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Back EMF Sensorless-Control
Algorithm for High-Dynamic
Performance PMSM
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL.
57, NO. 6, JUNE 2010,P.2092~2100
Fabio Genduso, Rosario Miceli, Member, IEEE, Cosimo Rando,
and Giuseppe Ricco Galluzzo
Adviser : Y.S. Kung
Student :Jin-Mu Lin
1
Outline
Abstract
 Introduction
 Control-algorithm description
 Experimental results
 Conclusion
 Appendix
 References

2
Abstract

1. a low-time-consuming and low-cost sensorlesscontrol algorithm for high-dynamic performance
permanent-magnet synchronous motors.

2. This control algorithm is based on the estimation
of rotor speed and angular position starting from
the back electromotive force space-vector
determination without voltage sensors by using the
reference voltages given by the current controllers
instead of the actual ones.
3

3. This choice obviously introduces some errors
that must be vanished by means of a compensating
function.

4. The mathematical structure of the estimation
guarantees a high degree of robustness against
parameter variation as shown by the sensitivity
analysis reported in this paper.
4
Introduction

1. in field-oriented control for brushless machines,
the exact knowledge of the rotor angular position is
needed.

2. when the rated power of an electrical machine is
small or fractional,the electrical-drive
comprehensive cost will raised.
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3. the signal transmission between sensor and
control systems can be subjected to
electromagnetic interference (EMI) coming from
external sources, producing an error in
measurement that may be significant for feedback
control.
4.So in this paper, a novel low-time-consuming and
low-cost sensorless-control algorithm for PMSM
drives, both surface or IPM mounted.

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Control-algorithm description

A. PMSM Mathematical Model
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8
the torque expression

in (1) becomes

Because of the constant PM flux, the
torque depends only on the quadrature
component of the stator current.
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B. Description of the Estimator

Assuming a balanced three-phase system,
the expression of the back EMF space
vector
components is
10

The argument of the back EMF clearly is
not the real rotor position.
11

A simple analysis on the machine model at
steady state with id = 0 gives the following
expression for correct rotor position:
12

Let T be the lag time introduced by the
inverter and be the first term of (4),
13

Now, after substitution, considering a wellknown calculus formula for the increment
of functions, we can write
14
and developing the partial derivatives of
the incremental term
(𝜕 𝐹 /𝜕𝑣 𝛼 )𝛿𝑣 𝛼 + (𝜕 𝐹 /𝜕𝑣 𝛽 )𝛿𝑣 𝛽
, we get

15

Now, neglecting all harmonics, consider that
𝑣𝛼 and 𝑣𝛽 are, respectively, cosine and sine
functions of ωt. The same can be
said for 𝑣 ∗ 𝛼 and 𝑣 ∗ β . In particular, it is
where V is the rms value of the stator voltage.
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
It is now clear that T being very small
compared with 2π/ω
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
In this way, our previous expansion of (8)
reduces to
18

that in a more compact form becomes

cos(ϕ) being the power factor in the motor
operation and V , I,and E are, respectively,
the rms values of the stator
voltages,currents, and back EMF.
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
Equation (12) may be written also in
complex-number form

where ( ∗ ) denotes the complex conjugate.
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
Furthermore, as with 𝑖𝑑 = 0, the motor
drive operates with near-unity power
actor, (12) can be further simplified as
follows:
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
Introducing these speed- and currentoffset corrections in (4), one finally gets a
suggestion for the first expression of
“estimated” position
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
Fig. 2 shows the sum of speed and
current offsets
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
Equation (15) may be rewritten in a
differential form by substituting 𝜔 with the
derivative of 𝜃est
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C. Estimator Realization

Taking the presence of the PI into
account, the ultimate estimator-equation
form is
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Estimator block diagram.(Fig.3.)
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Experimental results
A. Description of the Test Bench
 1) an IPMSM;
 2) a controlled hysteresis brake;
 3) a digital signal processing and control
engineering(dSPACE) board;
 4) a resolver (used only for comparison purpose).
A master Power PC 604E and a Ti slave DSP of the
type TMS320F240.
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Test bench for IPMSM
electrical-drive machine.(Fig.4.)
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B.Results and Discussion
 1)
step change in motor speed from
400 up to 4000 r/min (nominal speed)
and back again to 400 r/min.
 2) sudden application of a 1.8-N · m
load torque while the motor runs at
4000 r/min speed.
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Comparison between (solid line) real and
(dashed line) estimated speed during the
execution of test n. 1.

Fig. 5.
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(Solid line) Real and (dashed line) estimated
position during the execution of test n. 1.

Fig. 6.
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Comparison between (solid line) real and
(dashed line) estimated rotor position during
the execution of test n. 2.

Fig. 7.
33
Comparison between (solid line) real and
(dashed line) estimated rotor speed during
the execution of test n. 2.

Fig. 8.
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Estimation error for rotor speed during the
execution of test n. 2.

Fig. 9.
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Conclusion
this paper, a low-time-consuming and lowcost sensorless-control algorithm for PMSM
without voltage probes for position and
speed estimation has been introduced,
discussed, and experimentally verified.
 Drive starting is made with open-loop
operation.

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
in the proposed control systems, the
reference voltages instead of the actual
voltages are used for the back-EMF
estimation,therefore eliminating the presence
of voltage probes.
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
Clearly, the presented correction method is
intended, above all, to make the electrical
drive cheaper and suitable for industrial
drives both surface or internal mounted PM
working within the nominal speed range, as,
for example, for spindle drives, while the field
weakening is not taken into account.
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