RENESAS

2008

Field Oriented Control Application Note

Hamid KHAN

Hamid KHAN 2

ABSTRACT

AC induction motors of different power ratings and sizes can be utilized in

applications ranging from consumer to automotive goods. A few of these applications

from the multitude of possible scenarios demand for high speeds while high torque at

low speeds only. A common everyday example with these mechanical requirements

is of the motor installed in a washing machine. This requirement can be addressed

through Field Oriented Control or the FOC of an Induction machine.

The objective of this Application Note is developing and implementing an efficient

Field Oriented Control (FOC) algorithm that could be implanted on Renesas’ SH7125

microcontroller to control the speed and torque of three phase asynchronous motors

more effectively and efficiently.

FOC: Field Oriented Control principles applied to an asynchronous motor are based

on the decoupling between the current components used for generating magnetizing

flux and torque. The decoupling allows the induction motor to be controlled as a

simple DC motor. The field oriented control implies the translation of coordinates

from the fixed reference stator frame to the rotating synchronous frame. This

translation makes possible the decoupling of the stator current into two components,

which are responsible for the magnetizing flux and the torque generation.

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CONTENTS

Introduction ................................................................................................................. 5

1. Background .......................................................................................................... 6

1.1. AC Induction motor ........................................................................................ 6

1.1.1. Induction Machine Electrical Equations .................................................... 7

1.2. Three Phase Induction Motor ......................................................................... 7

2. Vector Control of Induction Machines ................................................................... 8

2.1. Introduction .................................................................................................... 8

2.2. FOC ............................................................................................................... 8

2.2.1. FOC Theory ............................................................................................. 9

2.3. The FOC Algorithm ...................................................................................... 11

3. MATLAB simulation of FOC ................................................................................ 12

3.1. Introduction .................................................................................................. 12

3.2. System Overview ......................................................................................... 12

3.3. Block FOC .................................................................................................... 12

3.3.1. Flux Estimator ........................................................................................ 13

3.3.2. �� Calculation ........................................................................................ 13

3.3.3. Park Transformation ............................................................................... 13

3.3.4. Inverse Park Transformation .................................................................. 13

3.3.5. ���∗ Calculation ........................................................................................ 13

3.3.6. Flux PI .................................................................................................... 13

3.3.7. Current Regulator ................................................................................... 13

3.4. SIMULINK model of FOC ............................................................................. 15

3.4.1. SIMULINK Block FOC ............................................................................ 16

3.5. SIMULINK sub FOC bocks .......................................................................... 16

3.6. FOC Simulation Results ............................................................................... 18

4. FOC Speed Regulator ........................................................................................ 20

4.1. Introduction .................................................................................................. 20

4.2. MATLAB simulation of FOC Speed Regulator ............................................. 20

4.2.1. Speed Controller .................................................................................... 20 4.2.1.1. Flux Table ............................................................................................ 21

4.3. FOC Speed Regulator Simulation Results ................................................... 22

Conclusion ................................................................................................................ 24

Reference .................................................................................................................. 25

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LIST OF FIGURES

Figure 1 : Classification of Electrical Motors ................................................................ 6

Figure 2 : Phasor Diagram describing FOC Scheme .................................................. 9

Figure 3 : Complete Schematic Diagram ................................................................... 12

Figure 4 : Block FOC ................................................................................................. 12

Figure 5 : Operational Principle of Hysterysis Modulation ......................................... 14

Figure 6 : Typical Hysterysis Current Controller ........................................................ 14

Figure 7 : Current Controller Bandwidth Hysterysis ................................................... 15

Figure 8 : Simulink Model of FOC ............................................................................. 15

Figure 9 : Block FOC ................................................................................................. 16

Figure 10 : Flux Estimator ......................................................................................... 16

Figure 11 : Flux Orientation Calculation .................................................................... 17

Figure 12 : Flux PI ..................................................................................................... 17

Figure 13 : i�∗ Calculation .......................................................................................... 17

Figure 14 : Current Regulator .................................................................................... 17

Figure 15 :Result FOC 1 ........................................................................................... 18

Figure 16 :Result FOC 2 ........................................................................................... 18

Figure 17 :Result FOC 3 ........................................................................................... 19

Figure 18 : FOC with Speed Controller ..................................................................... 20

Figure 12 : Speed Controller Block............................................................................ 21

Figure 21 : Result Speed Regualation 1 .................................................................... 22

Figure 22 : Result Speed Regualation 2 .................................................................... 22

Figure 23 : Result Speed Regualation 3 .................................................................... 23

