This paper investigates a robust neurofuzzy control (NFC) method which can accurately follow the speed reference of an interior permanent magnet synchronous motor (IPMSM) in the existence of nonlinearities and system uncertainties. A neurofuzzy control term is proposed to estimate these nonlinear and uncertain factors, therefore, this difficulty is completely solved. To make the global stability analysis simple and systematic, the time derivative of the quadratic Lyapunov function is selected as the cost function to be minimized. Moreover, the design procedure of the online selftuning algorithm is comparatively simplified to reduce a computational burden of the NFC. Next, a rotor angular acceleration is obtained through the disturbance observer. The proposed observerbased NFC strategy can achieve better control performance (i.e., less steadystate error, less sensitivity) than the feedback linearization control method even when there exist some uncertainties in the electrical and mechanical parameters. Finally, the validity of the proposed neurofuzzy speed controller is confirmed through simulation and experimental studies on a prototype IPMSM drive system with a TMS320F28335 DSP.
1. Introduction
The permanent magnet synchronous motor (PMSM) has been extensively used in variablespeed motor drives such as electric vehicles, home appliances, military or medical equipment, machine tools, and industrial robots because of its wide speed range operation and high power density
[1

4]
. Depending on the position of the permanent magnet on the rotor, the PMSM can be mainly classified into two types: surfacemounted PMSM (SPMSM) and interior PMSM (IPMSM). It is wellknown that the IPMSM is more difficult to control due to more complex dynamic model, but has better performance (i.e., a wider speed range operation capability due to flux weakening control and a higher torque generation capability due to inherent saliency) than the SPMSM. Thanks to these attractive advantages, the IPMSM is gaining more and more attention in industrial and home appliance application areas. However, it is complicated to precisely control the IPMSM because of the nonlinearities due to nonlinear properties resulting from the magnets and crosscoupling between the state variables (i.e., the
dq
axis currents and speed) in dynamic model equations. Also, there always exist system uncertainties such as motor parameter variations and unknown external disturbances. Therefore, the robust control design requirements should be satisfied, which are insensitive to the uncertainties mentioned previously. Consequently, the classical linear control schemes based on timeinvariant system model, e.g., the PI controller
[5]
, cannot achieve a good tracking performance.
To solve these difficulties, many advanced control approaches have been presented such as feedback linearization control
[6]
, adaptive backstepping control
[7]
, optimal control
[8]
, predictive control
[9

10]
, etc. In
[6]
, the control performance of the feedback linearization algorithm is not satisfactory because its property is sensitive to parameter uncertainties and external disturbances. In
[7]
, the design procedure of the adaptive backstepping control methods looks complicated since many parameters are adapted. In
[8

10]
, the control algorithms of the IPMSMs are comparatively simple because the
d
axis current reference is set to zero. However, the torque of the IPMSMs cannot be maximized by making the reluctance torque be zero. Also, the fuzzy control schemes
[11

12]
have been introduced to make up for the nonlinearities of IPMSM system. It is easy to see that the control scheme becomes complex and difficult to be designed as the number of fuzzy rules increases. The sliding mode control approach
[13

14]
has its favorable advantage which is insensitive to parameter uncertainties and external disturbances. However, the robustness of this control method can be guaranteed only within the bounds of the uncertainties, and it still suffers from a chattering problem. Beside the above control methods, many papers have concentrated to investigate the effects of both the mechanical and electrical parameter variations on the servo IPMSM drives
[15

16].
Some outstanding methods have been used to estimate the motor parameters, such as an online method
[15]
and a terminal slidingmode observer method
[16]
. These papers implied that the control scheme can significantly improve the system performance, if the motor parameters are accurately estimated and then directly used to design the controllers.
Recently, the intelligent control methods such as fuzzy logic control, neural network control, neurofuzzy control (NFC) have received a lot of attentions since these controllers do not need an exact mathematical model of the system and can achieve high performance. Especially, the NFC is a combination of the advantages of artificial neural network control and fuzzy logic control. That means the artificial neural network has learning ability that can acquire the appropriate information based on the data while the fuzzy logic control can reasonably characterize the input/output behaviors of an uncertain system. In
[17

18]
, the NFC is applied to tune the PI gains for IPMSM drives. However, its parameter training is optimized offline. In
[19

