speed control methods for field … control methods for field oriented permanent magnet ......

International Journal of Advancements in Research & Technology, Volume 2, Issue 12, December-2013 196 ISSN 2278-7763

Copyright © 2013 SciResPub. IJOART

SPEED CONTROL METHODS FOR FIELD ORIENTED PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE

NASEEB KHATOON 1 & SAJIDA SHAIK 2

(1.Electrical and Electronics Engineering, Nalla Malla Reddy Engineering College, India) &

(2. Electrical and Electronics Engineering, Audishankara Institute of Technology, India) ABSTRACT Model Reference Adaptive Fuzzy Controller for PMSM is proposed in which the system output tracks very closely the reference model even with increasing inertia, augmented stator resistance and load variations. In Model Reference Adaptive Fuzzy Controller, a direct fuzzy logic controller is employed as the main controller and model reference based fuzzy logic controller as the adaptation controller. The application of a PI Controller and Fuzzy Controller for the speed control of field oriented PMSM fed by voltage source inverter under load variations is considered. Then application of a Model Reference Adaptive Fuzzy Speed Controller for the speed control of field oriented PMSM fed by voltage source inverter under increasing inertia, augmented stator resistance and load variations is considered. A simulation analysis of the PI controller, Fuzzy controller and the Adaptive fuzzy controller are done and their speed, torque performances are compared. The adaptive fuzzy controller is better than the fuzzy controller based on the performance parameters considered. The fuzzy controller is better than the PI controller based on the performance parameters considered. Keywords - flc, mraflc, modelling and simulation, pmsm, pi controller.

I. INTRODUCTION

Permanent magnet synchronous motors are becoming very popular in high performance motor drives applications compared to other types of motors. Some of PMSM advantages features including high efficiency, small volume, high power density, fast dynamics, large torque to inertia ratio, and low maintenance costs. Their applications can be found in machine tools, servo and robots, in textile machines, electric vehicle, and ship propulsion [1]. Fast and accurate speed responses, quick recovery of speed from load disturbances and insensitivity to parameter variation are some of the important criteria of high performance drive system. The conventional PI and proportional integral derivative (PID) controllers have been broadly used as speed controllers in PMSM drives. However, the conventional fixed gain PI and PID controllers have difficulties in dealing with dynamic speed tracking, parameter variations and load disturbances. To overcome these drawbacks, various adaptive controllers have been demonstrated. Fuzzy Logic (FL) is used as an alternative for conventional control theory to control nonlinear complex plants where accurate mathematical modeling is difficult. The design of FLC does not require the knowledge of

the mathematical model of the plant. FLC provides a systematic way to incorporate human experience in the system modeling and design of the controller. The use of FLC as a better alternative to PI and PID, to overcome the limitations, However, FLC employ large number of rules which require powerful processors and large memories for implementation. Also, up to date, studies of FLC have not addressed the performance of the controller over a wide speed range (especially at low speeds). In addition, direct FLC cannot adapt themselves to changes in the operating conditions. They can adjust their behavior from one rule to another, but the rules themselves do not change. Therefore in order to get the desired system performance despite changes in the operating conditions, some form of adaptation is required. Model reference adaptive speed control (MRASC) for vector controlled PMSM drive consists of two functional blocks. The first one is direct FLC whose inputs are the error and change of error measured between the actual, motor speed and the desired speed, and its output is the command current (torque command). The second one demonstrates the model reference and fuzzy controller is adaptive scheme. In the proposed system, the output speed of equipment reference model is compared with the actual speed of the motor. The resulted speed error is

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applied to a simple fuzzy controller. The fuzzy output signal is added to the direct FLC output to compensate for any deviations of the motor speed from the reference speed. II VECTOR CONTROL OF PM SYNCHRONOUS MOTOR A. MATHEMATICAL MODEL OF THE PMSM

The electrical equations of the PMSM [2] in the rotor (dq) reference frame are as follows:

Vd = Rs id+Ld d/dt id -𝜔𝑟 R Lq iq

Vq= Rs iq +Lq d/dt iq + 𝜔𝑟 R (Ld id+ 𝐿𝑎𝑓)