Figure 24 : Result Speed Regualation 3 .................................................................... 23

Hamid KHAN 5

Introduction AC Induction motors offering desirable operational characteristics such as robustness, reliability and ease of control; are extensively used in various applications ranging from industrial motion control systems to home appliances. Until a few years ago the AC motor could either be plugged directly into the mains supply or controlled by means of the well-known scalar V/f method. When power is supplied to an induction motor at the recommended specifications, it runs at its rated speed. With this method, even simple speed variation is impossible and its system integration is highly dependent on the motor design (starting torque vs. maximum torque, torque vs. inertia, number of pole pairs). However many applications need variable speed operation. The scalar V/f method is able to provide speed variation but does not handle transient condition control and is valid only during steady state. This method is most suitable for applications without position control requirements or the need for high accuracy of speed control and leads to over-currents and over-heating, which necessitate a drive which is then oversized and no longer cost effective. The last few years have seen rapid growth in the field of electrical drives. This growth can be attributed mainly to the advantages offered by semiconductors in both power and signal electronics; hence giving rise to powerful microcontrollers and DSPs. These technological improvements have allowed the development of very effective AC drive controls marked with lower power dissipation hardware and increasingly accurate control structures. Using three phase current and voltage sensing has made the electrical drive controllers even more accurate. This application note describes the efficient scheme of vector control - the Field Oriented Control (FOC). On application of this control structure to an AC machine, with a speed/position sensor coupled to the shaft, the AC machine acquires every advantage of a DC machine control structure i.e. a very accurate steady state and transient control along with higher dynamic performance.

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1 Background

Figure 1: Classification of Motors

1.1 AC induction motor

The AC induction motor is a rotating electric machine designed to operate from a 3-phase source of alternating voltage. Asynchronous motors are based on the induction principle. The extreme simplicity and ruggedness of the squirrel cage construction are outstanding advantages of this type of induction motor which make it by far the most commonly used type of motor. In these types of induction motors aluminium conductors or bars are cast into slots in the outer periphery of the rotor. These conductors or bars are shorted together at both ends of the rotor by cast aluminium end rings. For variable speed drives, the source is normally an inverter that uses power switches to produce approximately sinusoidal voltages and currents controllable in terms of frequency and magnitude. Like most motors, an AC induction motor has a fixed outer portion, called the stator and a rotor that spins inside, with a well-optimized air gap between the two. All electrical motors except a three phase induction motor use magnetic field rotation to spin their rotors. In a three phase AC induction motors the rotating magnetic field is generated in the stator by virtue of the nature of the supply. In an AC induction motor, one set of electromagnets is formed by virtue of the AC supply connected to the stator windings. As per the Lenz’s law the alternating nature of the supply voltage induces an Electromagnetic Force (EMF) in the rotor (just as voltage is induced in the secondary transformer), thus generating another set of electromagnets; hence the name “induction motors”. Interaction between the magnetic fields produced by these two electromagnets a revolving force or torque is generated, causing the motor to rotate in its own direction.

Electric Motors

DC AC

Asynchronous Synchronous

Induction

Squirrel Cage Wound Motor

Brushless DC

Sinewave

Hysteresis

Step

Reluctance

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1.1.1 Induction Machine Electrical Equations

�� = ����� +�

����� + �����

�� = ����� +�

����� − �����

0 = ����� +�

����� + (�� − ��)���

0 = ����� +�

����� − (�� − ��)���

�� =3

2�

��

��(������ − ������)

Where

��� = ����� + �����

��� = ����� + �����

��� = ����� + �����

��� = ����� + �����

1.2 Three-phase induction motor Three-phase AC induction motor are widely used in many fields. They are classified in two categories:

� Squirrel cage motor � Wound-rotor motor

90% of the three-phase AC Induction motors are squirrel cage motors because of their lower cost and higher capability of starting heavier loads in comparison with wound-rotor motors. Induction motors with power ratings ranging from one-third to hundred horsepower can be commonly found. The wound-rotor motor is a variation of the squirrel cage induction motor. While the stator construction is same as that in the squirrel cage type motor, the rotor has a set of windings on the rotor which are not short circuited, but are terminated to a set of slip rings. These are helpful in adding external resistors and contactors.

