The Analysis and the Simulation of the SVM used for the Control of PMSM Machine with Fuzzy Logic Controller

The Analysis and the Simulation of the SVM used for the Control of PMSM Machine with Fuzzy Logic Controller

Chteoui Henchir Anis Sakly Med faouzi Mimouni Research Unit: ESIER of the National School of Engineers of Monastir, Tunisia

Abstract The Permanent Magnet Synchronous Motor (PMSM) has been widely used in the low to medium power system due to its characteristics of high efficiency, high torque to inertia ratio, high reliability and fast dynamic performance. With the advent of the vector control methods, permanent magnet synchronous motor can be operated like separately excited dc motor high performance application. The complexity of PI controller tuning and high response time is overcome by Fuzzy controller. Which has less response time and high accuracy without any mathematical calculation .This paper presents a simulation of speed control system on fuzzy logic approach for an indirect vector controlled permanent magnet synchronous machine drive by applying space vector modulation. The design, analysis and simulation of the proposed system is done using MATLAB\ SIMULINK

Index Terms Permanent magnet synchronous motor (PMSM), Fuzzy Logic Controller (FLC), Space Vector Modulation SVM.

1. INTRODUCTION

   Permanent magnets Synchronous machines are used as actuators in automated industries where they replace the DC motors because they have many advantages. In fact, they have better performance than DC motors in terms of torque mass and it dont have mechanical commutates (collector) which causes problems of maintenance and cant conduct in severe environments

   However, the DC motor is more used because it is powered by

   very quickly, and its a fact which allows the using of a complex strategy to control the PMSM motor [2].

   the methods used for controlling the speed of the synchronous machine is the method of vector control, using the SVM (Space Vector Modulation) strategy, a method which was described in [1].

   A solution of control which is proposed in the literature is a fuzzy logic control to provide a better performance for the PMSM in spite of the parametric variations [1].

   This paper presents

   The analysis and the simulation of SVM generator, an essential subsystem in the technique of space vector modulation.

   The results of simulation of the vector control based on two types of a speed controller: the PI controller for the tow currents (id,iq) and the fuzzy logic controller for the speed.

2. THE MODELING OF THE PERMANENT MAGNET SYNCHRONOUS MACHINE

   To obtain a simpler formulation and reduce the complexity of the machine model, the establishment of its mathematical model will be developed based on simplistic to say that the machine is symmetric assumptions, is operating in the saturated regime and the various losses and the effect of damping is negligible.

   The Park model of the synchronous machine with permanent magnet pole pairs P is defined by the following system of equations:

   a simple converter (rectifier or inverter) and the regulation of the currents armature can control the torque. For the PMSM, the functioning of the collector is ensured by an electronic circuit composed by a power inverter, a position sensor and a current regulatory control the torque. The progress of power electronics as well as the development

   Vsd Rsisd

   Vsq Rsisq

   L i

   dd dt dq

   dt

   rq

   • rd

     (1)

     of control techniques have made possible now to implement a control structure much more advanced.

     The PWM modern inverters in the electric drives with synchronous motors often use microprocessors, digital signal

     q q sq

     d L d isd r

     The mechanical equation is:

     (2)

     processors or ASIC (Application Specific Integrated Circuits) to generate the waveforms in real time. The wave shapes can be obtained now with an accuracy which couldnt be

     J d 2 f dt2

     d

     dt Cem Cr

     (3)

     generation. The advantages brought by these solutions are The electromagnetic torque is given by:

     bound both for getting of waveforms lacked for undesirable harmonics and also for the possibility of controlling the level of the amplitude of harmonics using different generation techniques. The control in real time offers the possibility of

     C 3 p( i (L L i i )

     em 2 r sq d q) sd sq

3. STATE MODEL OF PMSM:

   (4)

   changing the amplitude of voltage and the frequency of this,

   From the equations lasts, the system can be written in the following form:

   .

   X A.X B.U

   Y C.X D.U

   (5)

   reference currents idref and iqref . Vector control laws feeder machines voltages pose couplings between actions on the axes (d ) and (q) . In a reference (d )

   The model in matrix form is:

   d X A.X B.U

   (6)

   and (q) with the axis (d ) aligned with the rotor flow

   To decouple the evolution of currents, (id ) compared to

   dt

   with:

   X isd isq T

   controls, we will define the terms of compensation

   esq as:

   esd

   and

   esq r .Lq .isq

   U Vsd

   Vsq

   r T

   (7)

   e .L .i

   .

   (9)

   .

   Rs

   Ld 1

   sd r d sd r r

   vsd vsd1esd

   vsq vsq1esq

   (5)

   (10)

   i L r L i

   L

   0 0 Vsd

   sd d q . sd

   d

   .