21]
, the NFC faces a burdensome computation because of using a huge number of membership functions and rules. This is a major constraint for industrial applications. Furthermore, the NFC algorithms of
[22

23]
are quite complex when the reference models of the online selftuning algorithm are utilized.
This paper introduces a robust neurofuzzy speed control strategy that can accurately track the speed reference trajectory of IPMSM in spite of system uncertainties. The proposed NFC method contains a state feedback control term and a NFC term. The former stabilizes the system error dynamics and the latter makes up for nonlinearities and uncertain factors. Furthermore, the maximum torque per ampere (MTPA) control is combined with the proposed controller to maximize the torque generation in the constant torque region. Unlike the previous online selftuning algorithms
[17

23]
in which the quadratic cost function to be minimized includes only the speed error, the proposed control technique chooses the time derivative of the quadratic Lyapunov function as the cost function to be minimized. Thus, the global stability analysis can be simple and systematic. Furthermore, the design procedure of the online selftuning algorithm is comparatively simplified to reduce a computational burden of the NFC. A rotor angular acceleration is attained through the disturbance observer. To prove the robustness of the proposed NFC scheme and the effects of two kinds of parameter variations, in both simulation and experimental studies, the results of the proposed NFC and the feedback linearization control (FLC) methods are presented under the mechanical parameters variations as well as the electrical parameters variations using Matlab/Simulink software and a prototype IPMSM drive system with a TMS320F28335 DSP, respectively. The results show that the proposed observerbased NFC scheme can attain better tracking control performance (i.e., less steadystate error, more robustness) than the observerbased FLC method even when there exist some uncertainties in the electrical and mechanical parameters.
2. Neurofuzzy Speed Controller Design and Stability Analysis
 2.1 Mathematical model of IPMSM
In the synchronously rotating
dq
reference frame, where the
d
axis is aligned with the rotor flux vector and the
q
axis is always 90° ahead of the
d
axis, a threephase IPMSM can be modeled by the dynamic equations including system uncertainties
[9]
as
where
𝜔 is the electrical rotor speed;
i
_{ds}
and
i
_{qs}
are the
d
axis and
q
axis currents;
V
_{ds}
and
V
_{qs}
are the
d
axis and
q
axis voltages;
T
_{L}
is the load torque;
p
is the number of poles;
R
_{s}
,
L
_{ds}
,
L
_{qs}
,
J
,
B
, and λ
_{m}
are the nominal values of the stator resistance,
d
axis inductance,
q
axis inductance, rotor inertia, viscous friction coefficient, and magnetic flux, respectively; the disturbances
d
_{i}
(
t
) defined in
[9]
represent motor parameter uncertainties and unknown external load torque.
In this work, the speed controller design will be based on the assumptions and definitions described below:
Assumption 1
: 𝜔,
i
_{ds}
, and
i
_{qs}
are measurable.
Assumption 2
: The desired speed 𝜔
_{d}
and the disturbances
d
_{i}
(
t
) vary slowly for a sampling period
[9

10]
.
Definition 1
: The electrical angular acceleration is represented as
Definition 2
: To produce the maximum torque per ampere (MTPA) of the stator current, the
d
axis reference current is calculated
[12

13]
by
Definition 3
: The speed error, the
d
axis current error, and the error vector are introduced as 𝜔
_{e}
= 𝜔  𝜔
_{d}
,
i
_{dse}
=
i
_{ds}

