). Total Torque Profile of BSRM drive
5. Conclusion.
In this paper, the speed and displacement control of BSRM was done by using
Sliding Mode Controller. The robustness and the desired speed of BSRM was
achieved at different loading conditions by using Sliding mode controller and
compared with conventional PI controller to know its superior performance. The fast
convergence rate and more robustness and disturbance rejection capability properties
were carefully analyzed.
6. References.
[1] R. Bosch, "Development of a Bearingless Electric Motor," in Proc. Int. Conf. Electric Machines (ICEM’88), Pisa,
Italy, 1988: 373-375.
[2] J. Bichsel, "The Bearingless Electrical Machine," in Proc. Int. Symp. Magn. Suspension. Technol, NASA Langley
Res. Center, Hampton, 1991: 561-573.
[3] M. Takemoto, A. Chiba, H. Akagi and T. Fukao, “Suspending force and Torque of a Bearingless Switched
Reluctance Motor Operating in a Region of Magnetic Saturation” in Conf. Record IEEE-IAS Annual Meeting,
2002: 35–42.
[4] M. Takemoto, K. Shimada, A. Chiba, et al., "A Design and Characteristics of Switched Reluctance Type
Bearingless Motors, 4th International Symposium on Magnetic Suspension Technology," NASA/CP-1998-
207654, May 1998: 49-63.
[5] M. Takemoto, A. Chiba and T. Fukao, "A New Control Method of Bearingless Switched Reluctance Motors Using
Square-wave Currents," Proceedings of the 2000 IEEE Power Engineering Society Winter Meeting, Singapore,
CD-ROM, Jan. 2000: 375-380.
[6] H. J. Wang, D. H. Lee and J. W. Ahn, "Novel Bearingless Switched Reluctance Motor with Hybrid Stator Poles:
Concept, Analysis, Design and Experimental Verification," The Eleventh International Conference on Electrical
Machines and Systems, 2008: 3358-3363.
0
2000
4000
6000
8000
0 0.02 0.04 0.06 0.08 0.1
spee
d in
rp
m
time in sec
speed when switching angle is reduced
speed with PI
speed withSMC
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[7] Dong-Hee Lee, Jin-Woo Ahn, "Design and Analysis of Hybrid Stator Bearingless SRM", Journal of Electrical
Engineering & Technology, 2011, 6(1): 94-103.
[8] D.H. Lee, Z. G. Lee, Liang Jianing, J.W. Ahn, "Single-Phase SRM Drive With Torque Ripple Reduction and
Power Factor Correction", IEEE Trans. on Industry Applications, Vol 43, Issue 6, pp.1578 – 1587, Nov.-dec.
2007.
[9] H. J. Wang, "Design and Control of a Novel Bearingless Switched Reluctance Motor," Industrial System
Engineering of the Kyungsung University, Busan, Korea, PhD’s thesis, June. 2009:6.
[10] Zhenyao Xu, Dong-Hee Lee, Jin-Woo Ahn," Modeling and Control of a Bearingless Switched Reluctance Motor
with Separated Torque and Suspending Force Poles".
[11] Zhenyao Xu, Fengge Zhang, Jin-Woo Ahn." Design and Analysis of a Novel 12/14 Hybrid Pole Type Bearingless
Switched Reluctance Motor"
[12] Zhenyao Xu, Dong-Hee Lee, Jin-Woo Ahn," Control Characteristics of 8/10 and 12/14 Bearingless Switched
Reluctance Motor", the 2014 International Power Electronics Conference.
[13] L. Chen and W. Hofman, "Analytically Computing Winding Currents to Generate Torque and Levitation Force
of a New Bearingless Switched Reluctance Motor," in Proc 12th International Power Electronics and Motion
Control Conference, Portoroz Slovenia, 2006: 1058-1063.
[14] L. Chen and W. Hofman, "Performance Characteristics of One Novel Switched Reluctance Bearingless Motor
Drive," in Power Conversion Conference 2007 (PCC '07), Nagoya, 2007:608-613.
[15] L. Chen, W. Hofmann, "Analysis of Radial Forces Based on Rotor Eccentricity of Bearingless Switched
Reluctance Motors," in International Conference on Electrical Machines, Rome, 2010.
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