INTRODUCTION
DC motors were commonly used due to reliable speed and position control and costeffective driver system. With rapid development of semiconductors, microprocessors and control technology, a more complex control method has been implemented to improve the disadvantages of DC motors. Now, AC motor has become a leading motor in the industrial applications. As one type of AC motor, PMSM features lower maintenance cost, longer service life, improved efficiency and response speed, etc, while having maintenancefree brushes and commutators (Slemon, 1992). In recent years, Vector Control theory is wellproven in Permanent Magnet Synchronous Motor (PMSM) (Novotny and Lipo, 1996) and traditional vector control methods and ProportionalIntegral (PI) controllers present good results in speed control of PMSM. However, PI controllers shall be adjusted according to the running state, leading to changing load torque. In other words, PI controllers cannot achieve good output performance under wide range of operating conditions (Uddin et al., 2002).
PMSM with Fuzzy Controller has been widely applied to highperformance Server
drive systems (Kadjoudj et al., 2001; Heber et al., 1997; Cerruto
et al., 1997; Miki et al., 1991; Kung and Liaw, 1994). Since Fuzzy
Sets was proposed by Zadeh (1965), there was a fast growing trend of study and
applications related to fuzzy theory, such as: Artificial Intelligence (AI),
Control engineering, decision analysis, medical diagnosis, automaton and pattern
recognition, etc. (Singh et al., 1998; Cerruto et al., 1997; Erenay
et al., 1998; Uddin and Rahman, 2000; Emami et al., 1998; Bolognani
and Zigliotto, 1996; Yi and Chung, 1998), especially in terms of controller
design. In general, traditional design process of controllers requires an understanding
of the controlled system, namely, describing the controlled system with mathematical
models of Differential Equation (DE) or Difference Equation. When the controlled
system becomes more complex, modeling is impossible through System Identification
(ID). The advantage of fuzzy control is that it can integrate the knowledge
of anthropologists into the design process of controllers, without the need
of accurate vmathematical models. During fuzzy control, the behavior of controlled
system could be described using a set of linguistic fuzzy rules. Therefore,
the knowledge of anthropologists could be converted to fuzzy control rule, reducing
the complexity of design control system. According to state error between system
and feedback, a controller designed with fuzzy theory can select proper rules
to achieve an expected motor output response and highperformance PMSM speed
control system, irrespective of the changes of electrical parameters or load
of motor. Thus, this study applies fuzzy control to design a fastresponse controller
and improve traditional PI controllers with poorer response.
The output quality characteristics of PMSM generally include overshoot, rise time and settling time, featuring SmallTheBetter of multiresponse. In previous design of controllers, only individual quality characteristics were compared without consideration of Interaction amongst control parameters and tradeoff of multiple quality characteristics. So, the relationship between control parameters and overall multiquality characteristics output is difficult to measure. By combining Taguchi Method and MCDM of TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) (Hwang and Yoon, 1981), this study set up an analytical model for PMSM fuzzy controller parameters and output quality characteristics and used Genetic Algorithm (GA) to design optimum parameter levels and PMSM controller parameters featuring robustness and high output quality (Chou et al., 2004; Margaliot and Langholz, 1999;^{ }Zhou^{ }et al., 2000). Finally, this study demonstrated its methods with the help of Matlab/Simulink software, under a PCbased infrastructure comprising PC Based motor control systems.
MATHEMATICAL MODELS OF PMSM
The PMSM in this study has a permanent magnet rotor and sinusoidal stator windings
with a spacing of 120°. Under a synchronous reference coordinate system,
the voltage equation of PMSM is expressed by Eq. (1) (Uddin
and Rahman, 2000):
where:
R_{a}, L_{a} 
: 
Motor’ armature resistance and inductance 
V_{da}, V_{qa} 
: 
daxis and qaxis armature voltage 
i_{da}, i_{qa} 
: 
daxis and qaxis armature currents 
e_{da}, e_{qa} 
: 
Electromotive Force (EMF) daxis and qaxis armature coil 
P 
: 
Differential operators (d/dt) 
ω_{re} 
: 
Rotor electrical radian speed 
φ_{fa} 
: 
Field flux linkages
e_{da} = 0
e_{qa} = ω_{re}φ_{fa}

