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2010 International Conference on Power System Technology
Performance Improvement of a Linear
Permanent Magnet Synchronous Motor Drive
using Fuzzy Logic Controller J. Faiz, Senior Member, IEEE, M. Manoochehri, Gh. Shahgholian
Abstract--In this paper control system of a linear permanent
magnet synchronous motor is designed and modeled. This system
uses both traditional controller (PID) and fuzzy logic controller
(FLC) and their performances are compared. Disadvantages of
PID controller are uncertainty of load fluctuations, system
parameters variation, undesirable rise time, settling time and
large steady-state error. On contrary to PID controller, FLC
improves control criteria and provides more robustness against
load variation and system uncertainty. Application of FLC
decreases the force ripples and therefore motor current waveform
becomes sinusoidal.
Index Terms--Permanent Magnet Linear Synchronous Motor
Modeling, PID Controller, Fuzzy Logic Controller, Current
Source Inverter.
I. INTRODUCTION
EVER increasing applications of linear motors for linear
movement such as office and factory automation,
elevators, transportation systems, has led to more study on
linear motor drive systems. A linear permanent magnet
synchronous motor (LPMSM) is one of the linear motors that
widely used these days due to its advantages compared with
other linear motors. It can directly drive the load without any
mechanical transfer links. The main advantages of LPMSM
include high thrust density and low losses due to directly
driven load. Also Its efficiency and power factor are higher
than that of the linear induction motor (LIM); therefore in
many cases LIM has been replaced by LPMSM [1]. LPMSM
has certain unique features like large air-gap, open-wide slots,
pole and interloped PM configurations, flat or tubular
configurations and high normal forces in single-side flat
configurations. On the other hand, LPMSM cannot use
conventional gears or ball screws, so uncertainty in its drive
system largely affects its performance. These uncertainties
include parameter variations, extemal load disturbances, frict
ion forces, and unknown dynamics. As a result, LPMSM
control system must solve the above-mentioned problems [2].
1. Faiz is with the Center of Excellence on Applied Electromagnetic Systems, School of Electrical Engineering, University of Tehran. (e-mail: [email protected]).
M. Manoochehri and Gh. Shahgholian are with the Department of Electrical Engineering, Islamic Azad University - Najaf Abad Branch. (email: [email protected]).
978-\-4244-5940-7/1O/$26.00©201O IEEE
Development of the artificial intelligence systems especially
the fuzzy logic control (FLC) opens a new field in LPMSM
control. FLC system is more suitable to control the ensured
and nonlinear systems. Advantages of FLC include:
1) Designing FLC does not need the exact mathematical model
of the system.
2) FLC is more robust than that of the conventional
controllers.
3) FLC can better solve difficult nonlinear problem of any arbitrary complexity.
4) Rules of FLC are based on human logic.
Therefore, FLC is a desirable controller for LPMSM drive
system [2-4].
In this paper, mathematical model of LPMSM is first
derived for simulation. A drive system for LPMSM is designed
and two types of controllers (PID and FLC) are used to control
the speed of the drive system. It is shown that application of
FLC leads to desirable results compared to PID. FLC
improves control criteria, gives more desirable current and
electric force waves, produces fewer harmonic, and increases
efficiency.
II. MODELING OF LPMSM
To design and simulate a desirable drive system for LPMSM, its model must be available. Generally in this modeling the following assumptions are made:
a) Fundamental component is considered. b) Iron core saturation is neglected. c) Hysteresis and eddy current losses are ignored. d) Damping windings are not included.
There are several mathematical models for LPMSM including
dq model can be employed [5, 6]. The stator currents (ia, ib, ic) are transformed into the dq axis using 3/2 transformations. Then dq stator currents are transformed into dq current in rotor coordinates system. Voltage equations of dq axis in rotor coordinates system is are as follows:
(1)
Uq = Rriq +DAq +wrAd (2)
Flux equation of dq axis is: Ad = Ldid + Af (3)
Aq = Lqiq (4)
The electro-magnet force is:
FM = 3n [iqAf + (Ld - Lq)idiq] (5) 2. The associated mechanical equation is as follow:
(6)
Figs. 1-4 show the block diagram of the mathematical model. Table 1 defmes all symbols used in the figures.
P��
G::)...--__ ---+l:�s:., '" · vq 111....q
Fig. I. Deriving iQ using dq model
0 � � :" r� " ·
�� Iq Produot
Fig. 2. Deriving id using dq model
Fig.3. Mechanical equation of subsystem using dq model
FL1
Fig. 4. Dq model of LPMSM
TABLE I SYMBOLS DEFINITION
dq axis rotor current (A) dq axis rotor voltage (V)
Rotor inductance of dq axis (H) Rotor resistance (0)
Mover mass (kg) viscous friction coefficient (N.s/m)
Pole pitch (m) Flux linkage of perrnanent magnet (Wb)
Load force (N) D
Velocity (m/s) Angular speed (radls)
id, iQ Ud, UQ Ld, La
Rr M 8 1
Af FL
dldt V
(fJr=1tVh
III. DESIGN OF LPMSM CONTROL SYSTEM
2
Block diagram of a closed-loop control system for LPLSM has been shown in Fig. 5. In this control system the speed error is feedback to achieve the reference value of q axis current (zero). A PWM current source inverter is applied as a control system source.