i
_{dsd}
, and
x
= [𝜔
_{e}
𝛽
i
_{dse}
]
^{T}
, respectively.
From the above
assumptions
and
definitions
, the dynamic Eq. (1) can be converted to the following form:
where
Note that the above statespace model (4) is considered to construct the proposed control law and requires the rotor angular acceleration information
𝛽
which is usually immeasurable. Moreover, the functions
f
_{q}
and
f
_{d}
include the nonlinear terms and the uncertainty terms. Assume that there exists a constant parameter matrix
W
^{*}
^{2r×1}
such that
where
H
^{2×2r}
is a known function matrix, and
r
is a positive integer that denotes the number of fuzzy rules in the following subsection.
 2.2 Neurofuzzy speed controller design
Let the control law
u
be decomposed as the state feedback control term
u
_{fb}
and the adaptive compensating control term
u
_{nf}
First, the state feedback term design is based on a linear matrix inequality (LMI) condition. Assume that there is an existing pair of matrix solution (
X
,
Y
) that satisfies the following inequality
where
X
∈
R
^{3×3}
and
Y
∈
R
^{2×3}
are decision variables.
The gain matrix
K
of the state feedback term
u
_{fb}
is obtained by
Fivelayer NFC with weight normalization
Then the NFC is applied to construct the adaptive compensating term that deals with
f
_{q}
and
f
_{d}
.
Fig. 1
shows the structure of the NFC with weight normalization which consists of five basic layers. The first layer which is an input layer distributing the input variables to each of the nodes in the second layer is indicated. For the aim of reducing a computational burden, only three input signals
z
_{j}
(
j
= 1, 2, 3) are considered:
z
1
= 𝜔,
z
_{2}
=
i
_{qs}
, and
z
_{3}
=
i
_{ds}
. Layer 2 is a fuzzification layer and every node in this layer acts as the membership function. In this work, for easy implementation, the following Gaussian membership functions can be selected as
where
r
is the number of fuzzy rules, ε
_{ji}
and 𝜎
_{ji}
denote the center and the width of the membership function
m
_{ji}
, respectively. Next, layer 3 is a rule layer and the output of every node in this rule layer is defined as
Layer 4 is a normalizing layer with
r
nodes and every node in this layer can be regarded as the normalized weight of each rule.
Layer 5 is an output layer containing two nodes and eachoutput
u
_{nfk}
(
k
=
1
,
2
) of the kth node is denoted as
where
w
_{ik}
are the adjustable parameter vectors. Finally, the adaptive compensating term is denoted as
Then, the online selftuning algorithm is utilized to update all parameters in realtime, and the object function to be minimized is defined as
where
P
=
X
^{1}
. Based on the backpropagation learning rule that is computed recursively from the output layer backward to the input layer, the weights in the output layer are updated by
Then, the adaptive law can be expressed by
where
E
_{w}
=Diag(𝜂
_{11}
, 𝜂
_{21}
,…, 𝜂
_{r1}
, 𝜂
_{12}
, 𝜂
_{22}
,…, 𝜂
_{r2}
).
 2.3 Stability analysis
Theorem 1
: The following controller (17) enforces the error dynamics
x
to converge to zero.
Proof
: Assume that (7) is feasible, and then there exists a matrix
Q
> 0 such that
Let the Lyapunov function be chosen as
where
W
_{e}
=
W

