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A Novel Motor Drive Design for Incremental Motion
System via Sliding-Mode Control Method
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 2, APRIL 2005
Chiu-Keng Lai and Kuo-Kai Shyu, Member, IEEE
Student: Cheng-Yi Chiang
Adviser: Ming-Shyan Wang
Date : 31th-Dec-2008
Department of Electrical Engineering
Southern Taiwan University
Outline
Abstract
INTRODUCTION
FIELD-ORIENTED PMSM
INCREMENTAL MOTION CONTROL OF PMSM
A. Velocity Control Mode
B. Position Control Mode
C. Velocity Control Mode
D. Position Control Mode
SIMULATION RESULTS
EXPERIMENTAL SETUP AND RESULTS
A. Experimental System Setup
B. Experimental Results
CONCLUSION
REFERENCES
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Abstract
This paper proposes a particular motor position control drive design
via a novel sliding-mode controller.
The newly designed controller is especially suitable for the motor
incremental motion control which is specified by a trapezoidal velocity
profile.
The novel sliding-mode controller is designed in accordance with the
trapezoidal velocity profile to guarantee the desired performance.
A motor control system associated PC-based incremental motion
controller with permanent-magnet synchronous motor is built to verify
the control effect.
The validity of the novel incremental motion controller with
sliding-mode control method is demonstrated by simulation and
experimental results.
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INTRODUCTION
The control of motors used in high-performance servo drives requires
the prescribed torque accuracy, velocity, and/or position for all
operating conditions being achieved.
To obtain the desired performance, a precise system model is needed.
It is difficult to construct because of the inherent nonlinearity of
friction and dead zone, the parameter variations due to temperature,
the uncertain external disturbances, and so on.
PI-type control methods are not robust enough to accommodate the
variations of external disturbances, parameters, and perturbations
during operation
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INTRODUCTION
Variable-structure control (VSC) or sliding-mode control (SMC) has
been known as a very effective way to control a system because it
possesses many advantages.
such as insensitivity to parameter variations, external disturbance
rejection, and fast dynamic responses.
VSC has been widely used in the position and velocity control of dc
and ac motor drives.
The system dynamics of a VSC system can be divided into two phases:
the reaching one and the sliding one.
The robustness of a VSC system resides in its sliding phase, rather the
reaching phase.
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INTRODUCTION
This paper proposes a multisegment sliding-mode- control-method-based
motion control drive design in accordance with a trapezoidal velocity
profile.
It also shows that the reaching phase existing in the conventional VSC
does not exist in the designed multisegment sliding-mode controller.
The robustness of the controlled system can be assured from start to
finish.
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FIELD-ORIENTED PMSM
d
i d  R s i d  ws Lq i q
dt
d
v q  Ld i q  R s i q  w s Lq i d
dt
 q  Lq i q
v d  Ld
d  Ld id  Lmd I fd .
v d , vq
id , i q
Ld , L q
d , q
R s , ws
I fd
Lmd
(1)
(2)
(3)
(4)
the d, q-axes stator voltages.
the d, q-axes stator currents.
the d, q-axes inductance.
the d, q-axes stator flux linkages.
the stator resistance and inverter frequency.
the equivalent d-axes magentizing current.
the d-axis mutual inductance.
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FIELD-ORIENTED PMSM

