EVALUATION OF A NOVEL ANALOG BASED
CLOSED-LOOP SENSORLESS CONTROLLER
FOR SWITCHED RELUCTANCE MOTOR DRIVE
S K Mondal1,2, S N Saxena2, S N Bhadra3 and B P Muni2
1
Dept. of Electrical Engineering
University of Tennessee
Knoxville, TN 37996-2100
Tel: (865) 974 9886
e-mail: smondal@utk.edu
2
Bharat Heavy Elecricals Ltd.
Corporate R&D Division
Hyderabad - 500 093
India
3
Dept. of Electrical Engineering
Indian Institute of Technology
Kharagpur – 721 302
India
region of the phase at some angle before the instant at
which the positive-dL/dθ starts. The IGBT in series with
the stator phase must be turned-off in the positive-dL/dθ
region, at some angle ahead of the instant where the
inductance becomes maximum (Lmax).
Abstract - A novel analog closed-loop controller for a 4phase Switched Reluctance Motor (SRM) in variable
speed drive applications, dispensing with position and
speed sensors, has been proposed in this paper. The
scheme is based on comparing the active current of a
phase with a closed-loop switching reference current
(Ioref) with the intention of switching-on and switchingoff the other phase in the pair, which comprises of two
stator phases, whose Lmin-zones do not overlap. This
technique requires no parameter measurement and/or
estimation and without prior knowledge of stator fluxlinkage variation. Paper also includes an analog
controller with position sensors to evaluate the
developed sensorless controller. A detailed simulation
study of both the drive systems, supported by
experimental steady-state and transients results, are
presented to validate the proposed technique. A double
polynomial-fit is used in the simulation study to
describe the non-linear magnetization characteristics of
the SRM. The performance of the sensorless drive is
excellent and is in good agreement with the drive with
position sensors.
To overcome the drawbacks of using direct rotor position
sensors, various methods of sensorless rotor position
detection are available [2]. The general principle behind
most sensorless drives is that, if at a given instant, fluxlinkage (ψ) (or inductance (L)) and phase current (i) are
obtained, rotor position (θ) can be obtained from preknowledge of the SRM magnetic characteristics.
A number of papers have been published on the analysis,
design and control of SRM taking saturation into account
[3]. Authors propose a simplified mathematical model,
representing flux-linkage characteristics, for use in the
simulation study of a saturated SRM. A double
polynomial-fit is used to describe the non-linear
relationships between ψ, i and θ. This model does not
require mechanical details of the machine, but requires
only the experimental determination of the magnetization
characteristics.
1. INTRODUCTION
The Switched Reluctance Motor (SRM) is now a
recognised machine on account of its several advantages
[1]. It is a doubly-salient electric machine, with single
excitation to the stator winding. When a stator pole-pair is
energized, a flux-path is established. The torque is
generated by the tendency of the rotor pole-pair to align
with the stator pole-pair. However, SRM needs real time
rotor position detection, either directly or indirectly, for
energization and de-energization of its stator phases in
sequence with relation to its rotor position to obtain the
desired control of speed and torque and to maximize the
efficiency. The controller can be implemented using
analog, microprocessor or personal computer based
techniques. An inverter is a must with the SRM. The IGBT
in series with a stator phase must be turned on in the Lmin-
2. PHILOSOPHY AND CONCEPT OF DEVELOPED
SENSORLESS CLOSED-LOOP SRM DRIVE
The basic principle of a sensorless control scheme, without
prior knowledge of stator inductance variation to extract
the instantaneous rotor position information, is introduced
in this section. The proposed control approach requires no
parameter measurement and/or estimation. The controller
block diagram including its power circuit is shown in Fig.
1 for the most widely used 8/6-pole, 4-phase, 4 kW SRM.