W
^{*}
. The time derivative of (19) along the error dynamics (4) is given by
Integrating both sides of (20) yields the following equation
This implies
x
∈
L
_{2}
∩
L
∞ and
W
∈
L
∞. Using the above results and Barbalat’s lemma,
x
asymptotically converges to zero as time approaches infinity.
Remark 1
: Note that the LMI parameterization of the
K
(8) can be combined with various useful convex performance criteria (i.e., αstability, quadratic performance, generalized
H
_{2}
/
H
∞ performance, etc). For instance, if the
K
is given by (8) satisfying for some α > 0, then
It implies that
x
converges to zero with a minimum decay rate
α
.
Remark 2
: Note that the NFC algorithm consists of layers, nodes in each layer, and online selftuning algorithm. In general, the control performance can get better as the number of layers and nodes increases. However, this leads to a more complicated control system structure. Additionally, the updated laws for the parameters of all layers bring about a burdensome computation because of a large series of training data. Therefore, the structure and online selftuning algorithm of the NFC should be designed simply and reasonably. For the proposed speed controller, the updated laws can be applied only to extract the parameters of the output layer. Besides, the parameters of the inner layer such as the standard deviation parameters of the membership functions can be selected as fixed parameters according to the control engineering knowledge. This solution still guarantees the stability criteria of the control system (20).
Remark 3
: This remark discusses how the controller gains are chosen. The proposed control law in (17) consists of the control term
u
_{fb}
and the control term
u
_{nf}
. The weights
w
_{ik}
are integrated into the control term
u
_{nf}
in (12). To attain the fast convergence and transient response, the weights
w
_{ik}
are tuned to large values. As indicated in (15), these weights
w
_{ik}
are proportional to the parameters 𝜂
_{ik}
, so the large values of 𝜂
_{ik}
lead to those of
w
_{ik}
. Meanwhile, the gain matrix
K
of the control term ufb is achieved by solving the LMIs (7) or (22). Finally, the design parameters K and 𝜂
_{ik}
can be systematically tuned as follows:
Step 1
: Solving the LMIs (7) or (22) yields the gain matrix
K
;
Step 2
: Set 𝜂
_{ik}
to quite small values and then increase 𝜂
_{ik}
by a small amount;
Step 3
: If the transient and steadystate performances are satisfactory, then this process is completed. Otherwise, return to
Step 2
above.
3. Disturbance observer design
The proposed control law in (17) requires the rotor angular acceleration information 𝛽 which is usually unavailable. Based on
Definition 2
, the rotor angular acceleration information 𝛽 can be directly obtained from the time derivative of the speed. However, this calculation method can be affected by its highfrequency noises. To avoid directly calculating the time derivative of the speed, the rotor angular acceleration 𝛽 needs the knowledge of the disturbance
d
_{1}
(
t
). Thus, a simple disturbance observer is designed in this paper.
From the (1) and
assumption 2
, the disturbance observer can be established as
where
L
∈
R
^{2×1}
is an observer gain matrix, and
From (23) the error dynamics is expressed by
where
Theorem 2
: Assume that the following LMI condition is feasible
where
P
_{o}
∈
R
^{2×2}
and
Y
_{o}
∈
R
^{2×1}
are decision variables. Also, assume that the observer gain matrix
L
is calculated by
Then,
exponentially goes to zero.
Proof
: Assume that (25) is feasible, and then there exists a matrix
Q
_{o}
> 0 such that
Let the Lyapunov function be defined as
The time derivative of (28) along the error dynamics (24) is represented by
It indicates that
is asymptotically stable.
Remark 4
: Note that the LMI parameterization of the
L
(26) can be combined with various convex performance criteria (i.e., αstability, quadratic performance, generalized
H
_{2}
/
H
∞ performance, etc). For example, if the
L
is computed by (26) satisfying with some
α
> 0, then
It means that
converges to zero with a minimum decay rate
α
.
Using the NFC and the disturbance observer above, a disturbance observerbased control law can be designed, thus the control inputs (
V
_{qs}
and
V
_{ds}
) can be expressed as
Remark 5
: The design procedure of the proposed observerbased NFC method can be generalized as follows:
Step 1
: Solve the LMIs (25) or (30). Then obtain the observer gain (26) and construct the observer (23).
Step 2
: Solve the LMIs (7) or (22). Then obtain the controller gain matrix
K
using the formula (8).
Step 3
: Choose the membership functions of the speed,
q
axis current, and
d
axis current. Then, construct the matrix
H
using (10) and (11).
Step 4
: Using
Remark 3
