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35 Fuzzy Logic in Electric Drives 1007

NM NS PS PM

PLNL

Acceleration Error (rad/sec

)

Membership Value

3697 38

−738 −369

FIGURE 35.11 Membership functions for the acceleration error.

PLNL

Speed Error (rad/sec)

Membership Value

NMS

PMS

049

104

204

−209

−104

−49

FIGURE 35.12 Membership functions for the speed error.

TABLE 35.4 Decision table for speed control

Velocity error

NL NM NMS NS ZERO PS PMS PM PL

Acceleration error

PL NS NVVS PVVS PVS PS PMS PM PL PVVL

PM NMS NVS ZERO PVVS PVS PS PMS PML PVL

PS NMS NS NVVS ZERO PVVS PVS PS PM PL

ZERO NML NMS NVS NVVS ZERO PVVS PVS PMS PML

NS NL NM NS NVS NVVS ZERO PVVS PS PML

NM NVL NML NMS NS NVS NVVS ZERO PVS PMS

NL NVVL NL NM NMS NS NVS NVVS PVVS PS

Equation (35.17) shows the fuzzy centroid used to compute

the ﬁnal output of the controller.

Output =



+···+w

+···+W



(35.17)

The weights w

will be the strength of each particular rule’s

evaluation. The rule strength is evaluated as the product of

the membership values associate with the speed and accelera-

tion errors for the particular fuzzy variables involved in that

rule. Since the membership functions were comprised solely of

fuzzy singletons and the AND operator is evaluated as a prod-

uct, the strength of each rules evaluation (w

) will be either

0 or 1. Additionally, since the membership functions do not

overlap, only one rule will be evaluated as true at each sample

time. Thus all the weights w

will be zero except one. So the

actual implementation can be simpliﬁed.

35.3.3 Fuzzy Logic-based Position Controller

The task of the position control algorithm is to force the rotor

position of the motor to follow a desired reference track with-

out overshoot. The same method applied to the fuzzy speed

controller is applied to the position controller. The inputs to

the fuzzy position controller are, angular position error (θ

)

and motor speed error (ω

). The output from the controller is

1008 A. Rubaai

TABLE 35.5 Fuzzy variables of the speed error for position control

Fuzzy variable Speed error (rad/s)

(NL) x

≤−209

(NM) −209 < x

≤−104

(NS) −104 < x

< 0

(ZE) x

= 0

(PS) 0 < x

< 104

(PM) 104 ≤ x

< 209

(PL) 209 ≤ x

a change in the motor voltage. The two inputs are deﬁned as

follows

= θ

ref

−θ

act

(35.18)

= ω

ref

−ω

act

(35.19)

where

ref

= the desired position in radians.

act

= the measured position in radians.

ref

= 0, because we want to minimize the speed to zero.

act

= the measured speed in radians/second.

Nine fuzzy variables were deﬁned for the position error and

seven for the speed error. The fuzzy variables for the posi-

tion error and the speed error are deﬁned in Tables 35.5

and 35.6, respectively. After specifying the fuzzy sets for the

position controller, the membership functions can be fully

deﬁned, it is required to determine the membership functions

for these sets. The membership function for the fuzzy variable

ZERO is a fuzzy singleton. Additionally, the other member-

ship functions are of the type described in Eq. (35.6) and are

composed of fuzzy singletons within the region deﬁned for

each particular fuzzy variable. Figures 35.13 and 35.14 show

the resulting membership function for the speed and position

errors respectively.

NM NS PS PM

PLNL

eed Error

(

rad/sec

)

Membership Value

104 209

−209 −104

FIGURE 35.13 Membership functions for the speed error.

TABLE 35.6 Fuzzy variables of position error (θ

) for position control

Fuzzy variable Position error (rad)

(NL) θ

≤−2.21

(NM) −2.21 <θ

≤−1.05

(NMS) −1.05 <θ

≤−0.53

(NS) −0.53 <θ

< 0

(Z) θ

= 0

(PS) 0 <θ

< 0.53

(PMS) 0.53 ≤ θ

< 1.05

(PM) 1.05 ≤ θ

< 2.21

(PL) 2.21 ≤ θ

A corresponding output to the motor based on the speed

and the rotor position error detected in each sampling interval

must be assigned and thereby specifying the fuzzy inference

engine. This is done by the fuzzy rules. For example, IF the

position error is PL AND the speed is PS, THEN a large pos-

itive change in driving effort is used. The crisp (defuzziﬁed)

output signal of the fuzzy controller is obtained by calculating

the centriod of all fuzzy output variables. Fuzzy rule-base, on

which the required change in the motor voltage is generated,

is illustrated in Table 35.7.

