ISSN: 2454-1362, A Closed · PDF filefield vector controlled Permanent magnet Synchronous...

Imperial Journal of Interdisciplinary Research (IJIR) Vol-2, Issue-6, 2016 ISSN: 2454-1362, http://www.onlinejournal.in

Imperial Journal of Interdisciplinary Research (IJIR) Page 778

A Closed Loop Speed Control of PMSM

Drive Using Fuzzy Logic Controller

B.V.Lakshma Reddy1, U.Anjaiah

2& T.Srinivasa Rao

3

1PG Student Sch1or, AVANTHI Engineering College, Makavanpalem, Visakhapatnam. 2Assistant Professor,AVANTHI Engineering College,Makavanpalem, Visakhapatnam.

3Associate Professor,AVANTHI Engineering College,Makavanpalem, Visakhapatnam.

Abstract-This paper presents a fuzzy logic

controller (FLC) for speed control of permanent-

magnet synchronous motor (PMSM) drive. With the

approach of the field vector control methods,

PMSM can be operated like separately excited dc

motor in high performance applications. The

difficulties of PI controller tuning and high

response time is overcome by using fuzzy logic

controller, which has small settling time and high

percussion without any mathematical calculations.

The PM synchronous motor has advantages in

contrast with the AC induction motor. Because a

PMSM achieves higher efficiency and regulation by

generating the rotor magnetic flux with rotor

magnets, a PMSM is used in totally enclosed

traction motor, direct drive traction motor and

high-end white goods such as fans and pumps; and

in other appliances. Due to its high performance

and reliability it's creates closed-loop speed

control PM synchronous drive using a field vector

control technique. It fulfill as an example of a PM

Synchronous motor control design using a free

scale hybrid controller with PE support. The

proposed concept can be applied to fuzzy logic

control system in order to improve the stability of

the system by using MATLAB/SIMULATION

software and the results are verified. Keywords- PMSM, vector control, modeling, closed

loop, constant torque angle control, fuzzy logic

controller.

I.INTRODUCTION

Industry automation is mainly expanded around

motion control systems in which controlled electric

motors play a critical part as heart of the system.

Therefore, the high performance and efficiency

motor control systems contribute, to a great extent,

to the desirable performance of modern automated

manufacturing sector by enhancing the production

rate and the quality of products. In fact the

implementation of modern automated systems,

defined in terms of swiftness, accuracy, smoothness

and efficiency. The advancement of control

theories, power electronics and microelectronics in

connection with new motor designs, patterns and

materials has contributed largely to the field of

electric motor control for high performance

systems.

The necessity for energy conservation is also one of

the important motivations in the use of PM

Synchronous machines. Field oriented control of

PM Synchronous motor drive gives better

performance in terms of faster dynamic response

and more efficient operation. Field oriented control

or vector control method gives the performance

characteristics near to that of a dc machine which

are considered desirable in certain applications [1,

2]. For high performance servo drives, Pulse width

modulation current controllers are used to protect

that currents flowing through the PMSM motor

windings are as nearer to the as possible to

sinusoidal references [3]. The implementation of

field vector controlled Permanent magnet

Synchronous motor (PMSM) drive through current

controlled voltage source inverter has been

described in the literature [4]. The inverter sending

power to the PM Synchronous motor is normally

fed from a diode bridge rectifier. The diode bridge

rectifier has internal individual drawbacks such

high power loss which leads to the lower power

factor and it injects the harmonics into the AC

supply system [5]. To overcome these difficulties,

the diode bridge rectifier has been replaced by a

PWM current controlled converter. The current

controlled converter uses the high frequency self-

commutated converter. This provides some specific

benefit like higher power factor (Unity and

leading), low and reduced level of harmonics,

sinusoidal currents (i) and in reality the converter

has the regeneration capacity. However not much

attention has so far been paid to the examine the

real time system, which may lead to a higher

quality ,better understanding and deeper insight in

to the advancement of the Field Oriented

Control(FOC) of PMSM drive along with fuzzy

PID control. This requirement is therefore felt to

convey out the design of the PM Synchronous

motor drive which includes the PID, Fuzzy system

logic speed controller, converter, reference current

generator, Pulse Width Modulation current

controller, inverter and PMSM motor. Fuzzy logic

is recently finding increasing implementations in

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different fields that include management,

economics, and medicine and recent in closed loop

operation of changeable (variable) speed drives.

The objective of the fuzzy logic control is to design

a system with satisfactory performance

characteristics over a wide range of uncertainty [6,

7].

