Proceedings of the 35th Chinese Control Conference
July 27-29, 2016, Chengdu, China
A new speed control method of induction motor
NIU Ming-zhe, WANG Tao, ZHANG Qian, HE Xiang, ZHAO Ming-liang
School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031
E-mail: 1101396623@qq.com
Abstract: In recent years, the control of induction motor has become an important research topic and a variety of control methods have
been born.This paper proposes a new motor speed control approach based on methods of synergetic control thoery, which combines
the traditional speed closed-loop control and synergetic control. The new method gets rid of PI regulators compared to the traditional
conrtrol methods and the algorithm is very simple. The result of simulation shows that this control system has good dynamic and static
performance.
Key Words: induction motor, speed control, synergetic control
1
Introduction
From a control point of view, the induction motors are
nonlinear, high-order dynamic systems of considerable
complexity. They are amenable to a formal mathematical
analysis. However, it is not a trivial matter to comprehend
the principles of their operation in an imaginative way,
especially under transient conditions. Conversely, induction
motors are widely used in practical systems because of their
simple construction, low maintenance requirements, and
lower cost compared with other types of motors,such as
brushless DC motors.Therefore, it is a great significance to
investigate the control problems of induction motors [1].
With the development of power electronic technology,
control technology and control theory, a variety of general
and high performance control strategies have been born and
become more and more mature, some representative control
strategies of the induction motor are as follows: speed
opened-loop constant V/f control, field oriented vector
control (FOC), direct torque control (DTC), feedback
linearization control, sliding mode control(SMC), intelligent
control, etc. [2]. These strategies have different advantages
and disadvantages, hence, these strategies must be selected
appropriately according to the specific requirements in
practice.
regulation.
In section Ċof this paper,the model of the induction
motor is presented.
In section ċthe new speed control method is introduced
which includes the basics of synergetic control synthesis ,
hysteresis current control and the algorithm used in the new
control method.
Finally, in section ČMATLAB is used in the simulation
experiment, and the results demonstrate the ability of the
proposed control method to improve the static performance
and dynamic performance.
2
Model of the induction motor
According to the state representation of the induction
motor, with consideration of the stator current isd , isq , and
rotor flux UG, UT as the state vectors, we define x1=¹U , x2=
UG , x3= UT , x4= isd, x5= isq, for notation convenience. Then
the induction motor is described by the following system of
equations are given by [10]:
Traditional vector control methods depend on PI regulator
and the parameters of the regulator are difficult to regulate.
Though some new methods have good dynamic and static
performance but their algorithms are complex and have
many parameters to regulate.
Introduced in the last decades, synergetic control has
rapidly gained acceptance not only by the robust control but
also by the industrial partners as illustrated by its
implementation in power electronics field [3-9]. The good
robustness of the new control theory provides a new train of
thoughts of motor speed control.
This paper proposes a new control strategy combines
traditional vector control and synergetic control, which can
not only simplify the algorithm but also eliminate the PI
regulators compared with the traditional methods. What’s
more, this new control strategy can reduce the number of
parameters to be debugged and get good dynamic and static
performance just through a simple process of parameter
x1
P 2 Lm
P
(x2 x5 x3 x4 ) TL
JLr
J
x2
x3
Zs x2 x4
(Zs x1 ) x5 x5
E x1 x2 (Zs x1 ) x4 L
1
x2 Zs x3 m x4
Tr
Tr
L
1
x3 m x5
Tr
Tr
E
Tr
x2 J x4 Where
Rs : stator resistance
LS : stator self inductance
Lm : mutual inductance
Zs :slip angle frequency
TL : load torque, and
L
L ,
L2m
T = r E = m
V =1 Ls Lr
r
Rr
(1)
V Ls Lr
E
Tr
1
V Ls
usd
x3 J x5 1
V Ls
usq
Rr : rotor resistance
Lr : rotor self inductance
T2 : rotor time constant
Zr : rotor frequency
,
J
L2
1
( Rs m2 Rr )
Lr
V Ls
For a rotor-flux orientation we get
*
This work is supported by National Natural Science Foundation (NNSF)
of China under Grant 51477146.
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x2 \ rd
3
\r
x3
0
Zs
x5 Lm
x2Tr
(2)
3.2 Hysteresis current control
Design of proposed synergetic controller
In recent years, the synergetic control method has made
a great influence in field of power electronics. The design
process of synergetic control algorithm for an n-order
nonlinear dynamic system described by the equation (1) is
as follows [11]:
1. Select the macro variables defined in terms of eq. 3.
These macro variables can be defined as linear combinations
of state variables.