Hamid KHAN 8

2 Vector Control of Induction Machines 2.1 Introduction The construction of a DC machine is such that the field flux is perpendicular to the armature flux. Being orthogonal, these two fluxes don not interact with each other. Hence by adjusting the field current the DC machine flux can be controlled and independent to this the torque can be controlled by varying the armature current. But the control of an AC machine is not as simple because of the interactions between the stator and the rotor fields owing to their non orthogonal orientations to each other and varying orientations as per the operating conditions. A DC machine-like performance can be attained by maintaining a fixed orthogonal orientation between the field and armature fields in the AC machine. This can be achieved by orienting the stator current with respect to the rotor flux in a manner such that independent control of flux and torque is established. Flux Oriented Control or the Vector Control works on this principle. Vector control can be applied on both induction and synchronous motors. In this document the application of flux oriented vector control on induction motors has been elaborated. Vector control entails varying not only the magnitude but also phase of the variables. Control quantities have been expressed in terms of matrices and vectors. This method takes into account not only successive steady-states but real mathematical equations that describe the motor itself, so that the obtained results have a better dynamic for torque variations in a wider speed range. The Field Oriented Control (FOC) offers a solution to circumvent the need to solve high order equations with a large number of variables and nonlinearities and achieve an efficient control with high dynamic. This approach needs more calculations than other standard control schemes but has the following advantages:

� full motor torque capability at low speed � better dynamic behaviour � higher efficiency for each operation point in a wide speed range � decoupled control of torque and flux � short term overload capability � four quadrant operation

2.2 FOC FOC involves controlling the components of the motor stator currents, represented by a vector, in a rotating reference frame (with a d-q coordinate system). In a special reference frame, the expression for the electromagnetic torque of the smooth-air-gap machine is similar to the expression of torque in a separately excited DC machine. In the case of induction machines, the control is normally performed in a reference frame aligned to the rotor flux space vector. To perform the alignment on a reference frame revolving with the rotor flux requires information about the modulus and the space angle (position) of the rotor flux space vector.

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In order to estimate the rotor flux vector either of the below mentioned strategies can be adopted: � DFOC (Direct Field Oriented Control) -

In this strategy rotor flux vector is either measured by means of a flux sensor mounted in the air-gap or by using the voltage equations starting from the electrical machine parameters.

� IFOC (Indirect Field Oriented Control)- In this strategy rotor flux vector is estimated using the field oriented control equations (current model) requiring a rotor speed measurement.

The usual terminology “Sensorless” signifies that no position/speed feedback devices are used.

2.2.1 FOC Theory Considering the d-q model of the induction machine in the reference frame rotating at synchronous speed ��,

The field-oriented control implies that the ��� component of the stator current would be aligned with the rotor field and the ��� component would be perpendicular to ���.

This can be accomplished by choosing �� as speed of the rotor flux and locking the phase of the reference frame system such that the rotor flux is aligned precisely with the d axis, as illustrated in Figure 2 below.

Figure 2: Phasor diagram describing the FOC scheme

From Figure 2 it can be established that -

��� = 0 ⇒�

����� = 0

slrf θθθ +=

rdr ψψ =

0=qrψeω

eω

rω

rψr

dsi

si

qsi

fθ

rθ

Stator Reference

Rotor Reference Frame

d-axis

q-axis

slθ

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And ��� = ��

Hence the flux equation gets reduced to:

)(1

ds

r

m

r isT

L

+=ψ (Equation used for estimating the flux.)

And torque can be expressed as:

�� =

!�

"#

"$(������ − ������)

Following which the expression for ��can be reduced to:

�� =3

2�

��

��(������)

Which can be also expresses as:

�� = %��� , this equation is used to calculate the stator current torque component i*qs.

Hence the analogy with DC machine performance is clearly established, while keeping the flux constant. The electric torque is found proportional to the ���

component, and the flux �� and ��� component of current can be related through a

first-order linear transfer function with a time constant "$

&$.

The rotor flux orientation in a squirrel-cage induction machine cannot be measured

easily. It can be only estimated from terminal measurements. An alternative way is to

use the slip relation derived above to estimate the flux position relative to the rotor,

as shown.

The IFOC technique is described in this application note. Indirect vector control of the rotor currents can be implemented using the following data:

� Instantaneous stator phase currents, ia, ib, and ic � Rotor mechanical speed

To monitor the three-phase stator currents and speed, the motor must be equipped

with sensors and a speed feedback device such as a tachometer respectively.

Hamid KHAN 11

2.3 The FOC Algorithm An abbreviated version of the FOC (or vector-control) algorithm is summarized below: 1. Measure the stator phase currents ia, ib and ic. If only the values of ia and ib are

measured ic can be calculated as for balanced current ia + ib + ic = 0. 2. Transform the set of these three-phase currents onto a two-axis system. This

conversion provides the variables iα and iβ from the measured ia , ib and ic values where iα and iβ are time-varying quadrature current values, as viewed from the stator’s perspective. This conversion is popularly known as Clarke Transformation.

