Speed Control of Matrix Converter Based Pmsm Drive System

Speed Control of Matrix Converter Based Pmsm Drive System

AbstractThis project presents speed control of matrix converter based PMSM drive system. The speed of PMSM drive system can be controlled by using fuzzy logic controller, the speed of PMSM varies by changing the load which creates a drop in voltage. The matrix converter which compensates the drop and given to the PMSM. The simulations are carried out in the MATLAB Environment.

Keywords Matrix converter, fuzzy logic control, permanent magnet synchronous motor.

1. INTRODUCTION

   The permanent magnet synchronous motors are becoming more popular nowadays compared to other ac motors. The advantages of PMSM including high torque, high efficiency, high power and low noise. The high performance drive systems used for drive PMSM in robotics and many other applications. The conventional PI controllers and proportional integral derivative controllers have been widely utilized as speed controllers in PMSM drive systems. For good results d- q axis reactance parameters of the PMSM should be known exactly, but it is difficult and conventional fixed gain PI and PID controllers are very sensitive to the step change and load disturbance [3]. To overcome this problem other speed controller has been adopted.

   This paper describes the Rejection of Voltage Disturbance for Matrix Converter Using Fuzzy Based PMSM Drive System. The Matrix converter is a device used to convert the voltages ac to ac directly. The main advantage of matrix converter is, it does not have any storage element. Here fuzzy logic control is utilized for the speed control process to obtain the good results.

   Fig.1. General Block Diagram of Fuzzy Based PMSM Drive System.

   The output current of matrix converter is transformed from abc to dq(Park Transformation and vice versa. Here id is taken as 0 because Flux is zero. And iq can be taken as

   torque. The output current of matrix converter is 7.2 A. by varying the load of PMSM the speed varies, the matrix converter which compensates the drop and given to the motor.

   A. Mathematical Modeling of PMSM

   In d-q reference frame, the nonlinear differential equations:

2. PERMANENT MAGNET SYNCHRONOUS

   P

   3

   3

   T

   T

   e =

   m .iq (Ld Lq ).id .iq (1)

   MOTOR

   The Permanent Magnet Synchronous motor is a rotating electric machine where the stator is a classic three-phase stator like that of an induction motor and the rotor has permanent magnets.The use of a permanent magnet to generate a substantial air gap magnetic flux makes it possible to design highly efficient PM motors.

   Fig 1 shows the block diagram of fuzzy based PMSM drive system where the matrix converter which converts the AC to AC voltage directly where the input voltage is 230 V.

   2 2

   d (id ) vd rs .id r .Lq .iq

   dt Ld

   d (iq ) vq rs .iq r (Ld .id m )

   dt Lq

   d (rm ) Te TL Brm dt J

   P

   (2)

   (3)

   (4)

   (5)

   The matrix converter converts 230 V to 170 V.

   r 2 rm

   d

   (6)

   1. Operation and Control of the Matrix Converter

      r dt

      The voltages van , vbn , vcn at the output terminals are

      TL is the load torque, B is the viscous friction, J is the

      related to the input voltages vAo , vBo , vCo

      by the

      moment of inertia, vd

      and

      vq represents d-q axes stator

      equation.

      voltages,

      id and iq

      is the d-q axes stator currents,

      Ld and

      van

      SAa

      SBa

      SCa vAo

      v S S S

      i

      Lq are the d-q axes inductances, r represents electrical

      bn

      Ab Bb Cb Bo

      velocity of the rotor, is the flux linkage due to rotor

      vcn

      SAc SBc SCc iCo

      m

      magnets linking the stator, Te is the motor torque, rm is the

      mechanical velocity of the rotor, rs is the per phase resistance.

      (9)

      The input phase currents are related to the output phase currents by the equation

      iA SAa

      SAb

      SAc ia

      Here the output voltage of matrix converter is 170 V

      i S S S

      i

      (10)

      and output current is transformed from abc to dq.

      B

      Ba Bb Bc b

      iC

      SCa

      SCb

      SCc ic

      iq

      cos

      cos( 120) cos( 120) ia

      i 2 sin sin( 120) sin( 120) i

      (7)

   2. Switching States of Matrix Converter

      d 3 b

      Three phase voltages can be divided into six areas

      i0

      1 1 1

      ic

      2 2 2

      And again dq to abc transformation takes place.

      according to their instantaneous magnitudes, which are called input voltage areas. In each area, there are eight input current

      modes Ka , Kb , Kc .

      ia

      cos

      sin

      1 iq

      1, switch SKj closed

      i 2 cos( 120) sin( 120) 1 i

      (8)

      SKj (t) =

      (11)

      b 3 d

      0, switch SKj open

      i cos( 120) sin( 120) 1 i

      c 0

3. MATRIX CONVERTER

   It consist of nine bidirectional switches which needs commutation to minimize the losses and to produce desired output voltage with high quality input and output waveforms.

