Download Accurate Position Estimation in Switched Reluctance Motor With

Accurate Position Estimation in Switched Reluctance Motor With
Prompt Starting
Debiprasad Panda, Student member IEEE, and V. Ramanarayanan
Department of Electrical Engineering,
Indian Institute of Science, Bangalore 560012, India
email: [email protected], [email protected]
1.0 INTRODUCTION
This paper presents a novel method of position estimation for Switched Reluctance (SR)
Motor. The method is suitable from starting to full speed. It ensures smooth starting without
initial hesitation. The method further incorporates a better position estimating algorithm
incorporating corrections for excitation voltage and mutual inductance effects. The algorithm
is better suited in a digital control platform for its realisation. Digital signal processor (DSP)
with its high computation power has ushered in fresh possibilities for such schemes. In the
present work, a general purpose DSP platform is used for the position estimation as well as
control of the SR motor. A Texas Instruments make DSP (TMS320c50) is used for this
application.
2.0 POSITION ESTIMATION
A number of methods have been reported in the literature for the estimation of rotor
position in SR motors [1]. Among these methods, those based on the flux-linkage current
characteristics have become popular [1, 2]. Figure 1 shows the block schematic of the basis of
position estimation. Flux-linkage of any phase is computed from Eq. (1).
Ψ = ∫ (V − R i) dt
v(t)
i(t)
(1)
Compute ψ using
Eq. 1
ψ
Speed
ω
ψ − i characteristics θ computation
Fig. 1 Schematic of the Position Estimation Method
1
0A
18A
1
25°
Position
20°
20°
15°
12°
10°
Central Zone
22.5° 0.8
0.6
0.4
30°
Flux Linkage
30°
15°
7.5°
0°
0.2
5°
0°
0
0
Flux Linkage (Wb)
1
0
5
Fig. 2 Flux-Linkage Characteristics
10
Current
15
20
Pre-computed ψ - i characteristics as shown in Fig. 2 is stored in a look-up table to
compute position from the measured phase voltages and currents. Position update may be
carried out once in a cycle (discrete estimation) with measurement of voltage and current in
one phase or on a continuous basis (continuous estimation) with measurement on all four
phases.
3.0 IMPORTANT ISSUES IN POSITION ESTIMATION
There are several important issues involved in the position estimation method outlined
above. These are listed as follows.
1
The ψ - i characteristics are pre-computed. The precomputed characteristics are
obtained by tests done under static conditions. These methods do not take into
account the non-idealities associated with the dynamic conditions under which the
machine is operating. Such non idealities are related to two aspects.
i
The eddy current effects in dynamic condition may influence the ψ − i
characteristics of the SR motor. These influences may introdued an error in
the estimated position. The eddy current effects are well covered in
literature [2].
ii The static ψ - i characteristics does not take into effect the mutual coupling
between the various phases during dynamic operation. It is mentioned in
literature that these effects can introduce errors in the flux-linkage
characteristics as high as ± 10% [2].
2
2
Most position estimation methods do not cover starting condition. It is known that,
SR motors with sensorless operation may suffer from starting problem if proper
starting algorithm is not adopted.
4.0 POSITION ESTIMATION ALGORITHM
The position estimation algorithm reported in this paper is a composite method
incorporating the following features.
1. On starting, test excitation is employed to select the appropriate phases to be excited.
Direct control of the current injected during starting ensures test pulse in the
non-saturated zone of ψ - i characteristics. Following this approach hesitation free
prompt starting is possible.
2. On running, the algorithm incorporates the following corrections.
i
Appropriate phase is chosen for estimation. Whenever, a particular phase
is within 7.5° to 22.5° (central zone, c.f. Fig. 2), it is called the active
phase and that phase is chosen for position estimation during that period.
ii The nature and quantum of corrections required to account for eddy current
effects and mutual coupling effects are obtained through off-line
measurements. Such corrections are applied to the compke it compatible
with the stored static ψ − i characteristics.
