# Field Oriented Control Method Of Induction Motor Computer Science Essay

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Abstract- This paper proposes a fully digital high performance variable speed drive of induction motor implementing based on a single chip DSP motor controller. Some important models and features of the Field Oriented control are analyzed in detail and the implementing flowchart is given. The proposed speed control algorithm programming in C is realized by the TMS320LF2407 DSP offering a fast current response. Simulation results show that the performance of Field Oriented control of induction motor is exactly the same as performance of separately exited DC motor. FOC technology is regarded as a kind of controlling manner of AC asynchronous motor, and it is already become the first method of the high performance variable frequency speed regulating system. In induction motor speed control, from a DC voltage source, Pulse Width Modulation (PWM) techniques generate variable AC voltages (both amplitude and frequency). Space Vector Pulse Width Modulation (SVPWM) utilizes DC bus voltage more efficiently with less harmonic distortion in a three-phase voltage source inverter. In the present work, an efficient approach for implementing SVPWM technique is developed reducing the computational burden.

Index terms- Field Oriented control, SVPWM, Variable-frequency Speed governing system, Dynamic and static performances, DSP.

## I. INTRODUCTION

Not only because of its highly non-linear dynamic structure with strong dynamic interaction and variable parameters depended on temperature and saturation condition, but also the rotor currents and rotor flux-linkage cannot be measured directly and easily, the induction motor requires more complex control schemes than other types of electric machines.

However the field oriented control method based on rotor-field oriented of induction motor gives a completely decoupling control in theory. It offers a high dynamic response in the variable-speed induction motor drive, as well as a separately excited d.c. machine. It is hard to implement before the high performance Digital Signal Processor (DSP) was born, because of the intense computation for coordinate transformation and flux model. Thus a few years ago due to the limit of the hardware, many papers only stop their research at the simulated results in china. Even some implement the algorithm by using two DSP or microprocessors aboard ,

it has the more complex construct of control platform and higher cost. Furthermore, the sample period is relative long (<1OKHz) due to the low operating frequency of the controller, it is a disadvantage that the real-time current control cannot be realized by the delay

caused by the filters and the A/D conversion, which must be considered when designed the drive system.

This paper reviews the classic rotor-field-oriented control of induction motor and analyses some important features deeply, implements the variable-speed induction motor drive based on the new TMS320LF2407 controller of TI company designed special for motor control. It achieves a simpler construct, reduces the number of devices needed, saves cost, and offers higher reliability. 2407 improves the real time current control, eliminates the noise produced by switching of the IGBT , reduces the effect of delay to the drive system. At last by using the experimental results done with the hardware platform, the good steady dynamic performance of the variable-speed induction motor drive based on DSP2407 is proved.

Although a voltage-controlled inverter using hysteresis controller is easy to realize and can be used to satisfy the current control requirement, it has the following disadvantages:1) The switching frequency depend on the nature of the load.2) The current ripple is high.3) Performance at higher speeds is unsatisfactory. These disadvantages can be overcome by using a SVPWM.

The development and the application of Pulse Width Modulation (PWM) technology have optimized performance of the frequency converter device, and it is applied to all kinds of AC speed regulating system. The SVPWM control method has some advanced merits compared with classical SPWM controlling method, for example, direct physical significance, simple mathematical model, easy computer real-time controlling, and small torque wave, low noise, simple control, low cost of power, high effect of utilization of DC voltage. At present time, this technology would be applied widely whether in open loop or closed loop speed governing system.

The traditional SVPWM algorithm adopts largely

trigonometric functions and other nonlinearity functions.

When realized, it would need to compute the vector effect time and store a mass of data in advance. But these

compute is complex, the processing is also very difficult,

therefore, it would be not easy to realize the digital real time controlling especially.

In this paper, we introduced a simplified SVPWM algorithm, which can realize a conversion speed regulation system of influence motor. The theoretical analysis and the experiment results show that this system has some characteristics, such as realized simply, high utilization ratio of voltage and small harmonic current, and so on. Therefore, if adopted this system, the operation quality of the induction motor would be improved greatly, these results illustrate that this system would have some higher practical values.

## II. FIELD ORIENTED CONTROL ALGORITHM AND DIGITAL IMPLEMETATION

By considering induction motor model in the rotor-flux-oriented reference frame under the linear magnetic condition, the schematic of vector control strategy shown in Fig. 1 is obtained. In the Fig. 1, the induction motor is fed by voltage-source inverter included in the power drive block.