The principle of the proposed analog closed-loop
sensorless SRM drive, dispensing with speed and position
sensors, is based on comparing the active current of a
phase with a closed-loop switching reference current (Ioref)
0-7803-7116-X/01/$10.00 (C) 2001 IEEE
2073
with the intention of switching-on and switching-off the
other phase in the pair, which comprises of two stator
phases, whose Lmin-zones do not overlap [4]. The value of
Ioref, which is determined by the closed-loop speed control
of the SRM drive, depends on the state of the motor
(starting or running) and/or the load demand. This
approach offers a very cost-effective, simple and rugged
controller for the SRM drive.
Table-1.2: Switch-on logic
Phase of the falling current
1
4
3
2
Phase to be made ON
3
2
1
4
With the above logic, the phase-1 remains OFF as long as
i3 is above iref value; and the phase-1 remains ON as long
Fig. 1: Block Diagram of Sensorless Controller
The ON/OFF logic of the phases is selected in a way so as
to ensure that an incoming phase is switched-on in its Lminzone and the outgoing phase is switched-off near its Lmaxzone. For this purpose, the rising current in an incoming
phase is compared with Ioref; and when this phase current
exceeds the Ioref, a logic is used to switch-off the IGBT of
the other pair-phase which is nearing or has crossed the
Lmax-zone. This sequence of switching on and switching
off logic is illustrated in Fig. 2 with reference to phases 1
and 3, whose Lmin-zones do not overlap. Phase-3 is turnedon in Lmin-zone; and when the rising current i3 exceeds the
Ioref, this HIGH/LOW logic is used to switch-off the IGBT1 of phase-1. Similar switch-off logic is decided for the
other three phases also, as detailed in Table-1.1. Next,
when the same phase current i3 in its falling mode becomes
lower than the switching reference current Ioref, this rotor
position is detected and is used to switch-on the IGBT of
the other pair-phase (i.e. i1), which was turned-off by the
phase-3 during its rising current mode. The switch-on logic
of the four phases has been furnished in Table-1.2.
Fig. 2: Generation of Switch-on and Switch-off Signals
as i3 is below iref value. The principle is applicable for even
number of phases. The strategy, however, becomes
operative only after the motor starts. A starting logic
circuit has been incorporated in the scheme.
Phase to be made OFF
The actual phase currents of the 4 phases (i1 to i4) are
sensed through four respective Hall-effect current sensors
(HC1 to HC4). These phase currents are used for position
detection, as well as for speed estimation and for balancing
the split-link dc voltages. The phase currents are compared
with a switching reference current (Ioref) in a comparator
block CR (block-(1) in Fig. 1) to decide the switch-on and
switch-off logic for the appropriate phases. The particular
phase(s), which is(are) in Lmin-zone at that instant, will
only give HIGH output at the output of the comparator (as
di/dt=(v-Ri)/Lmin). This HIGH status will remain HIGH as
long as the value of the particular phase current is greater
than Ioref.
3
2
1
4
Ioref is obtained as the algebraic difference of the reference
current (Iref) and the offset current (Ioff) (block-(7) in Fig.
1). Iref is the output from the PI-block, limited by the
current limiter block. Ioff is a fraction of the reference
Table-1.1: Switch-off logic
Phase of the rising current
1
4
3
2
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current (k.Iref). If there is any change in speed and/or load,
the value of Iref is changed dynamically, which, in turn,
changes the value of Ioref dynamically with the changes in
the value of Iref. Switching reference current (Ioref) has
profound influence on dwell angle. The value of Ioref has
not been analytically established. However, the best course
has been found to be experimental tuning of Ioref. Extensive
tests carried out suggests that Ioref should be between 65 to
85 per cent of the reference current (Iref). Lower value of
Ioref suits the increase value of load torque.
generation of actual speed signal, using a frequency-tovoltage converter IC (block-(5) in Fig. 1), which gives a
voltage signal (ωact) proportional to the actual speed. Speed
error (ωerr) is processed through a PI block to generate the
reference current (Iref).