Eq. (1) is rearranged into:
It is observed from Eq. (2) that daxis and qaxis Armature
Current i_{da}, i_{qa} is controllable, but e_{qa} =
ω_{re}φ_{fa} is uncontrollable, since e_{qa}
is EMF generated by Field Flux Linkages of Permanent Magnet. PMSM’ torque
T_{e} is:
where, p_{n} is number of pole pairs. It can be seen from above deduction
process that, after change of coordinate, PMSM allows to decouple the electrical
equation and then obtain 2axis current i_{da}, i_{qa}. Given
a constant φ_{fa}, it is only required to control armature current
i_{qa} in order to control the torque of PMSM. It is learnt from Eq.
(3) that, if the position of magnetic pole is measured, twophase dand
qaxis armature voltage V_{da}, V_{qa} can be converted into
threephase output voltage (V_{ua}, V_{Va}, V_{Wa})
using Eq. (4).
Thus, it should be possible to control motors easily with V_{da} and
V_{qa} under d, q coordinate. It is also learnt from Eq.
(1) that, there exists mutual interference of dqaxis of PMSM. For the
purpose of control, noninterference control is discussed below. Let V_{da},
V_{qa}:

Fig. 1: 
Block diagram of PMSM with noninterference control 
Substituting Eq. (5) into Eq. (1) to
obtain Eq. (6), with the relationship shown by Fig.
1:
It is learnt from Eq. (6) and Fig. 1 that,
the current of two axes generates no interference and can be controlled individually.
Figure 2 depicts a vector control framework of common PMSM.
FUZZY LOGIC CONTROLLER
The design of fuzzy controller generally includes three steps: Fuzzification,
inference engine and defuzzification, as shown in Fig. 3.
Use linguistic value (or fuzzy sets) to convert input variables into fuzzy representation,
then use inference engine library to convert these linguistic values into fuzzy
sets of fuzzy variables and finally into identifiable controlled variables for
the controlled system.
Determination of fuzzification control strategy: The fuzzification process
is to convert the input Map of a definite value into a fizzy set, with the relationship
represented by a Membership Function. The definite value of fuzzy controller
must be related to speed.
In a PMSM vector control infrastructure, input and output of a speed controller
is: the difference of speed command ω*_{rm} and actual speed ω_{rm}
and command torque T*_{e}. So, the speed error ew(k) is taken as an
input and the variable of speed error cew(k) as the other input. c(k) is used
to replace command torque T*_{e} as the output of speed controller.
So, two inputs for every sampling time are:
where, ω*_{rm} and ω_{rm} is separately speed command
and actual speed of PMSM. The block diagram of speed control system with fuzzy
controller infrastructure is illustrated in Fig. 4.
To convert
definite variables ew(k) and cew(k) into fuzzy variables ew and cew during fuzzification
phase, proper Membership Function shall be used. However, Membership Function
is a subjective design element of fuzzy controller. Firstly, it is required
to decide which kind of function is used e.g., triangular Membership Function
in this study. Then, decide the number of fuzzy sets and respective range.