## Field Oriented control algorithm

It follows from Fig. 1 that it contains a closed-loop control of the rotor speed, rotor flux by means of rotor magnetizing current, the torque through the torque-producing current, and has a speed controller, a rotor flux controller, two current regulators, all of which are the PI controllers; a function generator (FG) block to realize the field weakening. A SVPWM generator giving the drive signals to power devices which supply the machine. In the Fig.1, the error between Ï‰ref and the actual rotor speed Ï‰r serve as the input of the speed controller, the output of which is the torque-producing stator current reference iTsref but not the torque reference in order to simplify the construct, since the torque and the T-axis current is proportional under the linear magnetic condition. The actual rotor speed Ï‰r , which is equal to the first time derivative of the rotor angle Î¸r obtained by the encoder fixed on the shaft of the machine, also serves as a input of FG, by which the field weakening is achieved automatically, and the output of FG is reference value of the modulus of the rotor magnetizing-current imrref , which is a constant value below base speed and is inversely proportional to the rotor speed above base speed. This reference signal is compared with the Actual value of rotor magnetizing current and the error serves as input to the flux controller, the output of which is the M-axis stator current reference iMref in the rotor-flux-oriented reference frame.

Then the error signals im-iMs and iTsref- iTs serve as inputs to their respective current regulators and the output of these are added by the output of decoupling block respectively, the M-axis and T-axis stator voltage component reference are obtained. They are variables in the rotor-flux oriented reference frame, thus the block ejÏr has to be used to transform them into the D-axis and Q-axis stator voltage components in the stationary reference frame. After that by using the SVPWM block, which is new technique and has some advantages compared with the normal PWM, the switching signals to command the power devices are obtained. It can be seen in the Fig. 1 that this strategy is very simple and easy to implement on a DSP, since all the quantities to be monitored are only rotor angle and the line currents of the machine. The currents can be obtained by the application of Hall sensors, and in practical only two phase currents are enough for the usually star connect of induction motor.

## B)The control algorithm flow chart

According to Fig. 1, the whole program of the control system is written by C language supported by TMS320LF2407. It is consisted of two parts: the main function completing the initialization of the system clock, 10, peripherals and so on, and the Interrupt Service Routines(ISR). The ISR included in this control system are: the ISR for FOC, the ISR for acquiring position, and the ISR for protecting. The flow chart of complete FOC is given below:

Fig2. Rotor-Field oriented control implementation

Flow chart

Because the motor speed changes more slowly than the

torque current component iT, it need not to perform speed control at every interrupt cycle. Instead, when the iT current regulator performs ten times, i.e. every 10 cycles, one speed control is enough. Therefore, when the inner counter is equal to 10, it will perform speed controller after flux model, otherwise, the program will run to the current regulator directly.

## III WORKING PRINCIPLES OF SVPWM

## A. The Relationship between Voltage Vector and Magnetic Linkage Vector

Where, we suppose that the AC induction motor's power is supplied from an ideal three-phase symmetrical

sine voltage, these stator's phase voltage USA, USB, USC is add on three-phase coils respectively, their direction is

always on the axis of each coil, and its value is exchanged in sine rule following on the time. That is

In this formula, UA, UB, UC are the three-phase phase voltage of the inverter output; The Un is the voltages of the midpoint O that relative to negative potential of the inverter DC side when the stator winding is star connection.

The US which is synthesized with the voltage space

vector of the stator winding is as follows

The above formula indicated: (1) The voltage space vector Us that synthesized by three phase voltage space vectors addition is a space vector rotating with power source angle frequency speed. (2) In the PWM inverter motor system, the analysis of motor stator voltage space

vector can change into the analysis of inverter space vector .In the same way, we can define the magnetic linkage space vector Î¨S is

If ignoring the effect of resistant motor stator, then Î¨S

can be obtained by integral the voltage space vector to

time. When the inverter outputs a voltage space vector

Ui (i = 0 7), the magnetic linkage space vectors Î¨S can

be expressed as follows:

In this form, Î¨S0 is an initial magnetic linkage space vector, is the action time of Ui . When Ui is a nonzero voltage vector, the magnetic linkage space vector sets off from initial location, whirligig with the radius âˆš(2/3)Ui/Ï‰ along the corresponding voltage space vector direction. While Ui is zero voltage vector, Î¨S = Î¨S0, the magnetic linkage space vector motion is restricted. Therefore, chose the operator order and work time of six nonzero voltage space vector rationally, that would make the space vector's head turning in clockwise or in anticlockwise, and would become the certain shape trace. Choose the different form, being the different magnetic linkage locus. In general, it makes the magnetic linkage locus approach a regular polygon or circular.