Ød = Ld id+𝐿𝑎𝑓 R

Øq = Lq iq

The mechanical equation can be written as:

ddt𝜔𝑟 R = (𝑇𝑒- TL -f r 𝜔𝑟)/J

𝑇𝑒=32𝑃 [Øf iq-( Lq- Ld )id iq ]

B .CURRENT CONTROLLER AND

DECOUPLING COMPENSATION

When a voltage source PWM inverter is used, the stator currents need to be controlled to track the reference currents. The dynamics of the stator currents with stator voltages as input are coupled and nonlinear. However, if the stator voltages commands are given in the form

Vd=ud-u d_comp

Vq=uq-u q_comp

Where

u d_comp = ωr R Lqiq

u q_comp= -𝜔𝑟 R (Ldid+ 𝐿𝑎𝑓 R )

Than the stator currents dynamics reduce to

Vd = Rs id+Ld d/dt id

Vq= Rs iq +Lq d/dt iq

Since the current dynamics are linear and decoupled, PI controllers can be used for current tracking.

u d = k Pid (i d_ref-id)+ kIid ∫ (i d_ref-id)dt

u q = k Piq (i q_ref-iq)+ kIid ∫ (i q_ref-iq)dt

B. VECTOR CONTROL OF THE PMSM

The objective of the vector control [3] of PMSM is to allow the motor to be controlled just like a separately excited DC motor. So, the direct‘d’ axis is aligned with permanent magnet flux linkage phase and the direct current ‘ id’ is forced to be zero. Then can be written as follows

Ød = 𝐿𝑎𝑓 R

Øq = Lq iq

And the electromagnetic torque is

𝑇𝑒=kt iq

kt = 32PØf

D.PULSE WIDTH MODULATED INVERTER

Pulse width modulation (PWM) technique is used to generate the required voltage or current to feed the motor or phase signals. This method is increasingly used for AC drives with the condition that the harmonic current is as small as possible. Generally, the PWM schemes generate the switching position patterns by comparing the three-phase sinusoidal wave forms with a triangular carrier. The inverter model is represented by the relationship between output phase voltages (va, vb, vc) and the control logic signals (S1, S2, S3) as follows:

Phase to negative bus voltage are va0 = igavdc vb0 = igbvdc vc0 = igcvdc Neutral to negative voltage is

vcommon = (va0 + vb0 + vc0)/3

Phase to neutral voltages are

van = va0 − vcommon vbn = vb0 − vcommon vcn = vc0 − vcommon

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Phase to neutral voltages also written as van = 2

3vdc s1 −

13

vdc s2 −13

vdc s3

vbn =23 vdc s1 +

23 vdc s2 −

13 vdc s3

vcn =13 vdc s1 −

13 vdc s2 +

23 vdc s3

i)FORWARD CLARKS TRANSFORMATION:

Rotating 2-phase currents in αβ0 reference frame are

�iαiβi0� = 2

3

⎣⎢⎢⎢⎡1

−12

−12

0 √32

−√32

12

12

12 ⎦⎥⎥⎥⎤�iaibic�

(ii) INVERSE CLARKS TRANSFORMATION:

Rotating 3-phase currents in abc reference frame are

�iaibic� =

⎣⎢⎢⎡

1 0 1−1

2√32

1−12

−√32

1⎦⎥⎥⎤�iαiβi0�

(iii). FORWARD PARKS TRANSFORMATION

Stationary 2-phase currents in dq0 reference frame are

�idiqi0� = �

cos θ sinθ 0−sinθ cosθ 0

0 0 1� �

iαiβi0�

(iv) INVERSE PARKS TRANSFORMATION:

Rotating 2-phase currents in (αβ0) reference frame are

�iαiβi0� = �

cosθ −sinθ 0sinθ cosθ 0

0 0 1� �

idiqi0�

II. PRINCIPLES OF CONTROLLER A) PI CONTROLLER

A PI Controller (proportional-integral

controller) [4] is a special case of the PID controller

in which the derivative (D) of the error is not used.