   L R isq

   1 r .V sq

   (8)

   With

   isq

   r d

   s

   0

   Lq Ld

   Ld Lq r

   vsd1 Lsd disd rsiq

4. VECTOR CONTROL OF PMSM

   The technique applied to the PMSM is to maintain Id

   zero to

   vsq1 Lsq

   dt disq dt

   rsisd

   (11)

   produce maximum torque and use Iq

   component for

   The currents id

   and iq

   are decoupled. The current id only

   achieving the cascade control to ensure the performance of the

   depends

   vd and the current iq

   depends only vq The (fig. 4)

   chase speed. The block structure of this control scheme is shown in (Fig. 1)

   the control theory by field oriented can assimilate the behavior of the synchronous machine with permanent magnets a continuous-current machine with separate excitation, in which the magneto motive force of the armature made an angle of 90° with the axis of field flow, and this, whatever the speed of

   represents the different stages of the vector controls structure with a rotors flux orientation.

   Decoupling bloc

   Current

   rotation.

   To achieve control, it is necessary to direct the flow in quadrature with the torque generating current. Thus, we obtain a model of the machine where the flux and electromagnetic torque are decoupled so that we can act on the torque without affecting the flow, since the torque depends only on the current iq . This will allow obtaining significant

   Fuzzy speed controller

   controller

   Current controller

   PWM PMSM

   Sensor of position

   performance, for the system response under dynamic similar to that of DC machines.

   The control flow is directed to guide the current along the axis q. Thus, the electromagnetic torque can be controlled by a single quadrature component iq . This amounts to maintain

   Fig. 1. System Configuration of Field-Oriented SynchronousMotor

   1. PI Controller

      The proportional integral (PI) controller is one of the famous controllers used in a wide range in the industrial applications. The PI controller is defined by the following function:

      the stator current in quadrature with the inductors flow, which gives a maximum torque, and to regulate the speed by

      C p k p

   • Ki

     p

     (12)

     the current iq via the voltage vq . This verifies the

     1. Fuzzy logic controller

   principle of the DC machine.

   Vector Control returns to control both components iq

   and

   The general structure of a complete PI fuzzy control system is given in Fig.2. The control voltage u is inferred from the two variables

   state, error e and variant of e . The actual crisp input are

   iq of the stator current tensions by imposing vd

   and

   approximates to the closer values of the respective universes of discourse. Hence, the Fuzzy fiend inputs are described by singleton

   vq

   appropriate. To impose voltages vd and vq , it

   fuzzy sets. The elaboration of this controller is based on the phase

   plant. the fuzzy logic controller executes the 49 control rules

   suffices to impose the reference voltages vqref

   and vdref

   shown in Table 1 taking the fuzzy variables e and ce as inputs

   at the input of the inverter [2]. Using the regulators, we get the

   and the output quantity iq* is processed in the

   defuzzification unit. The rules are formulated using the knowledge of the permanent magnets synchronous motor behavior and the experience of control engineers.

   Fig. 2. structure of PI fuzzy controller

   The continuity of input membership functions, reasoning method, and defuzzification method for the continuity of the

   mapping fuzzy e, e is necessary. In this work, the

   triangular membership function, the max-min reasoning method, and the center of gravity defuzzification method are used, as those methods are most frequently used in many literatures [1]

   TABLE I. FUZZY CONTROL RULES FOR SPEED CONTROLLER

   'e'

   e

5. SIMULATION OF THE SVM

   This modulation is represented by the vector only three sinusoidal output voltages as desired. We approximate the best vector for each modulation interval by influencing the control of three sets of complementary switch. This vector PWM does not rely on separate calculations for each arm of the inverter, but the determination of a global vector control approximated on a modulation period T

   Determination of reference voltages V, V. Identification of sector.

   Calculation of switching time for each sector. Generate of control signals.

   The Simulink scheme of the SVM generator (Fig. 1) is formed by subsystems disposed on the structure of the operating principle scheme, presented in [1], each of this having its own Simulink model.

   Well show the main blocks from the scheme, their role and the equations on which they were built

   Fig. 3. The Simulink scheme of SVM generator

   1. Determination of V, V:

      This block is used to project the three-phase voltages in the repository (, ) by performing the processing in Simulink Clarke, one obtains:

      Fig. 4. The Simulink scheme for transform. abc-

      Define abbreviations and acronyms the first time they are used in the text, even after they have been defined in the abstract. Abbreviations such as IEEE and SI do not have to be defined. Do not use abbreviations in the title or heads unless they are unavoidable.