## B. Mathematical Model of Voltage Form PWM Inverter

The power circuit adopted topology structure of the

three-phase voltage source inverter, as show in Fig.3 .The

up and down switch components of the inverter bridge arm can't pass at any the same time. These switch would

be reciprocal state when we don't consider the died area, Sa, Sb, Sc express three bridge arms state respectively, "1" indicated that the up-bridge arm pass, and "0" indicated that the down-bridge arm pass. UA, UB, UC are the three-phase voltage outputs, Take pursuing negative voltage shown by Fig.3 as a reference point, We can obtain:

UA = SaUdc, UB = SbUdc, UC = ScUdc

Fig 3. PWM inverter circuit

Change the three-phase voltage to two-phase dâˆ’q axis

system according to Clark Transform:

The inverter has 8 kinds switch patterns, which are 000, 001, 010, 011, 100, 101, 110 and 111. So, we could obtain the 8-voltage space vectors: U0, U60, U120, U180, U240, U300, O000, O111. In these vectors, O000 and O111 are zero vectors. The Fig.4 is inverter's spatial distribution of the eight voltage space vectors.

Fig 4. Voltage Space Vectors

## C. Control of Magnetic Linkage Track

While the inverter output the basic voltage space vector U0 alone, the arrow of the stator linkage vector Î¨ would move from A to B alone the direction of parallel U0, as show in Fig.5. When moving to B, if we change the basic voltage space vector into U60, then the vector arrow of the stator linkage vector Î¨ also moving from B to C in correspondingly. In this way, when 6 nonzero voltage space vectors export alone in turns respectively, the moving track of the head of stator linkage vector Î¨ is a regular hexagon, as show in Fig.5.

Fig 5. Regular hexagon magnetic linkage track

But there are only six basic nonzero voltage space vectors, if we want to obtain polygon rotating magnetic field as more as possible, it must has more switch states. One commonly used method is that it can obtain more switch states use the linearity time combination of these six nonzero basic voltage space vectors. The basic control principle was shown as follows.

In Fig.6, Ux and Ux+60 are represent two adjacent basic vectors of voltage space, Uout is the reference phase voltage vector of the output, whose amplitude represents the phase voltage amplitude, whose revolution angular velocity is to export sine voltage angle frequency. Uout was come from the linearity time composed by Ux and

Ux+60, it is equal to vector sum of t1/TPWM times Ux and t2/ TPWM times Ux+60. Of which, t1 and t2 is the operate

time of Ux and Ux+60 respectively, TPWM is effect time of Uout.

Fig 6. The linearity combination of the voltage

Space vectors

## D. Calculation of the Voltage Vector Operating Time

As mentioned above, the voltage space vector of linearity time combination is

In above formula, we projected Uout, Ux and Ux+60

to coordinate system 0dq. This formula may be wrote

down:

After when we would have obtained then can ascertain t1 and t2 right away.

In Fig.5, when the inverter alone output zero vectors O000 and O111, the magnetic linkage vector Î¨ of the motor stator would be fixed. According to theses characteristic, intervene the zero vector effects t0 in TPWM

period, make

By such method, it can adjust the angle frequency Ï‰, and

obtain frequency conversion's purpose.

## E. Ascertain Sector Number

We apart the Fig.5 into six sectors, every sector has a sector No.(as show in Fig.5, 0, 1, 2, 3, 4, 5). Only when we have known which sector that Uout is located in, then can ascertain which pair of adjacent basic voltage space vector would be used to compose Uout. After Uoutd and Uoutq were given, we should calculate B0,B1,B2 at first.

Then calculate the P value

In the form, the sign(x) is a sign function.

If x > 0, sign(x) = 1; x < 0, sign(x) = 0.

Finally, according to P value table and look-up TableI, then we can ascertain sector number.

If we adopt above algorithm, it only needs the plus minus and logical computation simply, then can ascertain the location sector where the reference voltage vector be in, and avoided calculating the complicated nonlinearity function, this feature have an actual meaning for simplified the calculation and improve the response

speed of the system. Not only it can decrease the requirement for controller calculation speed, but also the real time control can be realized easily.

## IV. REALIZATION OF SVPWM ARITHMETIC THROUGH DSP

## A. Event Manager of TMS320LF2407A DSP [5]

Event manager (EV) is a special module, which was designed for controlling the motor. It can produce all kinds of PWM waves, and these waves can adjust the blind area. It can measure the rotating speed, divert and angle displacement of the motor by the interface of the increment photo-electricity coder, and measure the pulse width by capture the power. There are 2 Event mangers in TMS320LF2407A DSP, which are EVA and EVB. Every event manger has 2 general timers of 16âˆ’bit, has 8 pulse width modulation passes PWM of 16âˆ’bit. 3 comparing units with programming bead area control can produce 3 pairs of absolutely PWM waves (ie.6 outputs), these 2 timers can produce 2 kinds absolutely PWM waves. They could be realized: output the symmetrical and asymmetric PWM wave; avoid output pulse at the same time in up and down bridges. During the application of the motor controlled, the PWM circuit could reduce the CPU overhead for producing PWM wave and the workload of the user, also could simplify the control soft for produce the symmetrical pulse width

modulation and symmetrical hardware.