The HC block (block-(2) in Fig. 1) is a hysteresis type
current regulator, which attains OFF or ON state according
to whether the phase current is greater or lower than the
reference current. This block is used for balancing the
phase currents. By introducing this block, it has been
ensured that all the four phases carry balanced currents.
This also takes care of the voltage balance in split-link dc
supply.
The HIGH/LOW comparator outputs of the four phases
from the CR block are fed to the LOGIC block (block-(3)
in Fig. 1). The LOGIC block consists of three sub-blocks.
To start the motor in a particular direction from any
starting position, initially all the phases are fired in a
sequence one after another. For example, for starting in the
forward direction, the starting sequence is 1, 4, 3 and 2.
Each output of the HC block is ANDed with the
corresponding ON/OFF signal output from the LOGIC
block to obtain the final signals (block-(4) in Fig. 1) for the
gate-drive circuits of the IGBTs, controlling the currents in
the four phases of SRM.
As soon as the motor starts rotating in a particular
direction, the starting sequence logic becomes ineffective.
Therefore, just immediately after the start, all the four
phases are ON. As can be seen from Fig. 3, there is always
at least one, or maximum two Lmin-zone (this overlapping
zone is small), at any rotor position. Thus, only that
particular phase current, which is switched-on in Lminzone, will cross the reference value (Ioref) first, and switchoff the IGBT of a pair-phase unambiguously as per Table1.1. Also in the Lmin-zone, since the back emf of rotor is
zero, the current-rise is independent of the motor speed.
Thereafter, depending on the logic (as given in Tables-1.1
and 1.2), the phases are switched-off and switched-on
sequentially.
3. PHILOSOPHY AND CONCEPT OF DEVELOPED
CLOSED-LOOP SRM DRIVE WITH POSITION
SENSORS
This section presents a direct control strategy based on
rotor position information obtained from a physical
position sensor. One rotor replica is mounted on the rotor
shaft of SRM at the non-drive end of the motor, and four
real time position sensors (which are proximity switches)
are mounted through the holes at 450 apart on an annular
circular frame mounted at the same end on the stator in the
plane of the rotor replica and concentric with it. Rotor
replica moves within this fixed circular frame. Fig. 3
shows the idealised variation of inductances (L1 to L4) of
the four stator phases with rotor angle (θ) over one rotor
pole pitch of the SRM. Four sensors for the four phases
occupy the positions, each of which is at 30 after the front
edge of the respective stator pole (Fig. 3). Each sensor
gives a HIGH signal whenever the leading edge of a rotor
pole replica passes under the sensor. The duration of this
HIGH signal is equal to the rotor pole-arc. Thus, four
signals (S1 to S4 in Fig. 3) are obtained, one each at the
position of 30 from the start of the positive-dL/dθ region of
one phase over the rotor pole arc. This signal would
become LOW as soon as the trailing edge of the rotor pole
replica crosses that proximity switch.
At low speed (<250 rpm), since the back emf is small, the
current-fall may be slower in its falling mode. Due to this,
phase current may not come down below the switching
reference current. This may lead to the continuous OFF of
a phase in a pair; and the motor may stop, as the logic in
Table-1.2 fails. To avoid this, external ON and OFF logic
signals are generated from variable frequency oscillator;
and these logic signals are ORed with the main logic
signals (which are LOW) to make the phases ON and OFF
sequentially. This low speed logic below 250 rpm operates
in open-loop control. Running in closed-loop operation
below 250 rpm requires the phase voltage to be made a
control variable. For this, a feedback loop to control the
dc-link voltage at low speed is under progress.
Depending upon the motor characteristics, it is possible to
have different ON/OFF signal sets for different speed
zones by changing the initial location of the position
sensors before starting. It is seen from the Fig. 3 that three
different ON/OFF signal sets for the three different speed
zones are generated from the existing fixed four ON/OFF
signals. In the low speed zone (0<w≤500 rpm), switch-on
angle is -5.50, and switch-off angle is 180. In the medium
At high speed (>250 rpm), the phases are switched off and
switched on sequentially, as given in Tables-1.1 and 1.2,
respectively.