One of the most advantages of this inverter is its quick response to the motor sampled current. The most important part of this control system is speed controller which generates the reference current. Therefore, design of a desirable controller based on system and load features, is the most important part of control system design [7, 8].
I. PID CONTROLLER
PID is a conventional controller that is employed in many control systems. In general PID controller is used to decrease the steady-state error and improve the stability of the control systems. However, there are some difficulties in adjusting PID coefficients. Always these coefficients are adjusted by trial and
Fig. 5. Closed-loop control system for LPMSM
0.51-----r----r:::::::===r:::j.i= ==r----,----.-------,�1 0.45
0.15 0.1
0.05
X: 0.887 Y: 0.4905
f loading
X: 1.896 Y: 0.3068
•
O L-� _ _L_�_��_�_�_��L_� o 0.2 0.4 0.6 0.8
time(s) 1.2 1.4 1.6 1.8
Fig. 6. Speed response with load changing applying PID controller
error routine [9]. Fig. 6 shows the time variations of speed where PID controller of Fig. 5 is applied. As shown in Fig. 6, a 2N load (Fd is applied at t=1.2 s which leads to a large steadystate error and rise time. It means that PID controller is not often a suitable choice.
II. Fuzzy LOGIC CONTROLLER
Fuzzy logic is a suitable strategy for controlling nonlinear systems. It is a robust controller and change of load and system parameters have no influence on the controller performance. Controller design is based on expert information or human experiences. Fig. 7 shows a FLC applied to LPMSM with control system shown in Fig. 5. To enhance performance and sensitivity of controller, in addition to the first error signal (e), its incremental value (�Ei') is used as the second input. The subset of the inputs language variables e and �e and output variable (u) is {NL, NM, NS, ZO, PS, PM, PL}.
The fuzzy rules are given in Table 2. It has been shown in [10] that the best form of membership function in electric drive systems is the triangular membership function. Fig. 8 shows the design of membership function. Surface view of fuzzy rules has been shown in Fig. 9.
Inl S�&J-'-I...I..II.."" atr.11ion - - M u)Q Gain2
Furry Conu-oR@r \'.it; Ruleviewer
Unit Delay
SalJration1
Fig. 7. Fuzzy logic controller
QJ Outl
�e NL NL NL NM NL NS NM ZO NM
PS NS PM NS PL ZO
de
NM
NM NL NM NM NS
NS ZO ZO
TABLE 2 Fuzzy RULES
NS ZO NM NM NM NS NS NS NS ZO ZO PS ZO PS PS PS
PS NS ZO ZO PS
PS PM PM
Fig. 8. Membership function
I' NS 20 PS
-2 Fig. 9. Surface view of rules
3
PM PL ZO ZO ZO PS PS PS PS PM
PM PM PM PL PL PL
6
j'
Fig. 10 shows the time variations of speed diagram with FLC application for the closed-loop control system shown in Fig. 5. In this case applying a 2 N load at t=0.45s has no influence on the speed response of the controller. Also control criteria such as rise time, steady-state error and settling time have been improved, compared to that of PID controller. So this controller provides a desirable result. Comparison between the controlling criteria in PID and FL controllers has been summarized in Table 3.
One of other important features in LPMSM performance is the force quality. Fewer ripples in the force improve the motor performance and moving part operates smoothly. Figs. 11 and 12 show LPMSM force by applying FL and PID controllers respectively. As seen FLC improves the performance of the motor and leads to less ripples.
0.5 . -----------------.----------�
0.45
0.4
0.35
i 0.3
Il � 0.25
0.05
0.1
X: 0.1412 Y: 0.4945
0.2 0.3
I loading
0.4 time(s)
X: 0.4782 Y: 0.4906
0.5 0.6 0.7
Fig. 10. Speed response with load variation applying FLC
TABLE 3 COMPARlSON BETWEEN TWO CONTROLLERS
Criterion PID FLC Steady state error 9.6x IO-2 9.6x IO-2
Rise time (s) 0.89 0.14 Steady-state error
200x10-2 9.4x IO-2 after loading
0.5
time(s)
Fig. I I. LPMSM force with FLC
0.2 0.4 0.6 0.8 time(s)
1.2 1.4 1.6 1.8
Fig. 12. LPMSM force with PID controller
TABLE 4 PMLSM PARAMETERS
Parameter Value
Rr 10.6Q Ld=La 2.33 mH
M 1.2 Kg B 4.3 N.s/m P I 1 43.2 mm
Af 0.1711 wb
4
Figs. 13 and 14 show motor currents by using FL and PID controllers respectively. It indicates that using FLC leads to almost sinusoidal waveform compared with that of PID controller; so less harmonics is expected in FLC and a higher efficiency is achieved. The parameters of LPMSM have been given in Table 4.