   The output side quantities of matrix converter are transformed into a direct and quadrature reference frame rotating at the electrical angular speed of the PMSM rotor with the d-axis aligned with the rotor flux vector.

   Fig.2. Matrix Converter Containing Nine Bidirectional Switches

   where K { A,B,C } , j ={a,b,c} and SKa +SKb +SKc =1 The equations which represents the switching states of matrix converter. The output current of matrix converter is 7.2 A.

   TABLE I. SIMULATION PARAMETER RATINGS OF MATRIX CONVERTER

   Simulation Block	System Block	Parameter value
   Matrix converter	LC filter L-Inductance	20e-3 H 1000e-6 F
   	C-capacitance
   	Bidirectional Switch
   	Internal resistance	1e-3
   	Snubber resistance	1e5

4. FUZZY LOGIC CONTROL

   Fig.3. Fuzzy Logic Control

   A matrix converter-based permanent magnet synchronous machine (PMSM) with fuzzy logic drive system to overcome the unflavored impact introduced by digital lter and guarantees the drive performance under input disturbance conditions.

   Three fundamental operations charactering a fuzzy system are

   1. Fuzzification of input crisp values.

   2. Fuzzy inference.

   3. Defuzzification of fuzzy output.

      Fuzzification is a process of transforming crisp values into grades of membership for linguistic terms of fuzzy sets. Here change of error ce (k) and Error e(k) can be taken as tw input variables to the fuzzy controller

      Where Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM) , Positive Big (PB).

5. SIMULATION AND ITS RESULTS

   The matrix converter input voltage is 230 V, which converts ac to ac voltage, the output voltage is 170 V. Under loading condition the speed of PMSM varies which creates a drop in voltage. The matrix converter which compensates the drop and given to the PMSM.

   The main advantage of matrix converter is to compensate the drop and to maintain the speed of PMSM.

   e (k) = r(k) – r (k)

   (12)

   ce(k) = e(k) – e(k-1) (13)

   Where r (k) is the actual speed and r (k) is the Reference speed

   Fig.4. FLC control process

   e(k) and e(k) are converted fuzzy variables E(k) and CE(k) by using the membership function

   E (k) = G1*e (k)

   CE (k) = G2*ce (k) U (k) = G3*u (k)

   (14)

   (15)

   (16)

   Fig.5. Simulation Block Diagram of Fuzzy Based PMSM Drive System

   1. Under Rated Load Condition

   Inference and Rule-Base is explained using IF-THEN rule statement between input and output functions. Mamdani method is used for FIS.

   Defuzzification is used to calculate the crisp value, Centroid Method is used in Defuzzification. The crisp value obtained is U(k).

   The output voltage of Matrix converter (170 V) with respect to Input voltage 220 V and the frequency is 50 hz. The peak voltage is constant 170 V .

   The output of fuzzy logic controller is

   calculated

   by integrating u(k) as in equation

   iqref which is

   iqref (k) = iqref (k-1) + u(k) (17)

   TABLE II. MEMBERSHIP FUNCTION TABLE

   	Error e
   Change of error ce		NB	NS	NS	Z	PS	PM	PB
   	NB	NB	NB	NB	NB	NM	NS	Z
   	NM	NB	NB	NB	NM	NS	Z	PS
   	NS	NB	NB	NM	NS	Z	PS	PM
   	Z	NB	NM	NS	Z	PS	PM	PB
   	PS	NM	NS	Z	PS	PM	PB	PB
   	PM	NS	Z	PS	PM	PB	PB	PB
   	PB	Z	PS	PM	PB	PB	PB	PB

   	Error e
   Change of error ce		NB	NS	NS	Z	PS	PM	PB
   	NB	NB	NB	NB	NB	NM	NS	Z
   	NM	NB	NB	NB	NM	NS	Z	PS
   	NS	NB	NB	NM	NS	Z	PS	PM
   	Z	NB	NM	NS	Z	PS	PM	PB
   	PS	NM	NS	Z	PS	PM	PB	PB
   	PM	NS	Z	PS	PM	PB	PB	PB
   	PB	Z	PS	PM	PB	PB	PB	PB

   Fig. 6 Matrix Converter Output Three Phase Voltage.