3
Te  p Lmd I fd iq  ( Ld  Lq )i d iq
2
d m
 wm
dt
dw
J m m  Bm wm  Te  TL
dt

(5)
(6)
(7)
p
the pole number of the motor.
wm
the rotor velocity.
m
the rotor angular displacement.
Jm
the moment of inertia.
Bm
the damping coefficient.
the external load.
TL
The inverter frequency is related to the rotor velocity as ws  wm .
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FIELD-ORIENTED PMSM
Since the magnetic flux generated from the permanent magnetic rotor
is fixed in relation to the rotor shaft position.
The flux position in the d - qcoordinates can be determined by the
shaft position sensor.
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FIELD-ORIENTED PMSM
The PMSM used in
this drive system is
a threephase four-pole
750-W 3.47-A
3000-r/min type.
Fig.1. (a) System configuration
of fiele-oriented
synchronous motor.
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FIELD-ORIENTED PMSM
Fig.1. (b) Simplified control
system block diagram.
Te  K t v
H p (S ) 
(8)
1
J m s  Bm
(9)
K t  2.2 N  m / v,
J m  0.0021N  m / s 2
Bm  0.0015N  m/s
v is the inverter torque command which is proportional to
the q –axis current, .
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INCREMENTAL MOTION CONTROL OF PMSM
The rotor dynamics and the torque equation of PMSM given
in (6)-(8) are rewritten as follows:
d m
 wm
dt
dwm
B
T
T
  m wm  e  L
dt
Jm
Jm Jm
Te  K t v.
(10)
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INCREMENTAL MOTION CONTROL OF PMSM
The incremental motion control is to move an object at rest at time t0 to a
fixed desired position  d at time t d, and then stop it.
The control process is subjected to the desired velocity and acceleration.
Therefore, the incremental motion control is performed under velocity
control in obedience to a desired velocity profile, whereas stopping is
done by position control mode.
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INCREMENTAL MOTION CONTROL OF PMSM
One first has to select a velocity profile which rapidly changes the load
position in discrete step.
The velocity profile should satisfy the motion constraints of the system.
The velocity and acceleration limitations are generally taken into
consideration for the determination of velocity profile.
To satisfy the velocity and acceleration limitations, a trapezoidal
velocity profile is usually used.
The object here is to design a multisegment sliding mode controller
according to the trapezoidal velocity profile
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INCREMENTAL MOTION CONTROL OF PMSM
Fig.2. Trapezoidal velocity profile for incremental motion control.
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INCREMENTAL MOTION CONTROL OF PMSM
With a specified rotor position  d , which is assumed to be a constant within
the control process, one first defines the position error and its derivative as
x1   m   d
(11)
x2  wm
Combining (11) with (6) and (7), one obtains
x1  x2
x2  
Bm
T
T
x2  e  L
Jm
Jm Jm
(12)
(13)
Note that (12) and (13) hold because the specified position  d is
a constant.
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INCREMENTAL MOTION CONTROL OF PMSM
According to the error dynamical equations (12) and (13), a
multisegment SMC is proposed to drive the motor from initial position
 0 to the specified position  d according to the trapezoidal velocity
profile given in Fig. 2.
The multisegment SMC is composed of two modes, the velocity
control mode and the position control mode.
The velocity control mode is used to drive the rotor to the desired
position and the position control mode is used to hold the rotor at the
desired position
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A. Velocity Control Mode
1) Acceleration segment s1
s1  x1 
1
2 d 1
x2  x10  0
2
(14)
x10  x0  xd : is the initial position error.
To check the motor acceleration on s1  0
ds1
1
 x1 
x2 x 2  0
dt
 d1
x1  x2
dwm
dt
Thus, the motor dynamics on the acceleration segment (14) have the desired constant
acceleration  d1.
x 2   d 1 
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A. Velocity Control Mode
2) Run segment s2
s 2  x2  wd  0
(15)
s2  0
wm  x2  wd
3)Deceleration segment s3
s3  x1 
s3  0
1
2
2 d 3
x 2   d 3 
x2  0
(16)
dwm
dt
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B. Position Control Mode
In the position control mode, the following position control segment is
proposed:
(17)
s4  x2  c4 x1  0
where c4 is a positive constant.
Lemma [6]–[8]: If a switching surface s (t ) of the controlled system
satisfies the following sliding condition:
ss  0
(18)
Te  K t v
 K t (h1  h2 x2 )
(19)
Where h1 and h2 are parameters to be designed in accordance with the
corresponding sliding segment, and K t has been defined in (8).
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C.Velocity Control Mode
First, the acceleration segment is considered. The parameters h1 and h2
in (19) will be designed to satisfy the sliding condition of the
acceleration segment
s1 s1  0
s1 s1  s1 ( x1 
(20)
1
 d1
x 2 x 2 )


1
 s1 x2 1 
( Bm x2  Kt h1  K t h2 x2  TL ).
  d1J m

(21)
h1  1 sgn( s1 x2 ) sgn(  d 1 )
(22)
h2  1 sgn( s1 ) sgn(  d 1 )
(23)
where 1  ( d1 J m  TL ) / K t , 1  Bm / K t , and sgn( ) is the sign
function.
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C.Velocity Control Mode
s2 s2  0
(23)
h1   2 sgn( s2 )
(24)
h2   2 sgn( s2 x2 )
(25)
where  2  TL / Kt and 2  Bm / Kt .
s3 s3  0
(26)
h1   3 sgn( s3 x2 ) sgn(  d 3 )
(27)
h2   3 sgn s3 sgn(  d 3 )
(28)
where  3  (TL   d 3 J m / K t and  3  Bm / K t .
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D.Position Control Mode
s4 s4  0
(29)
v  h1 x1  h2 x2  v0
Where
h1   4 sgn( s4 x1 )
(30)
h2   4 sgn( s4 x2 )
(31)
v0  T0 sgn( s 4 ).
(32)
 4  0,  4  ( Bm  J m c4 ) / K t , and T0  TL / K t .
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Position Control Mode
Fig. 3. Multisegment SMC-based incremental motion control for PMSM system
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SIMULATION RESULTS
Fig. 4. Simulated results of
multisegment sliding-mode
motion control.
(a) Velocity responses.
(b) Position responses.
(c) Control output.
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SIMULATION RESULTS
Fig. 5. Trajectories of four
switching functions of
multisegment slidingmode controller.
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SIMULATION RESULTS
Fig. 6. Simulated results of
conventional sliding-mode
motion control.
(a) Velocity responses.
(b) Position responses.
(c) Control output.
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SIMULATION RESULTS
Fig. 7. Simulated results with
external load 2 N‧m.
(a) Velocity responses.
(b) Position responses.
(c) Control output.
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SIMULATION RESULTS
Fig. 8. Simulated results
with external load
2 N‧m and J m  4 J m
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Experimental System Setup
Fig. 9. Pentium-800–based PMSM incremental motion control system.
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Fig. 10. (a)
Experimental results controlled
by multisegment SMC controller.
From top to bottom: velocity
responses, position responses,
control output, and phase-A
current.
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Fig. 10. (b)
Experimental trajectories
of four segments controlled
by multisegment SMC
controller.
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Fig. 11.
Experimental results controlled
by conventional SMC controller.
From top to bottom: velocity
responses, position responses,
control output, and phase-A
current.
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Fig. 12.
Experimental results with
generator load. From top to
bottom: velocity responses,
position responses, and
phase-A current.
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CONCLUSION
A particular incremental motion control using novel VSC strategy for a
PMSM is presented. It has been shown that the multisegment SMC has
the ability to control the motor system with a constant acceleration and
deceleration rate to match the trapezoidal velocity profile of the
incremental motion.
Furthermore, the proposed system is robust to the external timevarying load.
Both simulations and experimental results confirm the validity.
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REFERENCES
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REFERENCES
[6] K.-C. Hsu, “Variable structure control design for uncertain dynamic systems
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REFERENCES
[11] M. Ghribi and H. Le-Huy, “Optimal control and variable structure
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