25r----r----r----r----�--_r----�--_,
20
15
10
-5
-10
-15
-20 L-.J....,..!L ____ -'-__ -'-____ -'-__ -'-____ -'-__ -' o 0.1 0.2 0.3 0.4 0.5 0.6 0.7
time(s) Fig. 13. LPMSM current with FLC
25,--.---r--,---r--.--_r--.---.---.--,
.25 '----'-__ --'-__ -'-__ -'----' __ -'-__ ...L.. __ -'-__ '----' o 0.2 0.4 0.6 0.8
time(s) 1.2 1.4 1.6 1.8
Fig. 14. LPMSM current with PID controller
III. CONCLUSION
In this paper a desirable control system for a LPMSM was designed and simulated. A PWM current source inverter was applied as system source due to its quick and desirable response. Two types of controller, PID and FL, was used as
the speed controllers in the control system of LPMSM and their performance were compared. It was shown that FLC provides a better performance against load fluctuations, more qualified electrical force, less harmonics and lower losses compared with that of PID controller. On the other hand FLC improves the control criteria such as steady-state error, rise time and settling time and this leads to a robust controller.
IV. REFERENCES
[ I] G.R. Selemon, A. Straughen, "Electric Machines", Addison Wisely Publisher Company, 1980.
[2] Y.S. Huang, C.C. Sung, Y.T. Shih, "Simulation of a robust fuzzy controller for linear synchronous motor systems", IEEEIICSMC, pp. 2001-2006, Singapore, Oct. 2008.
[3] G. Yishan, Q. Na, "The synchronous drive system in gantry -moving milling machine based on dynamic compensation and fuzzy control", EEE/ISDA, Vol.3, pp. 45-48, Kaohsiung, Nov. 2008.
[4] J. Zhao, B.K. Bose, "Membership function distribution effect on fuzzy logic controlled induction motor drive", IEEE/IECON, Vol. I, pp. 214-219, Nov. 2003.
[5] Y. S. Kung, "Design and implementation of a high-performance PMLSM drives using DSP chip", IEEE Trans. Ind. Elec .. , Vo1.55, No.3, pp. 1341-1351, March 2008.
[6] FJ. Lin, P.H. Shen, P.H. Chou, S.L. Yang, "TSK-type recurrent fuzzy network for dsp-based permanent-magnet I inear synchronous motor servo drive", lEE Proc. Elec. Pow. Appl., Vol. 153, No. 6, pp. 921-931, Nov. 2006.
[7] B. Kwon, K. Woo, S. Kim, "Finite element analysis of direct thrustcontrolled linear induction motor", IEEE Tran. on Magn .. Vol. 35, No. 3, pp. 1306-1309, May 1999.
[8] C. Jiefan, W. Chengyuan, Y. Junyou, Y. Dongbo, "Research on force and direct thrust control for a permanent magnet synchronous linear motor", IEEE/IECON, Vol. 3, pp. 2269-2272, Nov. 2004.
[9] X. Zhang, H. Yu, H. Liu, "A novel control for linear elevator based on reference model sliding model", IEEE/ICAL, Shenyang, China, pp. 734-737, Aug. 2009.
[10] J. Zhao, B.K. Bose, "Evaluation of membership functions for fuzzy logic controlled induction motor drive", IEEE/IECON, Vol. I, pp. 229-234, Nov. 2002.
transformers.
5
V. BIOGRAPHIES
Jawad Faiz received his Ph.D. in Electrical Engineering from the University of Newcastle upon Tyne, England in 1988. He is now a Professor at School of Electrical and Computer Engineering, University College of Engineering, University of Tehran. Dr Faiz is a senior member of IEEE. He is also a member of Iran Academy of Sciences. His teaching and research interests are switched reluctance and VR motors design, design, control and modeling of electrical machines, drives, and
Mehdi Manoochehri received his B.Sc. degree in electrical engineering from Isfahan University of Technology (lUT), Esfahan, Iran, in 2007. He is now a graduate student at Department of Electrical Engineering, Faculty of Engineering, Islamic Azad UniversityNajaf Abad Branch. His research interests include application of power system dynamics, drive and power system simulation.
Ghazanfar Shahgholian received his B.Sc in electrical engineering from Isfahan University of Technology (lUT), Esfahan, Iran, in 1992. He received the M.Sc and PhD in electrical engineering from University Tabriz, Tabriz, Iran in 1994 and Islamic Azad University, Science and Research Branch, Tehran, Iran, in 2006, respectively. He is now an Associate Professor at Department of Electrical Engineering, Faculty of Engineering,
Islamic Azad University - Najaf Abad Branch, Esfahan. His teaching and research interests include application of control theory to power system dynamics, power electronics and power system simulation.