3. Calculate the rotor flux and its orientation. 4. Rotate the two-axis coordinate system such that it is in alignment with the rotor

flux, using the transformation angle calculated at the last iteration of the control loop. This conversion provides the id and iq variables from iα and iβ. This step is more commonly known as the Park Transformation.

5. Flux error signal is formed using flux reference and estimated flux value. A PI

controller is then used to calculate i*d using this error signal. i*q is generated using the reference torque value and the estimated flux value.

6. i*d and i*q are converted to a set of three phase currents to produce i*a, i

*b, i

*c.

7. i*a, i*b, i*c and ia, ib, ic are compared using hysterysis comparator to generate

inverter gate signals.

Hamid KHAN

3 MATLAB Simulation of FOC 3.1 Introduction To validate the algorithm developed, it SIMULINK, a powerful simulation software with very helpful in forming a complete model.

3.2 System Overview The motor to be controlled is in inverter switching commandmotor shaft.

Fig

3.3 Block FOC

PI

Flux Controller

���∗

Calculation

Park

Transformation

fθ

abci

*

rψ

*τ

rψ̂

rψ̂

abci

mω

*

rψ

*τ

3 MATLAB Simulation of FOC

developed, it was tested on MATLAB’s® simulation tool a powerful simulation software with many inbuilt blocks

very helpful in forming a complete model.

The motor to be controlled is in a close loop with the FOC block which generates inverter switching commands to achieve the desired electromagnetic torque at

Figure 3: Complete Schematic Diagram

Figure 4: Block FOC

Inverse Park

Transformation

Calculation

Transformation

fθ

dsi

qsi

Flux Estimator Calculation

*

abci

*

dsi

*

dqi

rψ̂

Gate

Signal

s

FOC

du

12

on MATLAB’s® simulation tool inbuilt blocks which proved

loop with the FOC block which generates the desired electromagnetic torque at the

Gate

Signal

�'

Calculation

fθ

Current

Regulator

abc

mω

ASIM

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3.3.1 Flux Estimator

This block is used to estimate the motor's rotor flux. This calculation is based on motor equation synthesis.

)(1

ˆds

r

m

r isT

L

+=ψ

3.3.2 () Calculation

This block is used to find the phase angle of the rotor flux rotating field using the following equations.

�' = �� + �� From which it can be established that,

��'

��=

���

��+

���

��

Which can also be written as? �*+

�,= �� + ��

Therefore,

�' = -(�� + ��)�� With �� ="#./0

&$12 $

3.3.3 Park Transformation

This block performs the translation of the a,b and c phase variables into dq components of the rotor flux rotating field reference frame.

3.3.4 Inverse Park Transformation

This block performs the conversion of the dq component of the rotor flux rotating field reference frame into a,b and c phase variables.

3.3.5 345∗ Calculation

This block uses the calculated rotor flux and the torque reference to compute the stator current quadrature component required to produce the electromagnetic torque on the motor's shaft.

3.3.6 Flux PI

This block compares the estimated rotor flux and the reference rotor flux as the input to a Proportional Integrator which calculates the flux to be applied to the motor which in turn is used to compute the stator current direct component required to produce the required rotor flux in the machine.

Hamid KHAN 14

3.3.7 Current Regulator

The current regulator is a bang-bang current controller with adjustable hysteresis band width.

Modulation Technique Used The hysteresis modulation is a feedback current control method where the motor current tracks the reference current within a hysteresis band. Figure 5 elaborates the operation principle of the hysteresis modulation. The controller generates sinusoidal reference current of desired magnitude and frequency which then is compared to the actual motor line current. If current exceeds the upper limit of the hysteresis band, the upper switch of the inverter arm is turned off and the lower switch is turned on. As a result, the current starts to decay. If the current passes the lower limit of the hysteresis band, the lower switch of the inverter arm is turned off and the upper switch is turned on. As a result, the current gets back into the hysteresis band. Hence, the actual current is forced to track the reference current within the hysteresis band.

Figure 5: Operation Principle of Hysteresis Modulation

Figure 6 details the hysteresis current control modulation scheme, consisting of three hysteresis comparators, one for each phase.