, choose the parameters 𝜂
_{ik}
, calculate the updated law (34), and construct the observer based neurofuzzy control term (33).
Step 5
: Construct the observerbased control inputs (31) based on (32) and (33).
4. Performance Investigation by Simulation and Experimental Results
To demonstrate the effectiveness of the proposed observerbased NFC algorithm, simulation and experiment studies are realized on a prototype IPMSM with the following specifications: rated power
P
_{rated}
= 390 W;
p
= 4;
R
_{s}
= 2.48 Ω;
L
_{qs}
= 114 mH;
L
_{ds}
= 75 mH; λm = 0.193 V.sec/rad;
J
= 0.00015 kg.m
^{2}
;
B
= 0.0001 N.m.sec/rad.
Let us design a disturbance observer that guarantees the minimum decay rate
α
= 300. By solving the LMI condition (30) and (26), the gain matrix
L
is calculated as
Next, let us design a speed controller that guarantees the minimum decay rate
α
= 70. By solving the LMI condition (22) and (8), the gain matrix
K
is achieved as
As described in
Remark 2
, considering a tradeoff between a simple implementation and a satisfactory performance, the fuzzy rules are selected as
r
=
3
×
2
×
2
=
12
. That is, the membership functions for three input variables (
z
_{1}
= 𝜔,
z
_{2}
=
i
_{qs}
, and
z
_{3}
=
i
_{ds}
) are adopted as
m_{11} =m_{12} =m_{13} =m_{14} =e^{(ω300)2/3002},
m_{15} =m_{16} =m_{17} =m_{18} =e^{ω2/3002},
m_{19} =m_{110} =m_{111} =m_{112} =e^{(ω+300)2/3002},
m_{21} =m_{22} =m_{25} =m_{26} =m_{29} =m_{210} =e^{(iqs 2)2/22},
m_{23} =m_{24} =m_{27} =m_{28} =m_{211} =m_{212} =e^{(iqs +2)2/22},
m_{31} =m_{33} =m_{35} =m_{37} =m_{39} =m_{311} =e^{(ids 1)2/22},
m_{32} =m_{34} =m_{36} =m_{38} =m_{310} =m_{312} =e^{(ids +1)2/22},
Then, this leads to the control term
u
_{nf }
with
Fig. 2
shows the overall schematic diagram of a laboratory prototype IPMSM drive system which contains an IPMSM, a threephase PWM inverter, an encoder, a control board with a TMS320F28335 DSP and load motor. The rotor position angle is measured through an encoder RIA402500ZO, and the two stator currents (
i
_{a}
,
i
_{b}
) are detected via halleffect current sensors. The threephase stator current signals (
i
_{a}
,
i
_{b}
,
i
_{c}
) are transformed to twophase signals (
i
_{qs}
,
i
_{ds}
) in the
dq
reference frame. Meanwhile, the rotor angular acceleration information 𝛽 is calculated via the disturbance observer, and then is provided for the proposed neurofuzzy speed controller. Considering the system efficiency, control performance and current ripples, the sampling and switching frequencies are chosen as 5 [
kHz
], and a space vector PWM (SVPWM) technique is employed. Furthermore, a servo IPMSM drive is used as a load motor to apply the load torque.
Overall schematic diagram of a prototype IPMSM drive system.
For a fair comparison, the observerbased FLC scheme in
[2]
, which consists of the control structure similar to the proposed observerbased NFC algorithm, is adopted in this paper. The control inputs (
V
_{qs}
and
V
_{ds}
) are represented by
where
u
_{fb1}
is the state feedback term,
u
_{ff}
is the feed forward term, and
is an estimate of
T
_{L}
. The information of
is attained by constructing the load torque observer in
[6]
. For a fair comparison like
[11]
, the gains of the proposed NFC and the FLC methods are tuned to reach the similar speed response such as overshoot, settling time and error in steadystate under the nominal motor parameters. The proposed NFC scheme consists of the control terms
u
_{fb}
and
u
_{nf}
, while the FLC method consists of the control terms
u
_{fb1}
and
u
_{ff}
. It notes that the performance of the proposed NFC scheme depends on the gain matrix
K
of the
u
_{fb}
and the parameters 𝜂
_{w}
of the
u
_{nf}
, whereas that of the FLC scheme mainly depends on the gain matrix
K
_{1}
of the
u
_{fb1}
. Additionally, the
K
and 𝜂
_{w}
can be easily tuned as in
Remark 3
. Meanwhile, the
K
_{1}
can be easily designed by using the pole placement technique. Consequently, the 𝜂
_{w}
of the proposed NFC strategy is adopted as 10,000, whereas the
K
_{1}
of the FLC method is elected as
k
_{11}
= 62,500,
k
_{12}
= 500, and
k
_{23}
= 3,000.
In this work, four case studies summarized in
Table 1
are simulated using MATLAB/SIMULINK and tested to verify the feasibility of the proposed observerbased NFC scheme and the observerbased FLC scheme.
Cases 1
to
3
show the speed dynamic behaviors after a sudden change in the desired speed (𝜔
_{d}
), i.e., when the 𝜔
_{d}
abruptly decreases from 209.4 [
rad/s
] to −209.4 [
rad/s
], but the
T
_{L}
keeps 0.75 [
N
⋅
m
]. Next,
Case 4
shows the torque dynamic behaviors after a sudden change in the load torque (
T
_{L}
), i.e., when the
T
_{L}
suddenly changes from 0.5 [
N
⋅
m
] to 1.5 [
N
⋅
m
], but the 𝜔
_{d}
holds 104.7 [
rad/s
]. As presented in
[24