5.0 POSITION ESTIMATOR REALISATION
The block diagram of the position estimator following the above method is shown in
Fig. 3. Six analog signals (the four phase currents and two dc link voltages) are taken as
inputs through ADC. All analog signals are processed through software low pass filter (LF) to
attenuate the switching and high frequency noises. The estimator logic generation block
decides on the active phase. Eddy-current effcet is decided by the rate of change of
flux-linkage in the active phase. Thus in this work, the eddy current correction term, K ce , is
made a function of
dψ j
dt
. The corrected gradient of flux as shown in the figure is
dψ je
dt
. The
computed flux obtained through the integration is further corrected for mutual flux due to the
other conducting phases. Notice that the integration shown in Fig. 3 is multidimensional.This
corrected flux may be treated as same as the static flux-linkage characteristics. From the
corrected flux ψ jj and the active phase current i j , position is looked-up from the stored static
3
i
1
LF
ij
i2
LF
i
3
i
4
Vdc1
Vdc2
Static Flux-linkage
characteristics
ij
θj
ψ
Eddy correction
LF
LF
LF
vj
Kce
Rj
Active Phase
-
+
+
+
Estimator
Logic
Generator
dΨ j
dΨ je
dt
dt
∫
Mutual Flux
ik
ψj
jj
+
−
ψjk
θ=
g(i,ψ)
Other conducting Phase
LF
θk
ψjk =φ
(
i k ,θ k )
Fig. 3 Block diagram of Continuous Position Estimator using Flux/current Method
including eddy-current and mutual flux correction (shown in blod line).
flux-linkage characteristics. From the figure, it may be seen that three look-up tables are
searched at every sample time, namely - (i) eddy current correction, (ii) mutual flux and (iii)
static flux-linkage. All three look-up tables are obtained through off-line measurements [2, 3].
The flow chart for the complete position estimator including starting algorithm is given in
Appendix.
6.0 CONTROLLER REALISATION
Apart from the above estimator, the control of SR motor involves a number of
operations such as speed computation, execution of speed and current controller, execution of
torque to current conversion, T-on and T-off angle selection (Turn-on and Turn-off angle of
each phase) and final switching logic generation etc. Besides the estimator, all these jobs are
to be carried out once in every sample period. The block diagram of complete controller is
shown in Fig. 4. A PI controller serves as speed controller and the current control is through
hysteresis.
The execution of the control scheme (including the estimator) as discussed above is time
critical. Digital controller is ideal choice for realising such controllers. In this work, a Texas
Instruments make, 16-bit fixed point DSP (TMS320c50) is used for controlling the SR
motor. A general purpose DSP board is fabricated for realisation of this controller. The
4
Ifb
Ω ref
Tq*
Speed
controller
+
-
I*
+
Vdc
Ω fb
Hysteresis
controller
T-on
Speed computation
SR motor
Converter
T-off
i
j
θj
Vj
Switching signal
generator
Fig. 4 Controller block diagram with Estimator
PAL
S/H
S/H
S/H
S/H
S/H
S/H
S/H
S/H
S/H
S/H
Serial Port Link
TMS320C5x
DSP Starter
Kit
Jumpers
Dig.
I/O
Timers
ADC
PWM Connector (P5)
Analog Outputs (P2)
Analog Inputs (P1)
MUX
9V AC
Conn.
+5V
-5V
DAC
Interrupt Connector (P7)
Power Supply Connector
DAC
RAM
Buffers
Analog Section
ROM
RAM
ROM
Digital Section
Fig. 5 General Purpose DSP Controller Board
schematic of the board is given in Fig. 5. The board consists of two quad DAC, one 16
channel ADC (1.5 µS conversion time for each channel) with 10 simultaneous S&H circuits,
two 8253/8254 timers and one 8255 digital port. Provisions for external RAM and EPROM
are kept in case the on chip RAM (9K) is not sufficient. For this particular application, one
digital output port and six ADC channels are used. With the help of DSP, the sampling and
execution time achieved for the whole process is 100 µs , which is quite satisfactory for this
5
applications. The algorithm is tested on a 4kW, 4-phase, 8/6 pole OULTON motor. A
split-capacitor link power converter is used for controlling the motor. The schematic of the
power converter is given in appendix.
