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Hybrid Terminal Sliding-Mode Observer
Design Method for a Permanent-Magnet
Synchronous Motor Control System
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,
VOL. 56, NO. 9, SEPTEMBER 2009, p.p. 3424-3431.
教授:王明賢
學生:胡育嘉
Outline
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Abstract
Introduction
Conventional Sliding-Mode Observer For Rotor
Position and Speed
Hybrid Terminal Sliding-Mode Observer For Rotor
Position and Speed
Simulations
Experiments
Conclusion
References
Abstract

This paper proposes a hybrid terminal sliding-mode observer
based on the nonsingular terminal sliding-mode (NTSM) and
the high-order sliding-mode (HOSM) for the rotor position and
speed estimation in the permanent-magnet synchronous motor
control system.
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An NTSM manifold is utilized to realize both fast convergence
and better tracking precision. In addition, a derivative estimator
is used to obtain the derivative of the sliding-mode function.
Meanwhile, an HOSM control law is designed to guarantee the
stability of the observer and eliminate the chattering, so that
smooth back-electromotive-force (EMF) signals can be obtained
without a low-pass filter.
Abstract
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According to the back-EMF equations, the rotor position and
speed of the motor can be calculated. Simulation and
experimental results arepresented to validate the proposed
method.
Introduction
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In order to achieve high performance of PMSMs, a vector
control strategy and a rotor position sensor are typically required.
Usually, both the position and speed of the motor are measured
by mechanical sensors such as encoders, resolvers, and so on.
However, these high-precision mechanical sensors would
increase the cost and size of thePMSM system, hence reducing
the reliability and limiting the applications under certain
conditions. The sensorless technique enables control of PMSM
without mechanical sensors as well as estimation of the rotor
position and speed by the stator voltage and current of the motor.
Introduction
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In [15], a hybrid structure integrating a flux observer and signal
injection techniques was utilized for a wide-speed-range
sensorless control of a surface-mounted permanent-magnet
machine, including zero-speed operation. In [16], an adaptive
full-order observer was augmented with the signal injection
method for PMSM drives equipped with aninverter output filter.
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By combining the nonsingular terminal sliding mode (NTSM)
with the high-order sliding-mode (HOSM) method, this paper
proposes a hybrid terminal sliding-mode observer for the rotor
position and speed estimation in PMSM systems.
Introduction
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The NTSM manifold is utilized to realize the convergence of the
observer in finite time. In addition, a derivative estimator is used
to obtain the derivative of the sliding-mode function.Meanwhile,
an HOSM control law is designed to guarantee the system
stability.
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Since the HOSM method can eliminate the chattering
phenomenon by using continuous signals instead of switching
signals [20]–[23], the smooth back-EMF signals can be obtained
directly from the observer, and the low-pass filter can be omitted.
Both the simulation and experimental results are presented to
validate the method
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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A typical structure of a sliding-mode-observer-based
PMSMvector control system is shown in Fig. 1 [11], [17]–[19].
In the system, a sliding-mode observer is utilized instead of the
mechanical position sensor of the motor. The stator voltage and
current measurements of the motor are used to estimate the rotor
position and speed using the observer based on the PMSM
model. Then, the estimated position and speed can be used for
the motor position or speed control and the coordinate
transformation between the stationary reference frame and the
synchronous rotating frame. The position sensor in the
motorsystem is replaced by a software algorithm, which can
reducethe cost of hardware and improve the reliability of the
motorsystem.
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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In the α–β stationary reference frame, the electrical dynamics of
the PMSM can be described using the following equations [11],
[17]–[19]:
where uα and uβ are stator voltages, iα and iβ are stator
currents, L is the α–β-axis inductance, Rs is the stator
winding resistance, and eα and eβ are back-EMFs
which satisfy the following equations:
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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It can be seen from (2) that the back-EMFs contain the
information of both the rotor position and speed of the motor.
Therefore, the rotor position and speed can be calculated from
(2) if the back-EMFs can be obtained accurately. From (1), the
conventional sliding-mode observer can be designed as follows
[11]:
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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Assume that the parameters satisfy ˆRs = Rs and ˆL =
L. Then, the error equations of the stator current can
be obtained by subtracting (3) from (1)
where iα =ˆiα − iα and iβ =ˆiβ − iβ are two stator current
errors, respectively. The control law for the observer
(4) can be designed using the method in [11]
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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The observer (4) with control (5) can reach two sliding modes iα
= 0 and iβ = 0, respectively, in finite time and then stay on it.
Once on the sliding-mode, the variable states of the system (4)
will be iα = ˙iα = 0, iβ = ˙iβ = 0. From (4), the following equations
can be obtained:
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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which means that the back-EMFs can be estimated by using the
equivalent control of the observer. However, the actual control
signals (5) in the conventional sliding-mode control method are
discontinuous switching signals. Therefore, a low-pass filter is
needed to extract the continuous back-EMF components. The
low-pass filter is designed as follows [18]:
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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where τ0 is the time constant of the filter. According to (2) and
(7), the estimated speed and position of the motor can be
calculated as
Conventional Sliding-Mode Observer
For Rotor Position and Speed
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This estimation algorithm based on the conventional
slidingmode observer is robust with respect to both internal
parameter uncertainties and external disturbances in the motor
system. However, the phase lag of the estimation is unavoidable
because of applying the low-pass filter (7). Therefore, the
estimated rotor position should be compensated to improve the
estimation precision. Usually, the phase-lag compensation to (9)
is made according to the frequency response of the low-pass
filter as follows [18]:
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
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Here, a hybrid terminal sliding-mode observer is proposed to
estimate the rotor position and speed of the motor. The
chattering in the control signals can be eliminated. Thus, the
low-pass filter is omitted, and the phase lag in the back-EMF
signals can be avoided. The stator current error equation (4) can
be rewritten as follows
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In order to achieve good performances, such as fast convergence
and better tracking precision, an NTSM manifold [24] is
designed as follows:
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
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The NTSM manifold s is used to realize the second-order
sliding-mode control and eliminate the chattering phenomenon
in the system. After s reaches zero in finite time, both is and˙is
will also reach zero in finite time; then, the system will stay on
the second-order sliding mode is = ˙is = 0. The HOSM control
law of the observer is designed according to the following
theorem.
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
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Fig. 3. Hybrid terminal sliding-mode observer.
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
Hybrid Terminal Sliding-Mode Observer
For Rotor Position and Speed
Simulations
Simulations
Experiments
Experiments
S Experiments
Experiments
Experiments
Conclusion
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This paper has proposed a hybrid terminal sliding-modeobserver
design method for estimating the rotor position and speed to
achieve sensorless drive for PMSM. The NTSM manifold has
been utilized to realize the convergence of the observer in finite
time and better tracking precision. Meanwhile, the HOSM
control law has been designed to eliminate the chattering. The
control signals of the observer are smooth enough to be used for
estimating the back-EMFs directly. The phase lag caused by the
low-pass filter in the back-EMF signals can be avoided, and the
motor position and speed can be calculated according to the
back-EMF equations. Simulation and experimental results show
that the hybrid terminal sliding-mode observer can converge fast
and has low sensitivity to parameter variations
References
References