Fig. 4: 
Block diagram of fuzzy speed controller applied to vector
control PMSM 

Fig. 5: 
Illustrates (a) speed error (ew) (b) speed error behavior
variables (cew) (c) membership function diagram for output cT _{e},
while fuzzy controller is adopted to PMSM 
In this study, five fuzzy sets of NL, NS, ZE, PS and PL are chose for ew and
three fuzzy sets of nm, ze and pm are chose for cew. However, five fuzzy sets
of tNL, tNS, tZE, tPS and tPL are chose for cT_{e}, as shown in Fig.
5. The value of Membership Function, u, for each fuzzy variable ranges between
0 and 1. The speed error, ew, for the designed fuzzy speed controller is at
the range from 25 to 25. However, error behavior variables, cew, are at the
range from 15 to 15 and the range of the output, cT_{e}, is set between
20 and 20.
Design of inference engine: The key point for the fuzzy controller is
the establishment of knowledge base, because the knowledge base is established
according to the experience of expert system. For fuzzy speed controller, the
input and output relationships of optima results for different controllers in
the motor system are stored in the knowledge base. Through the inference engine,
a suitable rule from rule base is adopted and then optima controlled variables
are generated.
Table 1: 
Control rule table for fuzzy speed controller 

In this study, the input variables, ew, for the designed fuzzy control rule
possess five membership functions and cew possesses three membership functions.
The rule is expressed with the form of Ifthen and fifteen control rules are
included in the rule, as shown in Table 1. The description
of the rule adopted in this study is expressed as following:
R^{i}: GIf ew is A_{i1} and cew is
A_{i2}, then cT_{e} is B_{i} i = 1,2,…..,15 
where, i is the number of the control rule, ew and cew are input variables.
cT_{e} is output variables and A_{i} and B_{i} are fuzzy
sets.
Defuzzification: During the defuzzification procedure, the output of
the fuzzy sets has to be transferred into identifiable value. In this study,
center of gravith method of Eq. (9) is used to obtain the
identifiable increment torque (cT_{e}).
Through the integration of Eq. (10), the torque, T*_{e}(k),
can be obtained.
where, cT*_{e} is the output of the fuzzy controller, cT_{ei} is the membership value of the input membership function corresponding to the ith control rule. u(cT_{ei}) is the membership value of the output membership function corresponding to the ith control rule. T is sampling time.
COMPUTER SIMULATION OF TAGUCHI METHOD
To demonstrate the feasibility of aforementioned fuzzy speed control methods
with Matlab/Simulink, computeraided simulation is performed according to the
controller infrastructure of Fig. 2 and by taking the parameters
of PMSM in Table 2 as the controlled objects.
Table 2: 
Parameters of PMSM 

The Taguchi experiments have recently offered a costeffective strategy for
the study of interactions between reaction variables in electronic engineering
quality improvement (Phadke, 1989). This method using signaltonoise ratios
(SN ratio) takes both the mean and the variability into account. The SN equation
depends on the criterion for the quality characteristic to be optimized and
provides accurate prediction of component levels for excellent performance.
The orthogonal arrays are designated by the notation L (L for Latin squares)
with a subscript, the SN ratio (η) is an index of robustness in experimental
processing and the definition of SN ratio for NTB response is as follows (Phadke,
1989):
where, n is the number of tests for various test level combinations, y_{i}
is ith observed value of the test level combination. In addition to optimization
of individual quality characteristics, it is also recommended to use Taguchi
Method for analysis of multiresponse quality characteristics. For instance,
in the case of conflict among various factor levels, engineering knowledge or
experience shall be required for optimized level selection and setting. However,
such a subjective method may not be suitable for all multiresponse quality
characteristics, while the selected settings of parameter levels may not present
optimum conditions (Tong et al., 1997). To reduce the interference and
influence upon operating environment and improve the output quality of PMSM,
Kid, Kiq of current controller and Gk of fuzzy controller are taken as control
factors, each of which has set three levels. In addition, motor load and speed
are taken as noise factor. The motor load is set at 1.0Nm and 2.0Nm, speed
set at 1800, 900 and 50 rpm, with the test results shown in Table
3. The simulation test with L_{9} (3^{4}) Orthogonal Array
is shown in Table 4.
To set up an analytic model of fuzzy controller and overall output quality,
this study converted the quality characteristics of PMSM Plant (overshoot, rise
time and settling time) into individual quality target values using TOPSIS.
As listed in Table 4, this research has used 9 test level
combinations (i = 1, 2,… , 9), each of which must consider the speed and
loading conditions. Thus, each combination requires 6 repetitive tests (n =
6), totalizing 56 times of tests. In this research, η_{OH}, η_{RT}
and η_{ST} represents SN values of overshoot, rise time and settling
time, respectively. TOPSIS of PMSM output quality is performed in the following
steps:
Table 3: 
Control factors, noise factors and level combinations 

