E Performance Improvement of a Linear Permanent Magnet Synchronous Motor Drive using Fuzzy Logic Controller

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

E

VER 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efficiency and power factor are higher than that of the linear induction motor (LIM); therefore in many cases LIM has been replaced by LPMSM [1].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:

jfaiz@ut.ac.ir).

M. Manoochehri and Gh. Shahgholian are with the Department of Electrical Engineering, Islamic Azad University - Najaf Abad Branch. (e­

mail: shahgholian@iaun.ac.ir).

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 coor­

dinates 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::)_vq ...--__

---+l :�

_111....q

s:.,

^{'" ·}

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

FL Af dldt

V (fJr=1tVh

III. DESIGN OF LPMSM CONTROL SYSTEM

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

•

OL-� _ _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 steady­

state 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

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

_{Il �} ^0.3

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

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.

25 r----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 thrust­

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[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.

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transformers.

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 Tech­

nology (lUT), Esfahan, Iran, in 2007. He is now a graduate student at Department of Electrical Engineer­

ing, Faculty of Engineering, Islamic Azad University­

Najaf 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 Depar­

tment 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 dyna­

mics, power electronics and power system simulation.