7.0 EXPERIMENTAL RESULTS
With the above estimation process and TI DSP, it has been possible to obtain position
estimation with errors less than ± 2° for the 8/6 SR motor at speeds upto 1500 rpm. In order to
illustrate the accuracy of the estimation, estimated position is compared with the actual
position obtained from a position sensor. A typical test result at 375 rpm is shown in Fig. 6.
The motor can start promptly from any position following the proposed method. Figure 7
illustrates the position estimation results and phase current of a particular phase during
starting. The speed transient from standstill to rated speed (1500 rpm in this case) with
estimated position and with position sensor are given in Fig. 8. The results confirm that the
proposed estimator may be used for all practical applications.
8.0 CONCLUSION
The discussion and test results in the preceding sections lead to the conclusion that truly
sensorless operation of SR motor in the entire speed range including prompt starting is
possible. The realisation of the above sensorless controller is feasible with appropriate control
platform and estimation strategy. TI DSP with powerful instruction set and high clock rate
helps realising such controller.
60
degree
50
30
20
10
0
40
20
0
-0.1
40
Current (A)
Position in degree
60
0
0.02
0.04
0.06
0.08
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
20
10
0
-0.1
Time (s)
Fig. 7 Estimated Position (Upper Trace)
and Phase Current (Lower trace) during
starting.
Time (s)
Fig. 6 Comparison of Actual Position
(Dotted) and Estimated position (bold) at 375
rpm (steady-state)
6
1600
(i)
1400
1200
rpm
1000
800
600
400
200
0
-2
0
2
4
6
Time (s)
8
10
0
2
4
6
Time (s)
8
10
1600
(ii)
1400
1200
rpm
1000
800
600
400
200
0
-2
Fig. 8 Test results of Speed Transient: (i) With estimated position, (ii) With actual position
from 0 to 1500 rpm
REFERENCES
1. W.F. Ray, I.H. Bahadly, "Sensorless Methods for Determining the Rotor Position of
Switched Reluctance Motor", Proc. of 5th Europeon Conference on Power electronics
and Applications, IEE publication no. 377, Sept. 93, Vol. 6, pp 7-13.
2. Debiprasad Panda and V. Ramanarayanan, "An Accurate Position Estimation Method
for Switched Reluctance Motor Drive", International Conference on Power
Electronics Drives and Energy Systems (PEDES'98), Perth, Australia, December,
1998, pp 523-528.
3. V. Ramanarayanan, L. Venkatesha, Debiprasad Panda, "Flux-linkage Characteristic of
Switched Reluctance Motor", Power Electronics Drives and Energy System
conference( PEDES-96 ) Delhi, December 1996, pp 281-285.
7
Appendix
(i) Flow-chart for the complete estimator including starting algorithm
Initialisation
Starting algorithm
Give Excitation to all the 4 phases and monitor
the current of all phases
If
Any phase Current>5A
No
yes
Detect the phase which is carrying maximum current
Choose the phase next to it in the sequence as Active
phase and use for position estimation
Acquire all the phase currents and dc link voltages ;Choose the Active
phase (j-th phase) and Compute the flux gradient of the active phase
dψ j
dt
= (v j − R j i j )
Correct the flux gradient for eddy currents
dΨ je
dt
= (v j − R j i j + K ce )
Compute the flux (eddy current corrected) of Active phase
Ψ j = ∫(v j − R j i j + K ce )dt
Apply the corrections for mutual fluxes
Ψ jj = Ψ j + ΣΨ jk (i k, θ k )
Find the position from the stored look-up
table using, θ j = f(Ψ jj , i j )
Wait for the next Interrupt
8
(ii) Schematic of the Split-link capacitor Converter
Current sensors
Q1
Q3
3-Ph
AC
R
D1
C1
Y
D3
Ph1
Ph3
Ph2
Ph4
C2
B
D2
Q2
N
D4
Q4
Current sensors
9
10