Table 4: 
L_{9} (3^{4}) Orthogonal array of Taguchi
Method 


Step 1: set up a Quality Decision Matrix: D
where, S_{i, k} represents η of kth quality characteristics in ith test level combination.
Step 2: standardize Quality Decision Matrix: D
Where:
w_{K} is weight of kth quality characteristics.
Step 3: Calculate ideal solution D^{+}_{1} and negative
ideal solution D^{+}_{1}
Step 4: Decide an optimum Taguchi factor level combination using quality
index QI. A bigger QI means better quality.
This research combined η_{OH}, η_{RT} and η_{ST}
using quality index QI of TOPSIS. The results of Taguchi Method are shown in
Table 4 and Fig. 6. The important factors
affecting output quality of PMSM are GK, Kid and Kiq, of which Gk has the strongest
influence as illustrated in Fig. 6. The optimum level combination
of orthogonal array of Taguchi Method is Kid = 1100, Kiq = 1100, Gk = 0.6 and
output quality index QI = 0.527 is an optimum value of test combinations. The
9th test results are listed in Table 4 and the speed simulation
response diagram is shown in Fig. 7 and 8 depict
different speedload response diagrams under optimum level combinations (Kid
= 1100, Kiq = 1100, Gk = 0.6), with simulation time as 0.0~1.0 and 0.0~0.1 sec,
of which Fig. 7 depicts a simulation response diagram of motor
speed, with 0.5 sec instantaneous loading of 1.0 and 2.0 Ntm and speed command
of 50, 900, 1800 rpm; Fig. 8 depicts a simulation response
diagram of motor speed, with fulldistance loading of 1.0 and 2.0 Ntm and speed
command of 50, 900, 1800 rpm. The results in Fig. 8 show that,
under different speeds, Rise Time of Taguchi Method is smaller than scheduled
setting speed: 0.02 sec. In addition, overshoot is also smaller than the setting
speed, while settling time is more obvious in the case of lower speed (50 rpm).

Fig. 6: 
Comparison diagram of SN ratio of Taguchi method SN 

Fig. 7: 
Results of Taguchi Method: Kid = 1100, Kiq = 1100, Gk = 0.6;
simulation response diagram of motor speed, with 0.5 sec instantaneous loading
of 1.0 and 2.0 Ntm and speed command of 50, 900, 1800 rpm 

Fig. 8: 
Kid = 1100, Kiq = 1100, Gk = 0.6; simulation response diagram
of motor speed, with fulldistance loading of 1.0 and 2.0 Ntm and speed
command of 50, 900, 1800 rpm 
OPTIMIZATION OF PARAMETERS OF PMSM
By using Taguchi Method, this study found that, at Kid = 1100, Kiq = 1100,
Gk = 0.6, the important factors to PMSM overall output quality characteristics
Kid, Kiq and Gk ensure reliable output quality (QI = 0.527) with minimum variance.
Of which, Gk has the strongest influence upon PMSM. To obtain an optimal parameterization,
this study made optimization analysis with Gk factor. GA is a functionrelated
optimization tool most commonly used to resolve the problem of solution space
and calculate global optimal solution. So, it is a method of searching target
function limit. Though GA is a random search mode, it often searches and amends
space to generate reasonable solutions according to cumulative information of
every generation of population. During optimization process of GA, possible
solution chromosome is composed of genes. In general, every gene is represented
by a series of binary strings, which complete the evolution through Selection,
Crossover and Mutation. Firstly, GA enables encoding of variables and then expresses
the search space in the form of encoding. Population Size represents the number
of every generation of chromosome. In the case of excessively small size, GA
will be converged too quickly, often leading to poorer solution owing to insufficient
information of population. Fitness function in GA process, also called target
function, is used to decide the degree of fitness of a chromosome under an environmental
condition, namely, measuring the performance of every chromosome. The fitness
function of this study is expressed by Eq. (16):
Population size of chromosomes is often fixed, but the percentage of fitter chromosome is increased by reproduction. This paper used 100 groups of chromosome, which were reproduced by common Roulette Wheel Method. So, the percentage of fitter chromosome dictates the probability of selection. With Twopoint Crossover method, two crossover points are selected randomly from all selected binary strings and all strings between two crossover points are exchanged. In general, the crossover ratio will affect the survival probability of mothers in next generation. A higher crossover ratio means a lower survival probability and higher birth rate. The crossover ratio is set as 0.8. When applied to a particular problem, GA only requires two elements: (1) an encoding of candidate structures (solutions) and (2) a method of evaluating the relative performance of candidate solutions. A simple GA procedure was introduced as follows (Hung and Huang, 2006):


