Fuzzy Adaptive PI Controller for Direct Torque Control Algorithm Based Permanent Magnet Synchronous Motor

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459,ISO 9001:2008 Certified Journal, Volume 3, Issue 5, May 2013)

570

Fuzzy Adaptive PI Controller for Direct Torque Control

Algorithm Based Permanent Magnet Synchronous Motor

R.Senthil Rama

1

, P.Latha

2 1

Assistant professor ,Udaya school of Engineering, Vellamodi, India

2_{Associative professor,Government College of Engineering, Tirunelveli, India}

Abstract—This paper proposes to describe a hybrid model

of Direct Torque Control and Space Vector Modulation Technique, which reduces the various ripples in the traditional DTC for the Permanent Magnet Synchronous Motor and make it easier to improve the performance of the drive. The fuzzy adaptive PI controller is used to adjust the different static error constants, as per the speed error. The improvement of the speed response, overshoot and speed steady precision is shown by a comparative study between conventional and fuzzy PI direct torque control approach. This technique displays a very strong robustness against parameter variation. The effectiveness and validity of the proposed control approach is verified by simulation results.

Keywords—Direct Torque Control (DTC), Fuzzy Logic

Controller (FLC), PMSM, Space Vector Modulation (SVM), THD.

I. INTRODUCTION

DIRECT TORQUE CONTROL (DTC) offers

advantages such as simplicity , accurate torque control ,

faster torque response, no need to co-ordinate

transformation, absence of current loop, elimination of voltage modulation blocks and robustness [1]-[3]. Direct torque and flux control or direct self control was introduced for voltage fed PWM inverter drives. The scheme, as the name indicates, is the direct control of the torque and stator flux of a drive by inverter voltage [4].Space vector selection through a lookup table. Space vector modulation (SVM) is an algorithm for the control of pulse width modulation PWM. It is used for the creation of alternating current waveforms.

Permanent magnet Synchronous motors are widely used in high performance drives due to some advantages like: more simplicity, low dependency on the motor parameters, good dynamic response high torque/inertia [2]. A permanent magnet motor can be fed by either rectangular current or sinusoidal current. The sinusoidal current fed motor is discussed here, which have distributed winding on the stator, provide smoother torque and are normally used in high power devices.

Some of the drawbacks in DTC with PMSM can be overcome by a variety of techniques and this paper proposes these techniques.

The Field Oriented control is a very widely used drive strategy for PMSM. FOC also has some disadvantages like high dependence on motor parameters. New control strategies, by name DTC and Direct Self Control (DSC) are developed, to reduce the above said disadvantages. The basic idea of DTC for PMSM remains to be the control of torque and flux linkage by the proper selection of voltage space vectors and the later is based on the relationship between the slip frequency and torque. This minimizes the ripples of the electro-magnetic torque and flux linkages and fixes the variable switching frequency produced in the conventional DTC system for the servo drive.

Compared with the FOC, the major drawback of the DTC method is the large ripples of torque and flux linkage. The switching state of the inverter is updated only once in every sampling interval. The inverter keeps the same state, resulting in relatively large torque and flux ripple [10]-[12]. Space vector modulated direct torque control preserve transient and steady state merits, furthermore, it produce good quality steady state operating performance in a wide range, SVM technique is used to achieve the voltage space vector reference at each cycle period, to exactly compensate the errors due to flux and torque angle. The DTC – SVM torque ripple in low speed can be improved significantly [6]-[9].

The introduction of fuzzy concept adjusts the real time parameters of Kp and Ki, through fuzzy inference mechanism. According to electro-magnetic torque, stator flux linkages error and flux angle, a method that fuzzy controller selecting the proper voltage vectors, controls the system.

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International Journal of Emerging Technology and Advanced Engineering

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II. MODELLING OF PMSM

The voltage equations that describe the performance of induction and synchronous machines. The co-efficient of the differential equations that describe the behavior of these machines are time varying except when the rotor is stalled. A change of variable is often used to reduce the complexity of these differential equations. This general transformation refers machine variables to a frame of reference that rotates at an arbitrary angular velocity. Real transformations are obtained from this transformation by simply assigning the speed of the rotation of the reference frame.

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(2)

With the field equation as

(3)

(4)

Substitution of (2) in to (1) it becomes

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(6)

The electro-magnetic torque is given by

P

(

)

(7)

(8)

Here is stator resistance,

are the stator d and q

axis inductances, B- Viscous friction co efficient, J- rotor

moment of inertia, permanent magnet flux,

motor speed,

are the d-q axis

currents, , are the d-q axis voltages,

-electro-magnetic torque, -load torque

The torque expression can be expression can be expressed in the vector form as

̅

(

)

̅̅̅

̅

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Where

̅

and

̅

In this equation,

̅

is to be replaced by rotor flux

̅̅̅

. In

the complex form,

̅

and

̅̅̅

can be expressed as functions

of currents as

̅

_̅

̅

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̅

_̅

̅

₍₁₁₎

In DTC, the optimum voltage space vector for the entire switching period controls the torque and flux independently and the hysteresis band maintains the errors. Only one vector is applied for the entire sampling period, in the conventional method. So, for small errors, the upper or lower torque limit may be exceeded by the motor torque. Instead, the torque ripple can be reduced by using more than one vector within the sampling period. The insertion of zero vector precisely controls the slip frequency [8]. For a smaller hysteresis band, the frequency of operation of the PWM inverter could be very high. The width of the hysteresis band causes variation in the switching frequency. Direct torque control based on space vector modulation preserve DTC transient merits, furthermore, produce better quality steady state performance in a wide speed range. At each cycle period, SVM technique is used to obtain the reference voltage space vector to exactly compensate the flux and torque errors. The torque ripple of DTC-SVM in low speed can be significantly improved.