25]
, the stator resistance (
R
_{s}
) of the IPMSM varies as a function of the temperature, while the λ
_{m}
,
L
_{ds}
and
L
_{qs}
vary as a function of the operating current. The
R
_{s}
increases as the temperature rises
[24]
, and the λ
_{m}
and
L
_{qs}
decrease as the
i
_{qs}
increases
[25]
. However, the
L
_{ds}
slightly increases as the
i
_{ds}
is negative
[25]
. Furthermore, the
J
and
B
may strongly increase as the external mechanical load is applied to the IPMSM drive. Thus, to demonstrate the robustness of the proposed observerbased NFC scheme, two kinds of parameter variations are given:
Case 2
is carried out under the electrical parameters variations (Δ
R
_{s}
= +0.5
R
_{s}
, Δ
L
_{qs}
= 0.3
L
_{qs}
, Δ
L
_{ds}
= +0.1
L
_{qs}
, Δλ
_{m}
= 0.2λ
_{m}
) based on
[24

25]
, whereas
Cases 3
and
4
are executed under the mechanical parameters variations (Δ
J
= +2.0
J
, Δ
B
= +1.0
B
). It is wellknown that the motor parameters can be easily adjusted in the simulation studies, but it is not an easy task to directly modify the motor parameters in the experiments. Generally, it can be an alternative solution to indirectly change the motor parameters in a real IPMSM drive by simply changing the motor parameters in the control scheme
[9

10]
. Thus, to conduct an experiment on the proposed observerbased control scheme under the variations of the motor parameters (
R
_{s}
,
L
_{qs}
,
L
_{ds}
, λ
_{m}
,
J
,
B
), the motor parameters in the controller are indirectly changed rather than those in the real IPMSM drive.
Case studies for simulations and experiments
Case studies for simulations and experiments
Figs. 3(a)

5(a)
show the speed step responses of the proposed NFC method under
Cases 1−3
, respectively, while
Figs. 3(b)

5(b)
show the speed step responses of the FLC method under
Cases 1−3
, respectively.
Figs. 6(a)
and
6(b)
show the torque transient responses of both control methods under
Case 4
, respectively. In
Figs. 3(a)
and
3(b)
, the overshoot, the settling time and the steadystate error of the proposed NFC method and the FLC method are obtained under nominal motor parameters as (0.0%, 66 ms, 0.0%) and (0.0%, 65 ms, 0.03%), respectively. These results imply that the comparative evaluation was satisfactorily conducted and the FLC scheme can precisely track the speed reference trajectory of the IPMSM in case of the nominal motor parameters. In
Figs. 4(a)
and
4(b)
, it is observed that the speed errors in steadystate of both methods are almost zero and 4.67%, and the settling times are 57 [
ms
] and 69 [
ms
], respectively.
Figs. 5(a)
and
5(b)
show that the undershoots of both control methods are observed as 1.45% and 6.66%, and the settling times are 66 [
ms
] and 82 [
ms
], respectively.
Figs. 6(a)
and
6(b)
show that the speed errors in steadystate are negligible, but the motor speed of
Fig. 6(a)
keeps much more stable than that of
Fig. 6(b)
during an abrupt load change.
Simulation results of the proposed observerbased NFC method and the observerbased FLC method under Case 1.
Simulation results of the proposed observerbased NFC method and the observerbased FLC method under Case 2.
Simulation results of the proposed observerbased NFC method and the observerbased FLC method under Case 3.
Simulation results of the proposed observerbased NFC method and the observerbased FLC method under Case 4.
In this work,
Cases 3
and
4
, which show the speed and torque transient responses under the mechanical parameters variations (
ΔJ
= +2.0
J
,
ΔB
= +1.0
B
), are chosen to experiment because of limited space.
Figs. 7
and
8
show the experimental results of the proposed NFC method under
Cases 3
and
4
, respectively. Meanwhile,
Figs. 9
and 10 show the test results of the FLC method under
Cases 3
and
4
, respectively.
Table 2
summarizes the control performance of two control strategies during the transient and steadystate based on the simulation and experimental results.
Experimental results of the proposed observerbased NFC method under Case 3.
Experimental results of the proposed observerbased NFC method under Case 4.
Experimental results of the observerbased FLC method under Case 3.
Performance summaries of two control strategies during transient and steadystate based on simulation and experimental results
Performance summaries of two control strategies during transient and steadystate based on simulation and experimental results
From
Figs. 3