The main advantage of adding the integral part to the

proportional controller is to eliminate the steady state

error in the controller variable.

The controller output is given

by 𝑘𝑝𝑒(𝑡) + 𝑘𝑖 ∫ 𝑒(𝜏)𝑑(𝜏)𝑡0

Fig.5. Responses of PI Controller for vector control

of PMSM under load

B) FUZZY LOGIC CONTROLLER

i) STRUCTURE OF A FUZZY INFERENCE

SYSTEM

Fig 1. Structure of FIS

ii) FUZZY LOGIC TOOL BOX:

There are five primary GUI tools for

building, editing, and observing fuzzy inference

systems in the Fuzzy Logic Toolbox. The Fuzzy

Inference System [5]or FIS Editor, the membership

Function Editor, the Rule Editor, the Rule Viewer,

and the Surface Viewer..

Fig.2. The Primary GUI Tools of the Fuzzy Logic

Tool box

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. iii) FUZZY LOGIC RULES:

1 If error ‘E’ is negative (N) and change in error ‘de’ is negative (N) then change in output ‘du’ is negative (N).

2 If error ‘E’ is zero (Z) and change in error ‘de’ is negative (N) then change in output ‘du’ is negative (N).

3 If error ‘E’ is positive (P) and change in error ‘de’ is negative (N) then change in output ‘du’ is zero (Z).

4 If error ‘E’ is negative (N) and change in error ‘de’ is zero (Z) then change in output ‘du’ is negative (N).

5 If error ‘E’ is zero (Z) and change in error ‘de’ is zero (Z) then change in output ‘du’ is zero (Z).

6 If error ‘E’ is positive (P) and change in error ‘de’ is zero (Z) then change in output ‘du’ is positive (P).

7 If error ‘E’ is negative (N) and change in error ‘de’ is positive (P) then change in output ‘du’ is zero (Z).

8 If error ‘E’ is zero (Z) and change in error ‘de’ is positive (P) then change in output ‘du’ is positive (P).

9 If error ‘E’ is positive (P) and change in error ‘de’ is positive (P) then change in output ‘du’ is positive (P).

iv) MODEL REFERENCE ADAPTIVE FUZZY LOGIC CONTROLLER

The reference model is used to specify the desired

performance that satisfies design specifications [6, 7].

A fuzzy logic adaptation loop is added in parallel to

the fuzzy control feedback loop. In the nominal case,

the model following is perfect and the fuzzy

controller adaptation loop is idle. When parameters

change, an adaptation signal produced by adaptation

mechanism will be added to the output signal of the

direct speed fuzzy logic controller to preserve the

desired model following control performance [8, 9].

Figure 3 shows a Simulink block diagram of the

proposed hybrid controller for vector control PMSM.

III. SIMULATION RESULTS

The control performance of the proposed scheme

in fig.3 is evaluated by simulation using

Matlab/Simulink software.The parameters of the

PMSM are as follow in table1.

TABLE 1

Stator inductance in

(d,q) frame

Ld=1.4mH, Lq

=2.8mH

Number of poles P 4

Stator resistance Rs 0.6 ohm

Rotor flux Laf 0.12 wb

Moment of inertia J 1.11e-3 kgm2

Friction coefficient f 1.41 e-3 Nm sec/

rad

Electromagnetic torque

Te

10 Nm

Load torque TL 0 to 10 Nm

Stator currents in (d,q)

frame

Id=0,Iq=20A

Rotor speed in rpm 716.56rpm

DC Voltage 300

The robustness is further evaluated by using increasing inertia (3*J), stator resistance augmented +50% and variation load 10Nm. Fig.6 shows the responses of the PMSM flux oriented control with FLC under load variation. Fig.7 Responses of MRAFLC for vector control of PMSM load variation. Fig8 Responses of MRAFLC under abruptly step load variation and increasing inertia 3*J. Fig.9 Responses of MRAFLC under abruptly step load variation, augmented inertia 3*J, and increasing stator resistance +50%