The speed control is done through a closed-loop PI control
(block-(6) in Fig. 1). The HIGH/LOW signal output of any
one phase current of the CR block is used for the
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speed (500<w<1200 rpm) zone, switch-on angle is -120,
and switch-off angle is 180. In the high speed zone
(w≥1200 rpm), switch-on angle is -20.50 and switch-off
angle is 180.
where
i
Wc(i,θ) = ∫ψ(i,θ)di
0
(2)
A phase winding of the SRM can be represented as a nonlinear (due to magnetic saturation effects), time-varying
(due to changes in rotor position with time) inductance.
Magnetization characteristic, neglecting hysteresis, for a
given θ between θu and θa may be represented by a
polynomial in phase current i with odd powers
(n=1,3,5…….) and coefficients that are function of rotor
position θ.
4. MODELING OF SRM – POLYNOMIAL-FIT
The simulation of electric drives helps in the pre-study of
the desired performance and in designing both power and
control circuits. Detailed simulation study to foresee the
performance of two drive systems has been done.
ψ(i,θ) = ∑an(θ)in
n
(3)
Fig. 3: Switching Logic Diagram for Controller with
Position Sensors with Idealized variation of L
Fig. 4: Typical Flux-linkage (i, ) and Inductance
L(i, ) characteristics for a SRM Phase Winding
The performance of SRM is influenced by its magnetic
(flux-linkage) characteristics and the control strategy. For
the SRM, ψ or L, is a non-linear function of i and θ, as can
be seen in Fig. 4; where, θu represents the unaligned rotor
position of minimum inductance and θa represents the
aligned position of maximum inductance. If iron losses are
neglected, the static magnetization characteristics can be
applied to evaluate the developed torque under dynamic
conditions when i and θ change continuously.
Odd powers of i have been taken since the same flux level
is set-up by both the positive and the negative values of i.
Coefficient an(θ) is again a non-linear function of θ, and
should exhibit a monotonous change in its value with the
increase in θ up to the maximum value of θ (i.e., aligned
position). Secondly, it should also exhibit periodicity as
the rotor poles move past the stator poles. Another
experimental evidence, viz torque is zero at aligned and
un-aligned positions, may be considered while giving
mathematical expression to an(θ). Considering these
aspects, an(θ) may be expressed as a polynomial in sinkθ
with even powers.
Like in any electromechanical energy converter [5], the
instantaneous electromagnetic torque Te(i,θ) produced by
one phase at any θ can be calculated from the winding coenergy Wc(i,θ) by the relationship :
Te(i,θ) = (∂Wc(i,θ)/∂θ)
(1)
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5. RESULTS
(n)
an(θ) = ∑dmsinmkθ
m
(4)
This section presents experimental waveforms obtained for
the same prototype SRM drive as well as the results for the
simulation study. The parameters of the SRM are given in
Appendix-II. The SRM was coupled to a dc generator. The
load on SRM was varied by varying the load on the dc
generator. The drive system was tested extensively under
both steady-state and transient conditions; but, only a few
pertinent results are furnished in this section.
for m=0,2,4,6……., and k is (Π/2θa).
Substituting the value of ψ from equation (3) to equation
(2) gives the following expression for co-energy Wc :
Wc = ∑an(θ)(in+1/n+1)
n=1,3,5
(5)
From equations (1), (4) and (5), the motor torque produced
by a phase current is:
(n)
Te(i,θ)=(Π/2θa)coskθ∑(∑mdmsinm-1kθ)(in+1/n+1)
n
m
(6)
for m=0,2,4…….; n=1,3,5…… ; and θ expressed in
radians.