II. MATHEMATICALMODEL OF PMSM

The mathematical model of PMSM is available in

the existing literature [1] and [5] has been

presented in this section to provide a basis for the

succeeding sections. The stator of the PMSM and

the wound rotor synchronous motor are similar.

The permanent magnets used in the PM

Synchronous motor are of a modern rare-earth

variety with high resistivity, so induced currents in

rotor are very small amount so they are negliable.

In addition, there is no dissimilarity between back

EMF developed by a permanent magnet and that

developed by an excited coil are same. Hence the

mathematical model of a PM Synchronous motor is

similar to that of the wound rotor SM. The rotor

reference frame is selected because the position of

the rotor magnets determines the immediate

induced emf and subsequently the stator currents

and torque of the machine independent of the stator

voltages and currents. The following assumptions

are considered in the derivation.

Saturation and parameter changes are

negligible

Stator windings are balanced with the

induced EMF is sinusoidal

Eddy current and hysteresis losses are

negligible or neglected

There are no field current dynamic

There is no cage on the rotor.

The equivalent circuits of PM Synchronous motor

in d, q axes in rotor reference frame are shown in

fig 1 and

Fig 2 respectively.

Fig. 1.Stator q-axis equivalent circuit.

Fig. 2.Stator d-axis equivalent circuit

Based on the above assumptions, the stator voltage

d-q equations of the PM Synchronous motor in the

rotor reference frame is given by equations (1) and

(2)

Vqsr = Rs iqs

r + pℷqsr + ωℷds

r (1)

Vdsr = Rs ids

r + pℷdsr − ωℷqs

r (2)

The stator flux linkages is given by equations (3) to

(5)

ℷqsr = Lq iqs

r (3)

ℷdsr = Ld ids

r + Lm ifr (4)

Lm ifr = ℷaf (5)

𝑉𝑞𝑠𝑟 and 𝑉𝑑𝑠

𝑟 are the d, q axes voltages, 𝑖𝑞𝑠𝑟 and 𝑖𝑑𝑠

𝑟 are

the d, q axes stator currents in rotor reference

frame, 𝐿𝑑and 𝐿𝑞are the d, q axis inductances and

ℷ𝑑andℷ𝑞 are the d, q axis stator flux linkages in

rotor reference frame, 𝐴 = 𝜋𝑟2and 𝜔𝑟 are the stator

resistance and inverter frequency respectively.

ℷ𝑎𝑓 Is the flux linkage due to the rotor magnets

related to the stator. Equations (6) and (7) is

obtained by substituting equations (3) to (5) in (1)

and (2)

Vqsr = Rs iqs

r + p Lq iqsr + ωr(Ld ids

r + ℷaf ) (6)

Vdsr = Rs ids

r + p Ld idsr − wr Lq iqs

r

(7)

Equations (8) and (9) is obtained by rearranging

equations (6) and (7) in matrix form

Vqs

r

Vdsr =

Rs + pLq ωrLd

ωrLq Rs + pLd

iqsr

idsr +

ωrℷaf

0 (8)





The electromagnetic given by the motor is given by

equation (9)

T =3

2

P

2 ℷds

r iqsr − ℷqs

r idsr (9)

The three phase stator voltage equations 𝑉𝑎𝑠 ,𝑉𝑏𝑠 and

𝑉𝑐𝑠 is given by equations (10) to (12)

Vas = Vm sin ωt(10)

Vbs = Vm sin ωt −2π

3 (11)

Vcs = Vm sin ωt −2π

3 (12)

𝑉𝑎𝑠 , 𝑉𝑏𝑠and 𝑉𝑐𝑠 are a-phase, b-phase and c-phase

stator voltages respectively. 𝑉𝑚 Is the maximum

value of the stator voltage.ω is the synchronous

speed or velocity in rad/sec. The stator voltages in

the „abc‟ axes𝑉𝑎𝑏𝑐 is transferred to the d, q axes

𝑉𝑞𝑑0by park‟s transformation.

The transformation matrix 𝐾𝑠 is given the by

equation

Ks =2

3

cos θ cos(θ −

2π

3) cos(θ +

2π

3)

sin θ sin(θ −2π

3) sin(θ +

2π

3)

1

2

1

2

1

2

(13)

Vqs

Vds

V0s

=

2

3

cos θ cos(θ −

2π

3) cos(θ +

2π

3)

sin θ sin(θ −2π

3) sin(θ +

2π

3)

1

2

1

2

1

2

Vas

Vbs

Vcs

(14)

III. CLOSED LOOP SPEED CONTROL OF

PMSM

A. Vector Control scheme for closed loop PMSM

drive: The Schematic scheme of the closed loop speed

control system for PMSM Drive is shown in Fig. 3.