Figure 6: Typical Hysteresis Current Controller

Hamid KHAN 15

ℎ

2

−ℎ

2

Current controller hysteresis band

The current hysteresis bandwidth refers to the total bandwidth distributed symmetrically around the current set point. Figure 7 illustrates a case where the

current set point is 8�∗ and the current hysteresis bandwidth is set to

9

!.

Figure 7: Current Controller Hysteresis Bandwidth

3.4 SIMULINK model of FOC

Figure 8: Simulink Model of FOC

As detailed in Figure 8 the Simulink Model of FOC consists of three blocks:

� The green colour represents the already existing SIMULINK models of the

hardware used to implement the FOC scheme namely the motor and the

inverter.

� Blocks in orange represent probes used for current acquisition and to

observe the electromagnetic Torque.

� The blue block is the software i.e. the FOC algorithm to be implanted in the

microprocessor.

� The reference values of torque and flux are in red.

The file ‘paramfoc.m’ contains all the machine and control parameters used in the

FOC block, namely:

Machine Parameters: � ‘Lm’ - Mutual Inductance � ‘Rs’ - Stator Winding Resistance � ‘Lls’ - Stator Leakage Inductance � ‘Rr’ - Rotor Winding Resistance � ‘Llr’ - Rotor Leakage Inductance

8�∗

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FOC Parameters:

� ‘kp’ - Proportional Gain (flux PI)

� ‘ki’ – Integral Gain (flux PI) � ‘csat’ - Flux output limits � ‘h’ - hysteresis band of the Current Regulator � ‘freq_max’ - Maxing Switching frequency � ‘fc - low pass’ - filter cut-off frequency used in Flux PI block to filter the

estimated flux � ‘Tfc’ - sampling time of the FOC block which must be a multiple of the

simulation time step.

These machine and control parameters can be modified for different machines to

achieve desirable performance.

3.4.1 SIMULINK Block FOC

Figure 9: Block FOC

In addition to the different blocks discussed above which make up the complete FOC

block, other blocks have also been used to discretize it. The switching control

block is used to limit the inverter commutation frequency to a maximum value

specified by the user.

3.5 SIMULINK sub FOC Blocks

Figures 10 - 13 represent the SIMULINK version of various FOC blocks explained

earlier i.e. blocks used for coordinate transformation namely the Park and Inverse

Park transformations.

Figure 10: Flux Estimator

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Figure 11: Flux Orientation Calculation

Figure 12: Flux PI

Before being compared to its reference value the estimated flux value is filtered by passing it through a low pass filter.

Figure 13: 345

∗ Calculation

This block uses the relation �� =

!�

"#

"$(������) to calculate i*qs.

Figure 14: Current Regulator

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3.5 FOC Simulation Results

The results elaborated below were obtained on varying the sampling times (Ts) while maintaining the reference torque and reference flux constant at 30N-m and 0.3wb respectively and the hysteresis comparator bandwidth set to 0.1A. The initial conditions as specified below and simulation time of 2 seconds was kept the same. Motor Initial Conditions:

� Initial Current, phase A = 0 � Initial Current, phase B = 0 � Initial Current, phase C = 0 � Slip Initial value = 1 � Initial Rotor Position = 0

1) For Ts=1µs

Figure 15: Result FOC 1

An error of ± 2% is observed.

2) For Ts=10µs

Figure 16: Result FOC 2

An error of -6% to +2% is observed.

Time (seconds)

To

rqu

e (

N-m

)

Time (seconds)

To

rqu

e (

N-m

)

Hamid KHAN 19

3) For Ts=100µs

Figure 17: Result FOC 3

For this case the error ranges from -50% to +13%, but for most of the time it

oscillates between -25% to -5%.

Time (seconds)

To

rqu

e (

N-m

)

Hamid KHAN 20

4 FOC Speed Regulation 4.1 Introduction

The final objective of this application is to enable the control of the motor speed by

applying desired torque. To achieve this objective a speed controller is added to the

existing system in a closed loop with the motor. This Speed Controller then provides

the flux and torque reference values to the FOC Block.

4.2 MATLAB Simulation of FOC Speed Regulator

Figure 17 details the complete SIMULINK model of the speed regulation system

using the FOC scheme (as explained earlier).

Figure 18: FOC with speed controller

4.2.1 Speed Controller In addition to the machine and FOC parameters, the file ‘paramspeed.m’ contains all

the control parameters of the Speed Controller block.