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III. DTC-SVMCONTROL STRATEGY

In conventional DTC, a single stator voltage vector of the inverter standard topology is selected during every control sampling period, and it is maintained constant for the whole period. By this switching technique, based on hysteresis, large and small torque is not differentiated, which causes an extra torque ripple in motor steady state operation.

In the proposed control scheme, a reference stator voltage space vector is calculated. This is done in each sampling period by properly selecting the switch states of the inverter and the calculation of the appropriate time period for each state. The coordinate transformation from the a-b-c axis to the x-y axis as given by

(

)

=

(

√ √

) (

)

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Which can also be written as

(

)]

√

₍

₎

The space vector representation as

( )

₍₁₃₎

Which is a vector of magnitude rotating at a constant

speed in

radian per second. Using the three phase to two

phase transformation in

( )

and the line voltage as the

reference, the α-β components of the rms output voltage

can be expressed as the functions of

(

)

√

(

√ √

) (

)

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If the output voltages are purely sinusoidal, then the

performance vector U becomes =

Where is the modulation index(0<

)

for

controlling the amplitude of the output voltage and is the

output frequency in radian per second

IV. FUZZY DIRECT TORQUE CONTROL

Initially each machine is operating with zero input torque with the excitation held fixed at the value that gives rated open-circuit terminal voltage at synchronous speed. The rotor speed begins to increase immediately following the step increase in input torque, whereupon the rotor angle increases. The rotor speed up until the accelerating torque on the rotor is zero.

The rotor angle is the displacement of the rotor generally referenced to the maximum positive value of the fundamental components of the terminal voltage of phase a. Therefore, the rotor angle expressed in radians is

Even though the accelerating torque is zero at this time,

the rotor is running above synchronous speed, hence and

thus Te will continue to increase. The increase in Te, which is an increase in the power output of the machine cause the rotor to decelerate towards synchronous speed. However, when synchronous speed is reached, the magnitude of rotor angle has become larger than necessary to satisfy the input torque.

Note that at first synchronous speed crossing of after

the change in input torque is approximately 42 electrical

degrees and Te is approximately 47 x 106 N-m. Hence, the

rotor continues to decelerate below synchronous speed and consequently load angle begins to decrease, which in turn decreases Te. Damped oscillations of the machine variable continue, and a new steady state operating point is finally attained.

During start up, high torque ripple and slow transient response to the step changes in torque are the common disadvantages of conventional DTC. The improvement of torque performance can be brought out by the development of several techniques. Figure 1 shows the block diagram of the proposed system of direct torque fuzzy control. Here, the flux linkages and torque hysteresis controllers are replaced by fuzzy controllers.

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V. SIMULATION RESULTS AND DISCUSSION

The quality of an inverter is normally evaluated in terms of the performance parameters like harmonic factor, Total harmonic distortion (THD), distortion factor and lowest order harmonic. THD gives the total harmonic content, but it does not indicate the level of each harmonic component.

A simulation work has been carried out on a permanent magnet synchronous motor, to show the effectiveness of the fuzzy DTC method. The proposed scheme is simulated with Matlab /Simulink

Fig.2. Speed and torque response curve of conventional DTC

Fig.3. Speed and Torque response curve of fuzzy-DTC-SVM

Fig.4. Comparison of Fuzzy control with reference

The behavior of the PMSM with conventional and fuzzy method are illustrated in fig.2 and fig.3. The motor operate at a speed of 800 rad/sec. By comparing the two figures, the torque ripple is reduced nearly 80 % by using the proposed method. Similarly the THD is also reduced to a considerable amount.

The torque and speed response for conventional DTC is shown in the fig.3. Here the torque response has more distortion and it settled down at around 0.027sec and the speed response is at 0.022sec. And the result of Fuzzy DTC-SVM control method is shown in fig.3. Here the torque response has lesser distortion and it settled down at 0.012sec and the speed response is at 0.013sec.The THD is 31.08%. The settling time is reduced by approximately 50%.The simulation results show that the proposed DTC has less torque ripple, and reduced THD while maintaining a good torque response s compared to the normal DTC method.

VI. CONCLUSION

In this control method, fuzzy adaptive PI controller scheme has been developed for the permanent magnet drive system. here, a SVPWM inverter is used to feed the motor, the stator flux and torque errors are fully compensated by the obtained stator voltage vector. The stator flux amplitude and the electro-magnetic torque errors, through the fuzzy logic controller, are used by the proposed method to generate a voltage space vector by acting on both the amplitude and the angle of its components, which is used by a space vector modulation to provide the inverter switching states. The torque ripple is smaller than that of the conventional DTC. Comparisons through simulations with conventional DTC have been carried out.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -100 0 100 200 300 400 500 600 700 800 900 Time (sec) S pe ed (r ad /s ) PI

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -15 -10 -5 0 5 10 15 20 25 30 35 Time (sec) Te (N .m ) PI

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -100 0 100 200 300 400 500 600 700 800 900 Time (sec) Sp ee d (ra d/ s) Fuzzy

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -10 -5 0 5 10 15 20 25 30 35 Time (sec) Te (N .m ) Fuzzy

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

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The results show that the torque and flux ripples are drastically reduced by the proposed DTC, while still one of the main characteristics of the performance of DTC method have a good dynamic torque response .

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