<s
Then we get the stator currents x4= isd and x5= isq
which should be tracked.
(x1 , x2 ......xn )
(3)
The control will force the system to operate on the manifold:
(4)
<s 0
Nowadays, the hysteresis current control has rapidly
gained acceptance because of its simple control mode, easy
hardware implementation, reliable operation and quick
dynamic response. For ac motors, a practical need is to make
sure that the input current should be a sine wave, because
only when the current in stator windings is three-phase
symmetrical, the torque would be a constant value. If we can
ensure the current’s sine waveform by using the hysteresis
current control method, the system will clearly get good
performance [12,13].
A common current closed-loop control method is
CHBPWM (Current Hysteresis Band PWM) control, the
current control principle of phase A is as shown in figure 1.
2. Set the dynamic evolution of macro-variables by the
following equation (5):
(5)
Ts < s M (< s ) 0
where M is the function of Vto be selected, Ts defines the
speed of convergence of macro-variables to manifolds s=0.
To ensure the stability of the equation (5), the function
M must satisfy following conditions:
Ts < s < s
(6)
0
Ms (0) 0,Ms (< s )< s ! 0
Load
Fig. 1: The current control principle of phase A
By setting hysteresis layer, we can control the output
currents fluctuate around the given values of currents as
shown in Fig. 2.
(7)
It’s obvious that the equation (5) will vary with function
M and parameter Ts .
In this paper, we select the function M which makes the
equation (8) established:
Ts < s < s
0
(8)
Fig. 2: Current tracking use CHBPWM
3.3 Diagram of the control method
3.1 Application of synergetic speed control for IM
Select the stator current x4= isd , x5= isq as the control
variables, and select two macro variables as follows:
<1 x1 x1ref
(9)
< 2 x2 x2 ref
The resulting diagram of the synergetic control applied to
an IM is given in Fig. 3.
Zrref
\ rref
i*sd
Synergetic
Control
i*sq
Park
1
i *a
i*b
i *c
CHB
PWM
Inverter
IM
From equation (8) and (9), we get˖
T1 <1 <1 T1 x1 (x1 x1ref ) 0
Zt
(10)
T2 < 2 < 2 T2 x2 (x2 x2ref ) 0
Combine equation (1), we obtain:
P 2 Lm
P
T1 (
(x2 x5 x3 x4 ) TL ) x1 x1ref =0
JLr
J
T2 ( ª x1 º
«x »
¬ 2¼
x5
x1ref x1 p
JLr
TL )
(
p 2 Lm x2
T1
Jr
Zr
Fig. 3: System configuration of the proposed control
Solve the equation (11), the control variables are:
Lr x2 ref x2 1
x2 )
(
Lm Rr
T2
Tr
isD isE
(11)
L
1
x2 Zs x3 m x4 ) x2 x2 ref =0
Tr
Tr
x4
Flux Observer
Clark
(12)
The flux observer figures out amplitude and angle of the
rotor flux online, the synergetic control algorithm figures
out the given values of currents, the inverter produces pulse
to make the input currents track the given values of stator
currents.
4
MATLAB simulation
Machine parameters has be shown in table 1.
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Table 1: Parameters of Induction Motor
4.85
Rr(oms)
3.8
Ls(mH)
274
Lr(mH)
274
Lm(mH)
258
P
2
J(kg.m²)
0.23
DC voltage˄V˅
500
100
80
60
40
Te(Nm)
Rs(ohm)
20
0
-20
-40
0
0.1
0.2
0.3
t(s)
0.4
0.5
0.6
Fig. 7: Electromagnetic torque
The simulation uses ode45 algorithm, control algorithm
(equation 11) is implemented by the S-function of
MATLAB. The total time of the simulation is 0.6S, and T1=
T2 =0.001, the load torque(Nm) jumps from 0 to 10 at 0.1Sˈ
the given value of the flux jumps from 1 to 0.8 at 0.3s, the
given value of the rotor speed jumps from 100 to 200 at
0.4s.
The results of simulation are shown in fig. 4-7.