The constant torque method of vector control

scheme has been examined for analysis. In this

method, the angle between the rotor field and stator

current phasor is called as a torque angle and is

maintained at900so that flux is kept constant, then

the torque is controlled by the stator current (is)

magnitude [1]. The machine, speed and position

feedback, speed and current controllers, and

inverter constitute the PM Synchronous motor

drive. The error in between the reference and actual

speed is given the input to the speed controller,

which creates the torque reference and is

proportional toKt,𝑖𝑞 by substituting 𝑖𝑑=0, equation

(25) and (26) is obtained

T = Ktiqse (15)

Kt =3

2

P

2ℷaf (16)

The stator current 𝑖𝑞𝑑𝑜 in the d, q axes is transferred

to the „abc‟ axes by use of the Inverse Park‟s

transformation given by equation (17)

iabcs = KS−1iqd 0s (17)

Ks−1 =

2

3

cos θ sin θ

1

2

cos(θ −2π

3) sin(θ −

2π

3)

1

2

cos(θ +2π

3) sin(θ +

2π

3)

1

2

(18)

The reference current𝑖𝑎𝑠 ,𝑖𝑏𝑠 and 𝑖𝑐𝑠 are created or

generated by substituting equation (28) in equation

(27) In the constant air gap flux method of

operation,𝐾𝑡 is constant up to base speed and is

equivalent to unity. Hence, the torque reference is

directly proportionate to 𝑖𝑞 , which is transformed to

„abc‟ axes by use of the Inverse Park‟s

transformation given by equations (27). The „dq0 to

abc‟ conversion block shown in Fig. 3 gives the

stator reference current 𝑖𝑎 ,𝑖𝑏 and 𝑖𝑐 in „abc‟ axes

which is compare with the real or actual current (i)

and the current error is given to a hysteresis

controller. The triggering pulses are generated by

the hysteresis current controller which is given to

the inverter in such a way that the actual current

follows the reference current.

Fig. 3.Block Diagram of Closed Loop Speed Control of PMSM.

IV.FUZZY LOGIC CONTROL

L. A. Zadehsubmits the first paper on fuzzy set

theory in 1965. Since then, a new language was

developed to describe the fuzzy logic properties of

reality, which are very inconvenient and sometime

even impossible to be described using conventional

methods. Fuzzy set theory has been commonly

used in the control area with some application to

power system [5]. A simple fuzzy logic control

theory is built up by a group of systematic rules

based on the human knowledge of system behavior.

Matlab/Simulink simulation model is constructed

to study the dynamic behavior of converter.

Furthermore, design of fuzzy logic controller can

provide advantageous both small signal and large





signal dynamic performance at same time, which is

not feasible with linear control technique. Thus,

fuzzy controller has been potential ability to

improve the robustness of compensator.

The basic scheme of a fuzzy logic controller is

shown in Fig 4 and consists of four principal

components such as: a fuzzy fication connection or

interface, which converts input data into suitable

linguistic values; a knowledge base, which

composed of a data base with the required

linguistic definitions and the control rule set; a

decision taking logic which, simulating a human

decision procedure, infer the fuzzy control action

from the knowledge of the control logic rules and

linguistic changeable definitions; a de-fuzzification

interface which yields non fuzzy logic control

action from an .

Fig.4.Block diagram of the Fuzzy Logic Controller (FLC)

For Proposed Converter.

Fig.5. Membership functions for Input, Change in input, Output.

Rule Base: the elements of this rule base table are

finding based on the theory that in the transient

state, large errors require coarse control, which

need coarse in-put/output variables; in the steady

state, small errors need fine control, which needs a

fine input/output variables. Based on this the

elements of the rule table are obtained as shown in

Table 1, with „𝑉𝑑𝑐 ‟ and „𝑉(𝑑𝑐−𝑟𝑒𝑓 )‟ as inputs.

V. SIMULATION RESULTS

For consistent speed operation, the reference speed

is set as 3000 rpm and the load torque varied from

0.6N-m to 0.8N-m at 0.25sec. Figure 6 and figure

17 shows the circuit simulation models of the

physical model and the developed (mathematical)

model respectively which comprise, speed and

torque response along with rotor position angle.

