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Department of Electrical Engineering Southern Taiwan University
Department of Electrical Engineering Southern Taiwan University
A Novel Motor Drive Design for Incremental MotionSystem via Sliding-Mode Control Method
A Novel Motor Drive Design for Incremental MotionSystem via Sliding-Mode Control Method
Student: Cheng-Yi Chiang Adviser: Ming-Shyan Wang Date : 31th-Dec-2008
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 2, APRIL 2005
Chiu-Keng Lai and Kuo-Kai Shyu, Member, IEEE
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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
Outline
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
FIELD-ORIENTED PMSM
, 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.
.fdmdddd ILiL
dqsqsqdq iLwiRidt
dLv
qqsdsddd iLwiRidt
dLv (1)
(2)
qqq iL (3)
(4)
dv qv
di qi
dL
d qqL
sR sw
fdI
mdL
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
FIELD-ORIENTED PMSM
the pole number of the motor.
the rotor velocity.
the rotor angular displacement.
the moment of inertia.
the damping coefficient.
the external load.
The inverter frequency is related to the rotor velocity as
qdqdqfdmde iiLLiILpT )(2
3
mm w
dt
d
Lemmm
m TTwBdt
dwJ (7)
(6)
(5)
.ms ww LT
mB
mJ
m
mw
p
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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 coordinates can be determined by the
shaft position sensor.
qd -
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
FIELD-ORIENTED PMSM
The PMSM used inthis drive system isa threephase four-pole 750-W 3.47-A 3000-r/min type.
Fig.1. (a) System configuration of fiele-oriented synchronous motor.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
FIELD-ORIENTED PMSM
Fig.1. (b) Simplified control
system block diagram.
vKT te
mmp BsJ
SH
1
)(
,/mN2.2 vK t 2s/mN0021.0 mJ
m/sN0015.0 mB
v
(8)
(9)
is the inverter torque command which is proportional to the –axis current, .q
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
INCREMENTAL MOTION CONTROL OF PMSM
The rotor dynamics and the torque equation of PMSM given
in (6)-(8) are rewritten as follows:
mm w
dt
d
m
L
m
em
m
mm
J
T
J
Tw
J
B
dt
dw
.vKT te (10)
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
INCREMENTAL MOTION CONTROL OF PMSM
The incremental motion control is to move an object at rest at time to a fixed desired position at time , 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.
d dt0t
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
INCREMENTAL MOTION CONTROL OF PMSM
Fig.2. Trapezoidal velocity profile for incremental motion control.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
INCREMENTAL MOTION CONTROL OF PMSM
With a specified rotor position , which is assumed to be a constant within
the control process, one first defines the position error and its derivative as
Combining (11) with (6) and (7), one obtains
Note that (12) and (13) hold because the specified position is
a constant.
d
m
dm
wx
x
2
1 (11)
(12)
(13)
d
21 xx
m
L
m
e
m
m
J
T
J
Tx
J
Bx 22
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
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
to the specified position 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
d0
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
A. Velocity Control Mode
1) Acceleration segment
: is the initial position error.
To check the motor acceleration on
Thus, the motor dynamics on the acceleration segment (14) have the desired constant
acceleration .
1s
02
110
22
111 xxxs
d(14)
dxxx 010
01 s
d1
21 xx
dt
dwx m
d 12
01
221
11 xxx
dt
ds
d
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A. Velocity Control Mode
2) Run segment
3)Deceleration segment 3s
022 dwxs
2s
02
1 22
313 xxs
d (16)
(15)
03 s
dt
dwx m
d 32
02 s
dm wxw 2
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B. Position Control Mode
In the position control mode, the following position control segment is proposed:
where is a positive constant.
Lemma [6]–[8]: If a switching surface of the controlled system satisfies the following sliding condition:
Where and are parameters to be designed in accordance with the corresponding sliding segment, and has been defined in (8).
01424 xcxs (17)
4c
)(ts
0ss (18)
vKT te
)( 221 xhhK t (19)
2h1h
tK
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C.Velocity Control Mode
First, the acceleration segment is considered. The parameters and in (19) will be designed to satisfy the sliding condition of the acceleration segment
where , and is the sign function.
