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Robot and Servo Drive Lab.
DSP-Based Control of Sensorless IPMSM Drives
for Wide-Speed-Range Operation
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, p720-727,FEBRUARY 2013
Gaolin Wang, Rongfeng Yang, and Dianguo Xu, Member, IEEE
學生: Guan-Ting Lin
指導老師: Ming Shyan Wang
Department of Electrical Engineering
Southern Taiwan University of Science and Technology
2016/7/13
Outline


Introduction
Control scheme




Position estimation at low-speed
Position estimation at high-speed



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Sensorless IPMSM Control Scheme Based on DSP
Mathematical Model of the Interior PMSM
Design of Sliding-Mode Position Observer
Dead-Time Compensation Strategy
Experimental results
Conclusion
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Introduction

The first class is based on the electromotive force(EMF) machine model for
the middle- and the high-speed operation.

The other class is the high frequency (HF) signal injection estimation for
low-speed operation.

The hybrid position observer combines the HF signal injection at low speed
with the extended EMF observer at higher speed.

To improve the performance , a dead-time compensation strategy are
adequately considered.
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Southern Taiwan University of Science and Technology
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Control scheme

Sensorless IPMSM Control Scheme Based on DSP
Vector control scheme drive based on
the HF signal injection and the slidingmode observer.
The HF voltage signal is superimposed
to the voltage reference from the PI
current controller.
A sliding-mode observer based on the
extended EMF is designed to obtain
the rotor position.
A software phase-locked loop (PLL)
and a dead-time compensation method
are adopted
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Fig. 1. Control scheme of sensorless IPMSM based on DSP.
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
Mathematical Model of the Interior PMSM
Define a d–q frame, which corresponds to the synchronous rotating reference frame.
the voltage model can be given by
By using the rotating inverse coordinate transformation,(1) can be transformed to the
stationary frame (α–β):
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Then, the electromagnetic torque can be expressed as:
The electromagnetic torque of the IPMSM consists of two terms:
the magnetic reaction and the reluctance torque.
The mechanical motion equation of IPMSM is given as:
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Position estimation at low-speed
Assuming that the frequency is far higher than the fundamental frequency
the HF voltage model can be expressed as:
(3)
To analyze the characteristic of the HF voltage model conveniently,
(3) can be rewritten as follows:
(4)
k 1  1 /( L0 2  L12 )
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transform (4) to the d–q rotating reference frame, and the expression
can be given as:
(5)
Defining the estimated rotating frame as de  qe ,then (5) can be transformed
into the estimated frame as:
(6)
where the subscript “e” means the corresponding component in the estimated
rotating frame and Δθe means the position estimation error.
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In order to extract the rotor position from the HF current, a measured
frame dm - qm is defined.
The dm - qm frame lags the de - qe frame with  0 . Moreover, (5) can be
transformed to the measured frame as follows:
(7)
In a special case, if the measured frame lags the estimation frame with
0.25π, then (7) can be simplified to
(8)
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If the rotor position estimation error Δθe is sufficiently small, then (8) can be
approximated as
(9)
As a result, the equivalent estimation error signal ε for the rotor position
observer can be obtained from the magnitude of the measured HF current
components according to (9), which is given by
(10)
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the position estimation error signal
can be acquired from the magnitude
of HF current components in the
measured axes.
Fig. 2. Signal process for rotor position estimation using HF signal injection.
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Position estimation at high-speed