10
, it can be seen that the variations of the mechanical parameters (
J
,
B
) mainly affect the transient response. In fact, the variations of the electrical parameters (
R
_{s}
,
L
_{qs,}
L
_{ds}
, λ
_{m}
) slightly affect the steadystate response. Also, it is obvious that the proposed observerbased NFC scheme can obtain a better control performance (i.e., less steadystate error and more robustness) than the observerbased FLC scheme in case that some uncertainties in electrical and mechanical parameters exist.
Experimental results of the observerbased FLC method under Case 4.
5. Conclusion
In this work, a disturbance observerbased NFC methodology of a servo IPMSM drive system has been proposed. The proposed observerbased speed controller is insensitive to uncertain factors such as motor parameter variations and load torque disturbances. Additionally, the maximum torque per ampere (MTPA) control was incorporated to improve the torque generator in the constant torque region. In this study, the global stability analysis is comparatively simple and systematic since the time derivative of the quadratic Lyapunov function is elected as the cost function to be minimized. Moreover, the design procedure of the online selftuning algorithm is simplified to reduce a computational burden of the NFC. Simulation and experimental results surely show that the proposed observerbased NFC scheme has a better speed tracking performance such as less steadystate error, more robustness than the observerbased FLC method in the existence of the uncertainties in electrical parameters and mechanical parameters.
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2012R1A2A2A01045312).
BIO
Dong Quang Dang received the B.S. and M.S. degrees in Electrical Engineering from Hanoi University of Science and Technology (HUST), Hanoi, Vietnam in 2005 and 2010, respectively. From 2006 to 2011, he worked at Hung Yen University of Technology and Education, Hung Yen, Vietnam, as a lecturer. He is currently pursuing the Ph.D. degree in the Division of Electronics and Electrical Engineering, Dongguk University, Seoul, Korea. His research interests are in the field of electric machine drives and control of distributed generation systems using renewable energy sources.
Nga ThiThuy Vu received the B.S. and M.S. degrees in Electrical Engineering from Hanoi University of Science and Technology (HUST), Hanoi, Vietnam in 2005 and 2008, respectively, and the Ph.D degree in Electronics and Electrical Engineering, Dongguk University, Seoul, Korea, in 2013. Currently, she is with the Department of Automation Control, Hanoi University of Science and Technology as a full lecturer. Her research interests are in the field of DSPbased electric machine drives and control of distributed generation systems using renewable energy sources.
Han Ho Choi received the B.S. degree in Control and Instrumentation Engineering from Seoul National University, Seoul, Korea, in 1988, and the M.S. and Ph.D. degrees in Electrical Engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 1990 and 1994, respectively. From 1994 to 1998, he was a Team Leader with the Advanced Technology Laboratory, DaeWoo Electrical Co., Ltd., Korea. He is currently with the Division of Electronics and Electrical Engineering, Dongguk University, Seoul, Korea. His research interests include linearmatrixinequalitybased control system design, microprocessorbased control systems, variablestructure systems, and microprocessorbased electric machine drives.
JinWoo Jung received the B.S. and M.S. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 1991 and 1997, respectively, and the Ph.D. degree in Electrical and Computer Engineering from The Ohio State University, Columbus, Ohio, USA, in 2005. From 1997 to 2000, he was with the Home Appliance Research Laboratory, LG Electronics Co., Ltd., Seoul, Korea. From 2005 to 2008, he was a Senior Research Engineer with the R&D Center and PDP Development Team, Samsung SDI Co., Ltd., Korea. Since 2008, he has been an Associate Professor with the Division of Electronics and Electrical Engineering, Dongguk University, Seoul, Korea. His current research interests are in the area of DSPbased electric machine drives, power conversion circuit design and control algorithm for electric vehicles (EV), control of distributed generation systems (DGS) using renewable energy sources (wind turbines/fuel cells, solar cells), and driving circuits and driving methods of ac plasma display panels (PDP) and liquid crystal displays (LCD).
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