Speed Control Parameters:

� ‘nf’ - nominal Machine Flux. � ‘ctrl_sat’ – Defines the torque output limits in N-m. � ‘ramp’ – Limits the acceleration and deceleration to the defined value in rpm/s. � ‘Skp’ - Proportional gain of the speed controller PI regulator. � ‘Ski’ - Integral gain of the speed controller PI regulator. � ‘Sfc’ - Speed measurement low pass filter cut-off frequency in Hz � ‘Tsc’ - Speed Controller Sampling time.

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Figure 19: Speed Controller Block

The speed controller block contains ‘Speed PI’ block and the ‘Flux table’ block. The Speed PI block is an ordinary PI regulator with the speed error signal calculated from the comparison of the Speed Reference value and the actual speed as its input. The torque reference value is its output which is then provided to the FOC block as input.

4.2.1.1 Flux Table The Flux Table contains the flux values corresponding to different speeds, which is

based on the fact that at low speed high torque is required and at high speed low

torque is required. Since torque is proportional to the machine flux, so at high speed

a fraction of the nominal machine flux is used while at very low speed the machine is

magnetized at the nominal flux to induce high torque.

Hamid KHAN

4.2 FOC Speed Regulator Simulation Results

In this section speed regulation

parameters such as maximum permissible torque

All results discussed are based on a

time of 100 µs.

1) Simulation result # 1

Figure

Motor at No-Load with,

Maximum permissible torque =

Maximum Permissible Acceleration

Observations:

Steady state error ≤ 1%

Rise Time ≈ 0.8s.

2) Simulation result # 2

Figure

Motor Load = 5Nm.

Maximum permissible torque

Maximum Permissible Acceleration

Observations:

Steady state error ≤1%

Sp

ee

d (

rpm

) S

pe

ed

(rp

m)

4.2 FOC Speed Regulator Simulation Results

speed regulation results obtained on varying

parameters such as maximum permissible torque and loads applied are discussed.

based on a 1400 rpm Speed Reference

Figure 20: Result Speed Regulation 1

issible torque = 20 N-m

cceleration = 1500rpm/s.

Figure 21: Result Speed Regulation 2

aximum permissible torque = 20 N-m

cceleration =1500rpm/s.

Time (seconds)

22

results obtained on varying speed control

and loads applied are discussed.

Speed Reference and a sampling

Hamid KHAN

Rise time ≈ 1.2s

3) Simulation Result # 3

Figure

Motor at No-Load with,

Maximum permissible torque

Maximum Permissible Acceleration =

Observations:

Steady state error ≤1%

Rise time ≈0.6s.

4) Simulation Result # 4

Figure 2

Motor Load = 5Nm

Maximum permissible torque

Maximum Permissible Acceleration =

Observations:

Steady state error ≤ 1%

Rise time ≈0.8s.

Sp

ee

d (

rpm

) S

pe

ed

(rp

m)

Figure 22: Result Speed Regulation 3

aximum permissible torque = 25 N-m

Acceleration = 1500rpm/s.

Figure 23: Result Speed Regulation 4

aximum permissible torque = 25 N-m

Acceleration = 1500rpm/s

Time (seconds)

Time (seconds)

23

Hamid KHAN 24

CONCLUSION

The simulation results validate FOC as a very powerful machine torque control

scheme with exceptional dynamics. Not only is the reference torque attained in less

than 8m seconds; a good torque control for both sampling times of the order of 1µs

and 10µs are also achieved. The degraded performance for a sampling time of

100µs order can be justified as the rotor time constant is no longer very small in

comparison to the sampling time.

The results obtained for the Speed Regulator; the speed regulator’s minimal error

margin of ±1%, under both loaded and unloaded condition, for a sampling time as

large as 100µs bears further testimony to the capability of vector control technique.

The low speed error can be attributed to the machine shaft inertia which filters out

any sharp impact on the speed caused by an oscillating torque.

By redefining the maximum torque and acceleration limit parameters the rise time

could also be modified easily.

This application note elaborates how by using the developed SIMULINK model of the

FOC Speed Regulator can be adapted to the various application requirements by

simply modifying the control parameters in the MATLAB file ‘paramspeed.m’.

Hamid KHAN 25

REFERENCE

1. Contrôle des machines tournantes, Jean-Pierre Plumey. 2. Commande des machines – ELT7, 4 November 2008, R. Chapuis. 3. EE8412 Advanced AC Drive Systems ABB. 4. Field Orientated Control of 3-Phase AC-Motors Texas Instruments. 5. http://www.mathworks.com/ Electric Drives. 6. Bose, B. K., Modern Power Electronics and AC Drives, Prentice-Hall, N.J.,

2002.