   2. The vector sector in coordinates

      The subsystem determines the sector (1 to 6) in which the voltage vector lies, comparing the signal Angle with the limits of every sector. the output signal is periodical, in six stages of amplitude. we present In (Fig. 3) the Simulink partial scheme of the subsystem for 1 and 2 sector and it is completed in the same way for the other sectors.

      Fig. 5. generation of sectors in the reference

   3. The switching time calculator

      In (Fig. 4) we present the block which corresponds to the A branch where a multiport switch chose one of the f1, f2, f3, f4, f5, f6 functions (from the Table I).

      Fig. 6. switching time calculator

      TABLE II. THE FUNCTIONS EXPRESSIONS

      integration in discrete time of a constant (here 4500 Hz), with reset controlled by the true value of the comparison ramp 1.

      The subsystem, whose Simulink scheme is presented in (Fig. 5), compares on every phase, the ramp signal with Loff (ramp Loff), respectively with Lon (ramp Lon) and it units with an AND operator the two results. The resultant signal and also the same denied signal are taken off at the output, and they represent the control signals on gate for activate the inverter switches.

      Fig. 7. generation of control signals

6. THE RESULTS OF SIMULATIONS

   We make simulations on the complete scheme of electric drive with synchronous motor presented in [1], which contains the SVM generator. We consider its following parameters:

   • switching frequency 5000 Hz.

   • SVM sampling time 0.5s.

     400

     Valpha

     200

     0

     -200

     -400

     400

     Vbeta

     200

     0

     -200

     -400

     0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

     time

     0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

     time

     Fig. 8. Voltage (Valpha, Vbeta)

   1. The gates logic

   The subsystem receives the six Loff, Lon signals through the input gate timing. the ramp signal obtained through the

   200

   150

   100

   angle

   50

   0

   -50

   -100

   -150

   -200

   0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

   time

   Fig. 9. angle(rad)

   6

   7 starting mode without load is done. The load Cr

   Sector

   5

   4 applied at t = 1 s.

   3

   2

   1

   4 Nm is

   0

   0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

   time

   Fig. 10. Sector

   Van,Vbn,Vcn

   400

   300

   Van

   Vbn

   200

   100

   2

   1.5

   0

   -100

   -200

   -300

   -400

   Vcn

   0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

   time

   Fig. 11. Voltages Va Vb Vc

   Fig. 16. speed

   Fig. 17. Current iq

   1

   0.5

   0

   -0.5

   -1

   0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5 0 .0 6 0 .0 7 0 .0 8 0 .0 9 0 .1

   time

   Fig. 12. Signal for gate 1

   2

   1.5

   1

   0.5

   0

   -0.5

   -1

   0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

   time

   Fi. 13. Signal for gate 2

   Fig. 18. Current id

   50

   40

   30

   20

   Loff

   10

   0

   -10

   -20

   -30

   50

   40

   30

   20

   Lon

   10

   0

   -10

   -20

   -30

   -40

   -50

   0 0.01 0.02 0.03 0.04 0.05 0.06

   time

   Fig. 14. L_on branch A

   Fig. 19. Torque cem

   The speed response of the permanent magnet synchronous machine is similar to a first order system.

   The application of load torque as using the fuzzy logic controller stay the speed invariable.

   The fuzzy controller rejects the load disturbance rapidly with no overshoot and with a negligible static error.

   The right choice of adjustment coefficients of the current regulator

   -40

   -50

   0 0.01 0.02 0.03 0.04 0.05 0.06

   time

   maintains the component id

   always equal to zero and the

   component iq

   with the same look and the same dynamics as the

   Fig. 15. L_off branch A

7. SIMULATION RESULTS OF VECTOR CONTROL FOR PMSM

   In order to validate the control strategies discussed above, digital simulation studies were made the system described in Figure 4. The speed and currents loops of the drive were also designed and simulated with PI current (Id,Iq) control and with fuzzy speed control.

   The transient response was tested on closed loop with two PI current controls and a fuzzy for the speed control. The simulation of the

   electromagnetic torque and that to meet the load torque.

8. CONCLUSION

WE simulate a SVM generator is used to control, through the technique of space vector modulation, of the electric drives with PMSM machine.

We present the Simulink schemes of the main subsystems of SVM generator, built on the corresponding equations.

We analyzed how the model works, observing the waveforms of various signals.

we noticed that the vector control and the proper choice of the coefficients of the controller can achieve decoupling of the machine and the production of a similar machine DC linear model and the other for good performance such as stability, precision and speed.

The fuzzy controller rejects the over current and the oscillations at starting. It decreases the influence of the load torque on the speed of the PMSM.

TABLE III. PARAMETER OF PMSM

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