   The output current of Matrix converter (7.2 A) with respect to Input voltage 220 V and the frequency is 50 hz . The peak current is 7.2 A which is constant.

   Fig. 7 Matrix converter output current

   The graph shows the output speed of PMSM by using fuzzy logic control is 1258 rpm. The settling time for the speed of 1258 rpm is 0.3

   Fig. 8 Permanent Magnet Synchronous Motor Speed

   The graph shows the output Torque of PMSM here for using fuzzy logic control we get the constant torque of -1 Nm. The Settling time for the torque is 0.32 sec .

   Fig.9 Torque Graph for Permanent Magnet Synchronous Motor

   Fig.10. Id and Iq After Comparing to the Reference Current.

   TABLE III. SIMULATION RESULTS OF PMSM DRIVE SYSTEM

   Parameters	Obtained Results
   Speed Voltage Current	1258 rpm 170 V 7.24 A
   Id Iq	1.22 A 7.75 A

   TABLE IV. SIMULATION PARAMETERS OF MATRIX CONVERTER BASED PMSM DRIVE SYSTEM

   Simulation Block	System Block	Parameter value
   PMSM	Stator phase resistance Armature inductance Frequency Inertia pole pairs	1.66 0.02875 H 50 Hz 0.0001051Kgm2 2
   Membership	NB	-1.8 to -0.2
   values	NM	-0.8 to 0.8
   	NS	0.2 to 1.6
   	Z	-1.667to -0.3334
   	PS	-1 to 0.3334
   	PM	-03334 to 1
   	PB	0.3334 to 1.666

   By increasing the load the speed of the PMSM varies with respect to the load, the advantage of the matrix converter is to compensate the voltage and current drop and given to the

   The graph shows the

   Id and

   Iq current after comparing to the

   motor.

   reference current.

   Id =1.2 A and

   Iq =7.7 A. The output

6. CONCLUSION

   waveform is sinusoidal. The settling time is 0.3 sec, after the settling the current is constant.

   This project presents speed control of matrix converter fed PMSM drive system. The speed of PMSM can be controlled by using fuzzy logic controller, the speed of PMSM varies by increasing the load which creates the drop in voltage and current of matrix converter. The matrix converter which compensates the drop and given to the PMSM. The simulation results proven that the speed of PMSM can be controlled by using matrix converter based fuzzy logic control.

7. REFERENCES

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2. Ruzlaini Ghoni, Ahmed N. Abdalla, Analysis And Mathematical Modelling Of Space Vector Modulated Direct Controlled Matrix Converter, Journal of Theoretical and Applied Information Technology.

3. Rahman, M. A., Hoque, M. A., 1997. On-line self-tuning ANN based speed control of a PM DC motor. IEEE/ASME Trans. On Mechatronics 2 (3), pp.169-178

4. Changliang Xia , Yan Yan, Peng Song, and Tingna Shi, Voltage Disturbance Rejection for Matrix Converter-Based PMSM Drive System Using Internal Model Control, IEEE transactins on industrial electronics, vol. 59, no. 1, January2012.

5. Bhagyashree Shikkewal & Vaishali Nandanwar, Fuzzy Logic Controller for PMSM, Vol-1, Iss-3, 2012.

6. Sharon D. Ronald, A. Sheela, S. Josephin Mary , Three Phase to Three Phase Direct Matrix Converter using SPWM Technique, Volume-3, Issue-2, May 2013.

7. Sneha Bhavsar, Dr.Hina Chandwani, Topological Advancements in Matrix Converter Technology, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, Issue 12, December 2013.

8. Radim Farana, Bogdan Walek, Fuzzy-Logic Control in Fast Technological Processes, 2014 IEEE.

9. Eisa Bashier M. Tayeb and A. Taifour Ali, Comparison of some Classical PID and Fuzzy Logic Controllers, International Journal of Scientific & Engineering Research, Volume 3, Issue 9, September-2012

10. Praveen Kumar, Anurag Singh Tomer, Modeling & Simulation of PMSM Drives with Fuzzy Logic Controller, International Journal of Modern Engineering Research Vol. 3, Issue. 4, Jul – Aug. 2013.