## B. Method of Output PWM Wave

We designed the method for produced PWM wave use the periodic value of the periodic register and the compared value of the comparator based on TMS320LF2407A DSP. The periodic value is used to produce PWM wave frequency (or period), the compare value is mainly used to produce PWM wave pulse width.

According to using different comparator, there are two methods to produce PWM wave: One use the timer and the comparison register to realized, another use the comparison unit to come true. The PWM wave that the latter produced can add a blind spot. For obtained an output Wave with ideal form, it is necessary not only set the value of control correctly, but also need adopt the correct algorithm. For output the space vector PWM wave, the consumer need sets up the following register (choose the EVB module): 1)Set the comparative form control register ARCTRB to define output form of the compare output part. 2) If enable the blind port, then must setup the blind port control register DBT-CONB. 3) Setup the register of timer no.3's period T3PR, that is the period of stipulating the PWM waveform. 4) Initialize the comparison register CMPR4 âˆ¼ 6. 5) Set the comparison control register COMCONB to enable to the compare operation and the pattern of the space vector PWM. 6) Set the timer no.3 to control register T3CON working in continuing increasing/ the subtraction pattern [6, 7].

## C. DSP Software Designs of SVPWM Wave

t0, t1 and t2 must be calculated out according to form eq(7) and eq(8). For programming easily, the period value of the periodic register is equal to TPWM/2, and the Form (7) can be simplified:

The program flow graph of the timer interruption

subprogram as show in Fig.7

Fig 7: The program flow graph of the timer interruption flow graph

## V. EXPERIMENT RESULTS

.Fig 8: Current waves of each coil in different frequency

Fig9: Line voltages of each coil in different frequency

Fig 10: Experimental results: (a) the measured phase current and the phase voltage reference with 1.0pu(bottom) under steady state operation with nominal conditions (b)the response with a step change in the reference speed with no load (c) the speed step response with nominal load using normal PI controller(d) the same speed response by using improved PI controller with correction gain (e) the dynamic behavior of the speed and measured magnetizing current with linear reference under field weakening by using normal PI controller (f) the same experiment with (f) but using improved PI controller (g) ,(h) the measured torque- and flux-producing current component, when accelerating and decelerating with the motor blocked.

Fig11: Field Oriented control results using MATLAB

Fig 12: SVM Wave Using MATLAB

## VI.CONCLUSION:

This paper has implemented the field-orientated-controlled variable-speed drive based on the TMS320LF2407 controller from TI Company. The features of FOC: complete decoupling and no stability limit are discussed in theory. The software flowchart is given in details together with the experimental results, proving the high torque at zero speed, the speed variation capability, the extended speed range, the direct decoupling control of torque and flux and the excellent dynamic behavior. It is proved that the real time processing capability of the proposed motor control device allows for a highly reliable and effective drive with no consideration on the delay of digital control system, and offers the potentiality of implementing more advanced or complex control schemes in the design of high-performance variable speed drives. We adopted TMS320F2407 to design a frequency speed control system of induction motor based on SVPWM controlling. This is a new method to realize the Variable-frequency speed governing system. Through the experiments, it is shown that this system could improve the performance of the produced PWM wave in the condition of non-increase the switch depreciation. At the same time, it is shown that square wave was output by the wave generator of TMS320LF2407DSP event manager module, this method simplifies the development of software and hardware. And the quality of the SVPWM wave were also very good. These results illustrated that the system has a high control precision and has good performance under both dynamic and static conditions. Hence, the

proposed controller is expected to find wide application due to its attractive features.

## VII.REFERENCES:

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[2] Zhiyong Du, Xianfang Wang: "SVPWM Speed Governing System of Induction Motor Based on DSP" EUROCON 2007 The International Conference of Computer as a Tool

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[4]Ying-Yu Tzou; Ming-Fa Tsai; Yuh-Famn Lin; Hwa Wu; "Dual DSP based fully digital control of an AC induction motor" Industrial Electronics 1996. ISIE '96., Proceedings of the IEEE International Symposium on Volume 2, 17-20 June 1996 Page(s):673 - 678 vol.2.

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[8] Drazen Dujic, Student Member, IEEE, Gabriele Grandi, Member, IEEE, Martin Jones, Member, IEEE, and Emil Levi, Senior Member, IEEE "A Space Vector PWM Scheme for Multi frequency Output Voltage Generation With Multiphase Voltage-Source Inverters" IEEE transactions on induction motor, VOL. 55, NO. 5, MAY 2008

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[12] TI Company, AC Speed Governing Controlling System,TMS320LF2407A, TMS320LF2406A, DSP Controller s2005