For each of the four phases of SRM, the electromagnetic
torque component can be found out using the
corresponding values of current and rotor angle; and the
total electromagnetic torque developed by the SRM would
be the algebraic sum of the torque produced by each phase
at an instant.
Measured points [6] and the best fit polynomial (equation
3) of the machine flux-linkage are shown in Fig. 5.
Reasonable agreement can be noted. Appendix-1 gives the
numerical values of the coefficients in equations (3) and
(4). Predicted static torque, based on equation (6) and
some measured values [6] show reasonable agreement.
Fig. 6: Phase Currents for Sensorless Scheme at 500
rpm; i1 Presented for Comparison and Reference
(Scale: 4A/Div.)
Fig. 6 presents typical steady-state phase current
waveforms for system without sensors at 500 rpm. The
corresponding simulated current waveforms are shown in
Fig. 7. The waveforms indicate that the machine phase
currents in all the four phases are well balanced with the
desired phase shifts of 450, 300, 150. It is observed that the
simulated results match closely with the experimental
results. The developed ON/OFF switching logics for the
sensorless drive has been confirmed both by experimental
as well as by simulated waveforms, as can be seen from
Fig. 8 for the simulated conditions and from Fig. 9 for the
experimental conditions at a speed of 1000 rpm. The
sequence of switching on and off logic is illustrated in
Fig. 5: Magnetization Characteristics with Pole
Alignments as Parameters
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these figures with reference to pair phases-1 and 3, whose
Lmin zones do not overlap. Figs. 10 through 12 show the
building-up of actual speed, reference current and phase-1
current upon sudden application in the set speed of 550
rpm from zero value for both the schemes. Overall
agreement in the response between the two schemes is
noted, inspite of starting the drive at any arbitary rotor
position with sensorless scheme. Responses for both the
schemes are almost identical. Similarly, Fig. 13 shows the
response for sudden change in load torque for the set
speed. Results are matching for both the schemes.
Therefore, the developed controller gives steady-state and
transient performances comparable to those of SRM drive
with position sensors whose controller has also been
developed.
Fig. 8: Phase-1 and Phase-3 Currents, Control Signals,
Iref and Ioref (Sensorless Scheme (Simulation))
at 1000 rpm (Scale for Control Signal: 7.5 V/Div.)
Fig. 9: Phase-1 and Phase-3 Currents and their Control
Signals (Sensorless Scheme) at 1000 rpm
Fig. 7: Phase Currents for Sensorless Scheme at 500
rpm (Simulation)
i1 Presented for Comparison and Reference
6. CONCLUSIONS
Fig. 10: Speed Response during Starting
Ref. Speed: 550 rpm; Shaft Torque: 2 Nm
(Top: Ref. Speed, Bottom: Actual Speed)
(Scale: 500 rpm/Div.; 200 ms/Div.)
The paper has described a novel position and speed
sensorless analog SRM controller without parameter
estimation and without using any complex control circuit.
The active phase current waveforms of the excited stator
phases have been used to sense the rotor position. This
avoids the need for pre-programmed ICs. The developed
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Fig. 13: Speed Response during Sudden Change in
Load Torque; Ref. Speed: 550 rpm
(Top: Actual Speed, Bottom: Phase-1 Current)
(Scale: 500 rpm/Div., 8 A/Div.; 1 s/Div.)
Fig. 11: Ref. Current and Actual Speed during
Starting; Ref. Speed: 550 rpm; Shaft Torque: 2 Nm
(Top: Ref. Current, Bottom: Actual Speed)
(Scale: 8 A/Div., 500 rpm/Div.; 2 s/Div.)
The starting of SRM is possible from any arbitrary position
and in any particular direction, without following the usual
approach of the inductance measurement at standstill by
diagnostic pulses. Total control circuit is based only on the
conventional analog and digital ICs, making the
measurement extremely fast. The power circuit cost is also
low due to the use of single device per phase.