Fig. 7 and 18 shows the starting current response of

the physical simulation system model and

developed simulation model respectively, which

has oscillations or vibrations during starting but

attains steady state within negligible time. For

constant torque operation the load torque is kept at

0.8 Nm and the reference speed is varied from

1500rpm to 3000rpm at 0.25sec.The simulation

results of the developed simulation model is

compared with the mat lab/simulink model of the

system. The simulation circuits are designed using

the fuzzy logic controller which can have the lower

settling time than the PI controller. When compare

the simulation results of both the controllers‟ fuzzy

system having the lower settling time than the Pi

controller. The simulation results of the physical

simulation system model and the developed

simulation model is shown in fig 6 and fig 17

respectively. Fig.16 and fig 27 shows the stator

current response of the physical model and the

developed simulation model respectively. It can be

notice the stator current frequency increased for a

increased reference speed. Since it is a constant

torque operation method, the current magnitude

remains constant for the entire duration. It can be

observed from, the simulation results of the

developed system simulation model and the circuit

simulation model well coincides with each other,

which shows the exactness of the developed model,

but the computation time of the developed

simulation model is normally very smaller when

compared to the circuit simulation done by any

simulation software‟s.

Case-1: Circuit Simulation Model of PMSM

using





Matlabsimulink with Fuzzy Controller

Fig.6 Circuit Simulation Model of PMSM using matlab /

simulink with Fuzzy Controller

(I)Simulation results for Constant speed

variable

Torque

Fig.7 Simulation Waveform of Constant Speed.

Fig.8 Simulation Waveform of Load Torque.

Fig.9 Simulation Waveform of Electromagnetic Torque.

Fig.10 Simulation Waveform of Rotor Angle.

Fig.11 Simulation Waveform of Stator Current.

(II) Simulation results for Constant torque

VariableSpeed

Fig.12 Simulation Waveform of Variable Speed

Fig.13. Simulation Waveform of Constant Load Torque

Fig.14. Simulation Waveform of Electromagnetic Torque

Fig.15. Simulation Waveform of Rotor Angle





Fig.16. Simulation Waveform of stator Current

Case-2:Circuit Simulation Model of

PMSM usingMathematical Model with

Fuzzy Controller

Fig.17 Circuit Simulation Model of PMSM using Mathematical

Model with Fuzzy Controller

(I) Simulation results for Constant speed

variable

Torque

Fig.18. Simulation Waveform of Constant Speed

Fig.19. Simulation Waveform of Load Torque

Fig.20. Simulation Waveform of Electromagnetic

Torque

Fig.21. Simulation Waveform of Rotor Angle

Fig.22. Simulation Waveform Stator Current

(II) Simulation results for Constant torque

Variable Speed

Fig.23 Simulation Waveform of Variable Speed

Fig.24. Simulation Waveform of Constant Load Torque




Imperial Journal of Interdisciplinary Research (IJIR) 84

Fig.25. Simulation Waveform of Electromagnetic Torque.

Fig.26. Simulation Waveform of Rotor Angle.

Fig.27. Simulation Waveform of Stator Current.

VI .CONCLUSION

An advanced simulation model of closed loop PM

Synchronous Motor drive system has been

developed by utilizing the mathematical model of

PM Synchronous Motor and hysteresis current

controlled three phase VSI inverter. The developed

simulation system model has been verified by

circuit simulation model of the similar scheme

which shows the accuracy of the developed model.

It has been observed that the torque and the stator

flux ripples are significantly reduced and a constant

switching frequency is achieved in fuzzy controller.

Other improvements observed in fuzzy controller

are the reduction in phase current distortion, fast

torque response and increase in efficiency of the

drive. This developed model can be well utilized in

the design and development of closed loop PM

synchronous motor drives system for

experimenting with different control algorithms

and topological differences but with a much

reduced computational time and memory size

REFERENCES

[1] R. Krishnan, “Permanent Magnet Synchronous and

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[2] PragasanPillay, R.Krishnan, “Modeling Simulation

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Part-I: The Permanent-MagnetSynchronus Motor

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[3] Paul C.Krause, Oleg Wasynczuk, Scott D.Sundhoff,

“Analysis of Electric Machinery and Drive

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[4] Byounk-Kuklee, MehrdadEhsani, “Advanced

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[5] H, MadadiKojabad, G.Ahrabian, “Simulation and

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[9] Sung Yu J., Mo Hwang S., Yuen Won C.,

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