To analyze the influence of T1 and T2 on the convergence
process of macro variables, select three sets of parameters:
T1
T2
k1
0.01
T1
T2
k2
0.001
T1
T2
k3
0.0001
The convergent waveforms of the two macro variables
and are as follows:
120
250
k1
k2
k3
100
80
200
60
ǻwr(rad/s)
wr(rad/s)
150
40
20
100
0
50
-20
0
0
0.1
0.2
0.3
t(s)
0.4
0.5
0
0.1
0.2
0.3
t(s)
Fig. 8:
0.6
Fig. 4: Rotor speed
0.4
0.5
0.6
1
k1
k2
k3
2
1.8
0.5
ǻpsir(wb)
1.6
rotor flux(wb)
1.4
1.2
0
1
0.8
0.6
0.4
-0.5
0
0.1
0.2
0.2
0
0
0.1
0.2
0.3
t(s)
0.4
0.5
Fig. 5: Rotor flux
¹U
30
0.5
0
-10
K1
K2
K3
-20
0
0.1
0.2
0.3
t(s)
0.4
Fig. 6: Stator current of phase A
0.5
0.6
(\ rref \ r )
100%
\ rref
Then we can get the table 2 and table 3.
Table 2: Static Error of ¹r
10
isa(A)
0.4
From Fig. 8 and Fig. 9, if we define the static errors of
and U as:
(Zrref Zr )
'Zr %
100%
Zrref
'\ r %
20
-30
Fig. 9:
0.6
40
0.3
t(s)
0.6
K1
K2
K3
0.1s-0.3s
0.3s-0.4s
0.603
0.606
0.068
0.061
0.04
0.038
Table3: Static Error of r
0.1s-0.3s
0.3s-0.4s
-9.13
-9.19
-0.85
-0.85
-0.1
-0.1
0.4s-0.6s
0.304
0.031
0.02
0.4s-0.6s
-9.2
-0.85
-0.1
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As we can see in the table 2 and 3, the smaller T1 and T2
are, the smaller static error will be. However, from the figure
9, we can see that transient time will be longer if T1 and T2
become bigger.
5
Conclusion
We have proposed a new speed control method of
induction motor which combines traditional vector control
with synergetic control. This new method can reduce the
complexity of algorithm and get rid of the PI regulators in
traditional control methods. In addition, there are only two
parameters need to be debugged. The results of simulation
show that this new method has a good dynamic and static
performance.
References
[1]
[2]
[3]
[4]
[5]
V. I. Utkin, J. Guldner, and J. Shi, Sliding mode control in
electromechanical systems, CRC Press, 2009:271-272.
Xing Bing-suo, Summary of the control strategy for induction
motor, Electric Drive Automation, 35(4):11-14, 2013.
I. Kondratiev, R. Dougal, General synergetic control
strategies for arbitrary number of paralleled buck converters
feeding constant power load: Implementation of dynamic
current sharing. IEEE ISIE, 1:257-261, 2006.
Anatoly Kolesnikov, Gennady Veselov, Andy Popov, Alex
Kolesnikov, Roger A.Dougal, Igor. Kondratiev, A synergetic
approach to the modeling of power electronic systems, 7th
Workshop on Computers in Power electronics, 2000.
A. Kolesnikov,G. Veselov, A Monti, Synergetic synthesis of
Dc-Dc boost converter controllers: Theory and experimental
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
analysis, Applied Power Electronics Conference and
Exposition, 1:409-415, 2002.
A. Monti, R Dougal, E Santi, et al, Compensation for
step-load variations when applying synergetic control,
Applied Power Electronics Conference and Exposition,
1:334-340, 2003.
A.Monti, E.Santi, K.Proddutur, R.Dougal, Synergetic control
for DC-DC boost converter : implementation options, IEEE
Trans. on Industry Applications,39(6):1803-1813,2003.
Young-Dae Son,Tae-Won Heo,Santi, E.,Monti, A synergetic
control approach for induction motor speed control,
Industrial Electronics Society, 1:883-887,2004.
Z. Jiang and R. Dougal, Synergetic control of power
converters for pulse current charging of advanced batteries
from a fuel cell power source, IEEE Trans. on Power
Electronics, 19(4):1140-1150, 2004.
Zhang Yong-chang, High performance control technology of
induction motor without speed sensor, China Machine Press,
2015:45-50.
M. Laribi, M.S. Ait Cheikh, C.Larbes, N.Essounbouli, A.
Hamzaoui, A sliding mode and synergetic control approach
applied to induction motor, Proceedings of the 3rd
International Conference on Systems and Control, 2013.
S. Sathiakuma, et al. Microprocessor-Based field-oriented
control of a CSI fed induction motor drive, IEEE Trans. Indus.
Electron., 33(3):39-43, 1986 .
Kazmierkowski, M.P., Sulkowski, W. A novel vector control
scheme for transistor PWM inverter-fed induction motor
drive, IEEE Trans. Indus. Electron., 38(1):41-47, 1991.
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