52
Speed Controller of Three Phase Induction
Motor Using Sliding Mode Controller
Dr.Farazdaq R.Yaseen
1,Walaa H. Nasser2
1,2Control and System Eng. Dep.at Unversity of Technology
drfarazdq@gmail.com,walaahussain321@gmail.com
Abstract— A Sliding Mode Control (SMC) with integral surface is employed to control
the speed of Three-Phase Induction Motor in this paper. The strategy used is a modified
field oriented control to control the IM drive system. The SMC is used to calculate the
frequency required for generating three phase voltage of Space
v
Vector Pulse Width
Modulation (SVPWM) invertor. When the SMC is used with current controller, the
quadratic component of stator current is estimated by the controller. Instead of using
current controller, this paper proposed estimating the frequency of stator voltage
whereas the slip speed is representing a function of the quadratic current. The simulation
results of using the SMC showed that a good dynamic response can be obtained under
load disturbances as compared with the classical PI controller; the complete
mathematical model of the system is described and simulated in MATLAB/SIMULINK.
Index Terms—
Induction Motor, Space Vector Pulse Width Modulation, Sliding Mode Control
and Field Oriented Control.
I. INTRODUCTION
The three phase Induction Motors (IM) have earned a great interest in the recent years
and used widely in industrial applications such as robotics, paper and textile mills and
hybrid vehicles due to their low cost, high torque to size ratio, reliability, versatility,
ruggedness, high durability, and the ability to work in various environments. Some control
methods have been improved to adjust these IM drive systems in high-performance
applications [1]. The Field-Oriented Control (FOC) method can be considered as one of the
most popular techniques which is used to control the IM. Nowadays, the FOC strategy is
the most common method since it ensures the decoupling of the motor flux and torque, this
property of FOC gives an assurance that the IM drive sysytem can be controlled linearly as
a
a separately exited DC motor [1, 2, 3].
Conventional speed control of IM drives with a restricted gain such as PI controllers
did not provide an acceptable response for tracking the required trajectory. In order to
overcome the parameter variation and/or load changes obstacles, the variable structure
control strategy uses the SMC for controlling the AC drive because the SMC provides
many advantages, such as: good performance, robustness to the load disturbances, or
parameter variation, fast dynamic response, and simple implementation.
The SMC design requires two steps: The first step of this design is selecting the
suitable sliding surface S(t) in terms of tracking error while the second step is designing
control signal of the system u(t). Two types of the sliding surface can be recognized in the
sliding mode control, the first type is the conventional sliding surface and the other is the
integral sliding surface. In this work, an integral sliding surface is presented and its
interpretation is compared with the application of the conventional PI controller.
DOI: https://doi.org/10.33103/uot.ijccce.19.1.7
53
II. MATHEMATICAL MODEL OF THE THREE PHASE INDUCTION MOTOR
The equivalent circuit of IM in the stationary d-q reference frame is presented in
Fig.1. The IM dynamical model is given by [4].
DC
Vqs
Rs
LIs=Ls‐Lr Lir=Lr‐Lm Rr
Vqr
e e‐rr
qr
Lm
Iqr
Iqs
(
A
)
C
IRCUIT
DC
Vds
Rs
LIs=Ls‐Lr Lir=Lr‐Lm Rr
Vdr
e e‐rqr
dr
Lm
Idr
Ids
(
B
)
C
IRCUIT
F
IG
.
1.
IM
EQUIVALENT CIRCUIT A
)
CIRCUIT B
)
CIRCUIT
The stationary reference frame can be derived simply by substituting e=0. The
corresponding stationary frame equations are presented below:
Stator equations
λ
1
λ
2
Rotor equations
0
λ
λ
3
0
λ
λ
4
Where
=
=0.
Where represents the value of the flux linkage, V represents the voltage; R is the resistance, refer
to the value of the current and
represents the speed of the rotor. The subscript r denotes the
quantity of the rotor, s refers to the quantity of the stator, and the subscripts q and d are symbols for
the quadrature axis and direct axis components, respectively in the stationary reference frame.
The fluxes are combined with the currents according to the following expressions
5
6
7
8
54
Where
refers to the magnetizing inductance,
is the rotor inductance and
is the stator
inductance [1].
The equation of electromagnetic torque is given by:
3
2
2
9
Where p refers to the poles number of the motor. The mechanical dynamic equation which relates
the motor characteristic speed r to the torque is:
T
T
2
PJdω
dt 10
Where
and J refer to the load torque and the moment of inertia, respectively,
refer to the slip
frequency and
and it can be obtained as:
ω
L
R
Ψ
L
11
The dynamic model of the IM can be expressed in Fig 2.
F
IG
.2
T
HE
D
YNAMIC MODEL OF
IM.
III. SPACE VECTOR PLUSE WIDTH MODULATION INVERTER
This inverter consists of three legs with 6 controlled swithches (S1 to S6). The idea is
generation of a vector with amplitude Vref which moves with an angle () across 6 sectors
shown in Fig.3 . The SVPWM can be performed in the following three steps:
Step 1. Calculation of Vref and angle () from Vd and Vq
Step 2. Calculation of the time duration T1, T2 , and T0
Step 3. Calculation of the switching time of every switching device (S1 to S6) [5].
55
F
IG
3.
T
HE
B
ASIC SWITCHING VECTORS AND SECTORS
.
F
IG
.4
M
ODEL OF
SVPWM.
IV. PI CONTROLLER
The conventional Proportional plus Integral controller (PI) is a simple speed controller in
industrial applications. Under the load condition, the PI controllers try to modify the motor speed to
attain the desired system speed. The output of the PI controller is a function of the speed error and the
integral of error [6]:
12
56
F
IG
.5
T
HE BLOCK DIAGRAM OF CONVENTIONAL
PI
CONTROLLER
.
V. SLIDING MODE CONTROLLER
The overall block diagram of the IM using (SMC) speed control system is shown in Fig.6, where
the quantity of the actual speed (
) generated by the IM is compared to the desired value
∗
) to
produce an error signal ().
This error signal and its derivative () are fed to the SMC, which generates a slip frequency and
estimates the required frequency for SVPWM where this value is the input to the VSI.
These inputs are used by the VSI for generating a three phase voltage whereas the variation of
amplitude and the frequency is done by the SMC.
Generally, the mechanical equation of an IM can be presented as follows [7, 8]:
13
Where B is the friction factor of the IM,
refers to the external applied load ,
refer to the
mechanical speed of the rotor, while
is a point to the electromagnetic torque which can be
represented in Eq. (9) as:
3
2
2
9
According to the FOC principle, the ccurrent component
is lined up the direction of the rotor
flux vector
and the current vector
is lined up perpendicular to it, so the flux vector
|
|, and Eq.(9) becomes:
3
2
2
14
Where
denotes the constant of the torque, and it can be defined as follows:
3
2
2
15
Using Eq. (14) into (13) then we can get
bi
ω
aω
f16
Where
,
and
Eq. (16) can be presented with uncertainties ∆ ,∆ and∆, as follow:
∆
∆ ∆
17
The error of the tracking speed can be define as
∗
18
Where
∗
is a point to reference speed of the rotor, then by taking the derivative of the
pervious equation with respect to time it produces:
6
7
8
9
10
11
1
/
11
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