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PERFORMANCE COMPARISON BETWEEN PI, FUZZY AND MRAFLC CONTROLLER

TABLE 2

START UP

LOAD APPLICATION

(0.1sec TL=10 Nm)

CONTROLLER Speed

error

Torque

ripple

percentage

Speed

error

Torque ripple

percentage

Efficiency

THD

PI -37.5

rpm

60% 110 rpm 25% 53.6% 6.55%

FLC -7.4

rpm

50% 55 rpm 15% 68.18% 4.57%

MRAFLC -3.8

rpm

30% 27.5rpm 5% 75% 2.80%

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CONCLUSION

Model reference adaptive speed controller

for vector controlled PMSM drive fed by voltage

source inverter with a Fuzzy signal based adaptation

technique has been presented. In the proposed

system, the correction signal produced by the

adaptation loop is added to the output of the main

Fuzzy controller so that the actual system output is

forced to follow the reference model output.

The performance of the system is evaluated

by simulation studies. The speed adaptive FLC is

insensitive to the system parameter variations. A

comparison between adaptive FLC and direct FLC

and PI controller reveals the superiority of the first

one.

Simulation results obtained have confirmed the efficiency and robustness of the proposed fuzzy adaptive controller for changing load torque compared to direct FLC and PI controller

REFERENCES

[1] Kung,Y.S-Tsai, M.H, Fpga – based speed control, IC for PMSMdrive with adaptive fuzzy IEEE Trans. vol. 22, n°6,pp. 2476-2486,2007.

[2] Meroufel, A, Massoum,A Belabès, B Fuzzy adaptive model following speed control for vector controlled permanent magnet Synchronous Motor, Leonardo Electronic Journal of Practices and Technologies, 7:13 (July-December), 2008, p. 19-33. [3] Yin, T. K: Fuzzy model reference adaptive control, IEEE Trans. On Syst. Man. And Cybernetics, vol.25, No 12, Dec. 1995. [4] Minh, T.C- Hoang, L.H: Model reference adaptive fuzzy controller and fuzzy estimator for high performance induction motor drives, Proc. Of the annual Meeting of the IEEE, Industry ApplicationsSociety California 1996. [5] Pragasan Pillay, R. Krishnan“Modeling of Permanent Magnet Motor Drives”, IEEE Transactions on Industrial Electronics, 1988. [6] Model Reference Adaptive Fuzzy Control of a Permanent-Magnet Synchronous Motor H. Le-Huy P. Viarouge I. Kamwa Dkpartement de G6nie Clectrique Dkpartement de Genie klectrique IREQ Universitk Laval Universitk Laval HydrO-QUkbec. [7] Generalized Theory of Electrical Machines, by Dr.P.S.Bimbhra. [8]Power Electronics by Mohan, undeland, Robbins. [9] Hybrid model reference adaptive fuzzy controller .Nitin J.Patil,2009 IEEE

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FIGURES

Fig.3. Simulink model of MRAFLC for PMSM

Fig.4.Reference profile inputs

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

Time (sec)

Loa

d to

rque

(N

m)

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Fig.5. Responses of PI Controller for vector control of PMSM under load

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-30

-20

-10

0

10

20

30

TIME (SEC)

Ia, I

b Ic

(A)

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Fig.6. Responses of FLC for vector control of PMSM under load

0 0.2 0.4 0.6 0.8 1-30

-20

-10

0

10

20

30

TIME (SEC)

Ia,I

b,Ic

(A

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Fig.7 Responses of MRAFLC for vector control of PMSM load variation

0 0.2 0.4 0.6 0.8 1-30

-20

-10

0

10

20

30

TIME (SEC)

Ia,I

b,I

c (

A)

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Fig.8 Responses of MRAFLC under abruptly step load variation and increasing inertia 3*J

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

10

20

30

40

TIME (SEC)

Ia,Ib

,Ic (

A)

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Fig.9 Responses of MRAFLC under abruptly step load variation, augmented inertia 3*J, and increasing stator resistance +50%

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

10

20

30

40

TIME (SEC)

Ia,I

b,Ic

(A

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speed control methods for field … control methods for field oriented permanent magnet ......

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