References
Fig. 12: Ref. and Actual Phase-1 Current during
Starting
Ref. Speed: 550 rpm; Shaft Torque: 2 Nm
(Top: Ref. Current, Bottom: Actual Current)
(Scale: 8 A/Div.; 2 s/Div.)
controller is conceptually simple and gives steady-state
and transient performances comparable to those of SRM
drive with position sensors whose controller has also been
developed. It provides a simple and cost-effective
alternative to the complex sensorless controllers described
in the literature. The applicability of the developed
sensorless technique has been validated by means of
extensive simulation and experimental results.
2079
1.
T J E Miller, “Switched Reluctance Motors and their
Control”, Magna Physics Publishing and Clarendon
Press, 1993.
2.
B Fahimi, G Suresh and M Ehsani, “Review of
Sensorless Control methods in Switched Reluctance
Motor Drives”, IEEE Industry Applications Conf., Oct
2000, Vol. 3, pp.1850-1857.
3.
G S Buja and M I Valla, “Control Characteristics of
the SRM Drives. Part-II: Operation in the Saturated
Region”, IEEE Trans. on Indus. Electronics, Vol. 41,
No. 3, 1994, pp. 313-321.
4.
S K Mondal, S N Saxena and S N Bhadra, “A Novel
Analog Method for Sensorless Closed-Loop Control
of SRM without Parameter Estimation”, Conf.
Records, IEEE Power Elec. Spec. Conf, May 1998,
Vol. 2, pp. 2076-2082.
5.
A E Fitzgerald, Charles Kingsley, Jr., and Stephen D
Umans, “Electric Machinery”, 5th Metric Edition,
1992.
6.
S K Panda and G Amaratunga, “Waveform Detection
Technique for Indirect Rotor-Position Sensing of
Switched-reluctance Motor Drives. Part 1:Analysis”,
IEE Proc. B, Vol. 140, No. 1, January 1993, pp. 8088.
II. SWITCHED RELUCTANCE MOTOR
PARAMETERS
Output Power - 4.0 kW
Number of Phases - 4
Number of Stator Poles - 8
Number of Rotor Poles - 6
Aligned Inductance, Lmax - 110 mH
Un-aligned Inductance, Lmin - 10 mH
Stator Pole Arc - 200
Rotor Pole Arc - 21.50
Inertia, J - 0.002 kg/m2
Phase Voltage, Vdc - 280 V
Nominal Phase Current - 9 A
Phase Resistance - 0.7 ohm
Rated Speed - 1500 rpm
APPENDIX
I. COEFFICIENT VALUES
For the level of saturation generally encountered in the
normal operating range of the motor, a 7 degree
polynomial with 4 odd terms in equation (3) and 6 degree
polynomial with 4 even terms in equation (4) are found to
be adequate. Thus, the flux-linkage variation of the test
motor with current and rotor position is described by the
following polynomial equation.
ψ(i,θ) = a7(θ)i7 + a5(θ)i5 + a3(θ)i3 + a1(θ)i
(7)
where,
a7(θ) = 10-7(-0.1714sin63θ+0.0350sin43θ-0.0793sin23θ
-0.0027)
a5(θ) = 10-5(0.5540sin63θ+0.0589sin43θ+0.2840sin23θ
+0.0018)
a3(θ) = 10-3(-0.6821sin63θ-0.1097sin43θ-0.4909sin23θ
+0.0130)
a1(θ) = (-0.0401sin63θ+0.1043sin43θ+0.0442sin23θ
+0.0099)
in which, θ is the rotor position in radian with reference to
the un-aligned position.
Co-efficient ‘a1’ estimates the linear inductance value for
any position. Thus, by (7), linear inductance values for unaligned (00) and aligned (300) positions are, respectively,
9.9 and 118.3 mH, which are in reasonable agreement with
10 and 110 mH, as available from manufacture’s data.
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