1h 2h
011 ss (20)
)1
( 221
1111 xxxsssd
.)(1
1 22121
21
Lttm
md
TxhKhKxBJ
xs
(21)
)sgn()sgn( 12111 dxsh
)sgn()sgn( 1112 dsh
(22)
(23)
tmtLmd KBKTJ /,/)( 111 )sgn(
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
C.Velocity Control Mode
where and
where and
033 ss
)sgn( 221 sh
)sgn( 2222 xsh
tL KT /2
022 ss
)sgn()sgn( 32331 dxsh
)sgn(sgn 3332 dsh
tmdL KJT /( 33 ./3 tm KB
./2 tm KB
(23)
(24)
(25)
(27)
(26)
(28)
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D.Position Control Mode
Where
and
044 ss (29)
02211 vxhxhv
)sgn( 1441 xsh
)sgn( 2442 xsh
).sgn( 400 sTv
,/)(,0 444 tmm KcJB ./0 tL KTT
(30)
(31)
(32)
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Position Control Mode
Fig. 3. Multisegment SMC-based incremental motion control for PMSM system
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Fig. 4. Simulated results of multisegment sliding-mode motion control.
(a) Velocity responses.
(b) Position responses. (c) Control output.
SIMULATION RESULTS
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Fig. 5. Trajectories of four switching functions of multisegment sliding- mode controller.
SIMULATION RESULTS
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Fig. 6. Simulated results of conventional sliding-mode
motion control.
(a) Velocity responses. (b) Position responses. (c) Control output.
SIMULATION RESULTS
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Fig. 7. Simulated results with external load 2 N m. ‧
(a) Velocity responses.
(b) Position responses.
(c) Control output.
SIMULATION RESULTS
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Fig. 8. Simulated results with external load 2 N m and‧ mm JJ 4
SIMULATION RESULTS
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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 time-varying load.
Both simulations and experimental results confirm the validity.
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REFERENCES
[1] K. Ohnishi, Y. Ueda, and K. Miyachi, “Model reference adaptive system
against rotor resistance variation in induction motor drive,” IEEE Trans.
Ind. Electron., vol. 4, no. 3, pp. 217–223, Aug. 1986.
[2] F. J. Lin, R. F. Fung, and Y. C. Wang, “Sliding mode and fuzzy control
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[3] T. H. Liu and M. T. Lin, “A fuzzy sliding mode controller design for
a synchronous reluctance motor drive,” IEEE Trans. Aerosp Electron.
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[4] G. J. Wang, C. T. Fong, and K. J. Chang, “Neural-network-based selftuning
PI controller for precise motion control of PMAC motors,” IEEE
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[5] B. Grcar, P. Cafuta, M. Znidaric, and F. Gausch, “Nonlinear control of
synchronous servo drive,” IEEE Trans. Contr. Syst. Technol., vol. 4, no.
2, pp. 177–184, Mar. 1996.
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REFERENCES
[6] K.-C. Hsu, “Variable structure control design for uncertain dynamic systems
with sector nonlinearity,” Automatica, vol. 34, no. 4, pp. 505–508, Apr.
1998.
[7] “Decentralized variable structure control for uncertain large-scale systems
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[8] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: A
survey, ” IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2–22, Feb. 1993.
[9] F. J. Lin, “Real-time IP position controller design with torque feedforward
control for PM synchronous motor,” IEEE Trans. Ind. Electron.,vol. 44,
no. 3,pp. 398–407, Jun. 1997.
[10] F. J. Lin and S. L. Chiu, “Robust PM synchronous motor servo drive with
variable-structure model-output-following control,” Proc. IEE—Elect.
Power Appl., vol. 144, no. 5, pp. 317–324, 1997.
Department of Electrical Engineering Southern Taiwan UniversityDepartment of Electrical Engineering Southern Taiwan University
REFERENCES
[11] M. Ghribi and H. Le-Huy, “Optimal control and variable structure
combination using a permanent-magnet synchronous motor,” in Conf.
Rec. IEEE-IAS Annu. Meeting, vol. 1, 1994, pp. 408–415.
[12] K. K. Shyu and H. J. Shieh, “A new switching surface sliding-mode
speed control for induction motor drive systems,” IEEE Trans. Power
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[13]“Variable structure current control for induction motor drives by space
voltage vector PWM,” IEEE Trans. Ind. Electron., vol. 42, no. 6,
pp. 572–578, Dec. 1995.
[14] K. K. Shyu, C. K. Lai, and J. Y. Hung, “Totally invariant state feedback
controller for position control of synchronous reluctance motor,” IEEE
Trans. Ind. Electron, vol. 48, no. 3, pp. 615–624, Jun. 2001.
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