Fig. 9 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 1 Ntm and speed command of 50 rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 1 Ntm and speed command of 50 rpm 

Fig. 10 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 2 Ntm and speed command of 50 rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 2 Ntm and speed command of 50 rpm


Fig. 11 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 1 Ntm and speed command of 900 rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 1 Ntm and speed command of 900 rpm 

Fig. 12 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 2 Ntm and speed command of 900
rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 2 Ntm and speed command of 900 rpm


Fig. 13 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 1 Ntm and speed command of 1800 rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 1 Ntm and speed command of 1800 rpm 

Fig. 14 (a): 
Motor speed simulation response diagram of GA and Taguchi,
with 0.5 sec instantaneous loading of 2Ntm and speed command of 1800 rpm
(b): Motor speed simulation response diagram of GA and Taguchi, with fulldistance
loading of 2Ntm and speed command of 1800 rpm 
Hundred generations are set according to abovespecified GA. By using the analytical
model of PMSM fuzzy controller parameters and output quality characteristics,
GA searches optimum fitness function. Under different rotational speed of GA,
if Kid = 1100, Kiq = 1100, Gk = 0.585, QI = 0.53161, the design results with
Taguchi method at QI = 0.527 have good simulation response results. Fig.
914 depict the speed simulation response of GA and Taguchi
under different speedload conditions. Of which, Fig. 914a
depict the comparative speed simulation response of GA and Taguchi at 0.0~1.0
sec; Fig. 914b depict the comparative
speed simulation response of GA and Taguchi at 0.00~0.02. The simulation results
from Fig. 914 suggests that, under low
speed (50 rpm), medium speed (900 rpm) and high speed (1800 rpm), the overall
quality output simulation response (overshoot, rise time and settling time)
of GA at 1.0 and 2.0 Ntm is better than the simulation response of Taguchi,
especially for rise time within 0.015 sec.
CONCLUSIONS
This study attempted to design a controller based on the fuzzy theory, such that the controller could select proper rules according to the state error between system and feedback. It then sets up an analytical model with PMSM controller parameters, combines three STB quality characteristic (η_{OH}, η_{RT} and η_{SR}) into an overall Quality Index (QI) based on TOPSIS method and computes optimum parameters of motor using GA method to achieve a highperformance PMSM controller system based on Taguchi experimental results. So that a robust PMSM speed control system can be developed through PCBased motor controller. The PCbased simulation and experimental results showed that the FLC in this study presents excellent speed control and robustness against PMSM parameter or load change. The simulation results showed that under low speed (50 rpm), medium speed (900 rpm) and high speed (1800 rpm), the overall quality output simulation responses (overshoot, rise time and settling time) of GA at 1.0 and 2.0 Ntm are better than those of Taguchi, especially for rise time within 0.015 sec.