Design of Sliding-Mode Position Observer
A sliding-mode observer is designed using an equivalent extended EMF
model of IPMSM. It can provide fast convergence and low sensitivity
to parameter variations. It can be expressed as:
(11)
Where A2 =
B2=
,
z is the sliding-mode control function.
zeq is the equivalent control function. l
is the equivalent feedback gain.
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From (11), the difference between the actual stator current and the
estimated one is used to establish the sliding-mode control function z. Due
to the action of the sliding-mode controller, the current difference can be
reduced to zero. Moreover, the position estimation value will converge to
the actual one.
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From fig.3, It can be seen that the α–β-axis components of zeq
contain the sine and cosine functions of the rotor position signal,
respectively. Conventionally, the position can be calculated directly
through the arc-tangent function
However, the existence of noise
signal may influence the accurate
estimation of position. In particular,
during the EMF crossing zero,
using the arc-tangent function will
cause obvious estimation error.
Fig. 3. EMF-based sliding-mode observer adopting a software PLL.
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a software PLL is used to acquire rotor position according to the
estimated EMF information. In this way, the equivalent position
error signal from the EMF model can be obtained as:
Therefore, the position observer based on software PLL can
be expressed as:
where ξ1 and ξ2 are the gain coefficients of the PLL.
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
Dead-Time Compensation Strategy
To prevent the two insulated gate bipolar transistors (IGBTs) in an
inverter leg from conducting simultaneously, a small delay time is
added to the IGBT turn-on/turn-off.
Since no voltage sensors adopted to detect the stator voltage, the
voltage reference is used for the sliding-mode observer as the input.
The dead-time setting will produce an additional position
estimation error. Therefore, the dead-time compensation is
important for the sensorless control.
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The equivalent dead time ( terr ) can be expressed as:
where sign( iaf ) =
td
ton
toff
tavon
is the dead-time set value.
is the turn-on delay time.
is the turn-off delay time.
is the equivalent error time, representing the
average voltage drops of the IGBTs and the diodes
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us
ud
is the collector-emitter saturation voltage of the IGBT.
is the forward voltage of the freewheeling diode.
As a result, the average voltage error in one carrier period
can be expressed as:
where Ts is the PWM control period.
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An average dead-time compensation scheme based on the
voltage-error vector is adopted.
the voltage errors in the three-phase a-b-c stationary frame can
be obtained. Moreover, the voltage errors in the two-phase α–β
stationary frame can be calculated from
The voltage-error vectors in the α–β reference
frame can be described as Fig. 4.
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Fig. 4. Voltage-error vector in the stationary coordinate scheme.
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The dead-time compensation is carried out in the α–β reference
frame according to iαf and iβf .
The relation between the voltage references ( u 1 and u 1 ) and the
compensated voltage references ( u and u ) can be described as:
＊
＊
＊
＊
Where g (if ) can be expressed as:
where m is a small constant value related to the rated stator current;
it can be selected experimentally.
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Experimental results
The rated parameters of the IPMSM are listed as follows:
380V, 5.0A, 14 N  m, 75 Hz, 1500 r/min, Pn  3,
Rs  2.75Ω, Ld  45 mH, Lq  60 mH, and ψf  0.48 Wb.
The PWM switching frequency of
the inverter is10K Hz.
The dead time is set as 3.2 μs.
The magnitude and the frequency
of the injected HF voltage are
57 V and 1 kHz.
Fig. 5. Platform of 2.2-kW IPMSM sensorless control system
based on DSP.
(a) Drivers with dc-bus connection. (b) Load test platform.
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The two switching points of the hybrid position observer
are set as 150 and 300 r/min.
The parameters of the current PI regulator
Kp2 = 4 , Ki2 = 25.
The parameters of the speed PI regulator
Kp1 = 35 , Ki1 = 10.
The parameter of the sliding-mode observer is l = 1
The parameter of dead-time compensation m is selected as
2% rated stator current value.
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Fig. 6 shows, According to the sample value of stator current, the HF
current signal is obtained through the digital filters, and the estimated
position can be got.
Fig. 6. Signal process results of the HF signal injection at 50 r/min with 25% rated load.
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Fig. 7 shows, It can be seen that the speed estimation error is
within ±10 r/min during the transients, and the estimated speed
tracks the actual speed well. The IPMSM sensorless drive can
operate at zero speed with full load disturbance.
Fig. 7. Zero-speed sensorless operation with step rated load disturbance
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The estimation error is within ±0.05π. Moreover, the speed estimation error is
within ±8 r/min during the transients and the steady state.
Fig. 8. Motoring and regenerating sensorless operation at ±20 r/min with rated load.
(a) Actual speed and position. (b) Speed and position estimation error.
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From the dotted line area, the transient of the estimation errors during the
switch-over area is obvious. According to the actual speed, it can be seen
that the switching of the two different estimation methods is smooth.
Fig. 9. Position and speed estimation error during the switch-over area from
0 to 400 r/min with rated load.
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Fig. 10 shows, It can be seen that the sensorless IPMSM can operate at fullspeed range. The estimation error is within ±12 r/min in the whole speed
range.
Fig. 10. Sensorless operation from 1 to 1500 r/min, then back to 1 r/min with 50% rated load.
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At the beginning, the dead-time compensation is disabled, and the stator current
is distorted obviously. The dead-time effect results in large position estimation
error reaching 0.055π. Then, the dead-time compensation is enabled. The
aximum position estimation error is decreased to within 0.035 π.
Fig. 11. Dead-time compensation results at 600 r/min with 75% rated load.
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Conclusion

A position estimation method combining the HF signal injection and the slidingmode observer based on the EMF model for sensorless IPMSM.

The robust characteristic of the hybrid position observer can be achieved at fullspeed range.

The software PLL and the dead-time compensation method are effective for the
position estimation.

Even at the zero-speed operation, the sensorless IPMSM drive has strong
robustness to step rated load disturbance.
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