35.4 Hardware System Description

The BLDC drive system under control consists of the compo-

nents illustrated in Fig. 35.15. The drive system is made up

of several distinct subsystems: the motor, a personal computer

(PC), the driving circuit, and the microprocessor evaluation

board. The motor is 1/4 HP, 3000-rev/min BLDC motor, and

was manufactured by Pittman Company. The BLDC motor is

equipped with a hall-effect sensor and an incremental opti-

cal encoder. The hall-effect sensors detect the rotor position

to indicate which of the three phases of the motor is to be

excited as the motor spins. The optical position encoder with

35 Fuzzy Logic in Electric Drives 1009

PLNL

Position Error (rad)

Membership Value

NMS

PMS

0 0.53

1.05

2.21

−2.21

−1.05

−0.53

FIGURE 35.14 Membership functions for the position error.

TABLE 35.7 Decision table for position control

Position error

NL NM NMS NS ZERO PS PMS PM PL

Speed error

PL NS NVVS PVVS PVS PS PMS PM PL PVVL

PM NMS NVS ZERO PVVS PVS PS PMS PML PVL

PS NMS NS NVVS ZERO PVVS PVS PS PM PL

ZERO NML NMS NVS NVVS ZERO PVVS PVS PMS PML

NS NL NM NS NVS NVVS ZERO PVVS PS PML

NM NVL NML NMS NS NVS NVVS ZERO PVS PMS

NL NVVL NL NM NMS NS NVS NVVS PVVS PS

Reference

Track

Microprocessor

Evaluation

Board

DAC

Brushless

Motor

Position

Decoder

Host

Computer

Direction

Position

Speed

Converter

Speed

Hall

Feedback

Pulse

Switching

Logic

DC/AC

Converter

Direction

Gating

Signals

Integrated Circuit

(UDN2936-120)

Control Signal

(k)

Load

Motor

Encoder

FIGURE 35.15 Block diagram of the laboratory setup.

resolution of 500 pulses/revolution is used to give speed and

position feedback.

The controller is implemented by software and executed

using a microprocessor. The control algorithm is written and

loaded into the microprocessor using the PC. The computer

used is an IBM 486 PC. The driving circuit is constructed

using two major components: (1) the integrated circuit

(UDN2936W-120) designed for BLDC Drives [13] and (2) the

digital to analog converter (DAC) and power ampliﬁer. The

inputs to the integrated circuit are the rotor position (which

is obtained from hall-effect sensors), the direction of desired

1010 A. Rubaai

rotation, and the magnitude of the control voltage. The out-

put of the switching logic section is a sequence of gating signals

that are pulse width modulated (PWM). These signals are used

to drive the power converter portion of the chip. The power

converter is a DC/AC inverter utilizing six MOSFETs. The

output of the power converter is a chopped three-phase AC

waveform.

The microprocessor used was the Motorola MC68HC11E9

microprocessor [14]. The on board memory system includes

8k bytes of read only memory (ROM), 512 bytes of electrically

erasable programmable (ROM) (EEPROM), and 256 bytes of

random access memory (RAM). The processor also has four

eight bit parallel input/output ports, namely, A, B, C, and E.

The program is completely contained in the microprocessor

and the computer is only required to load new programs

into the processor. Additionally, it has an internal analog-to-

digital converter, and can accept up to four analog inputs.

Figure 35.15 includes the integrated circuit (UDN2936W-120)

designed for operating the BLDC motor. The range of the

input voltage (control voltage) is between zero and 25 V. The

motor speed for any control voltage less than 7 V is zero. This

indicates that the motor requires a minimum of 7 V to start.

This limitation is actually a protective feature of the circuit

to prevent malfunctions [13]. Thus, the actual output of the

microprocessor (the control signal V

(k)) is added to a seven

FIGURE 35.16 Photograph of the hardware implementation.

volt DC offset, using a summing ampliﬁer. The current out-

put of the summing ampliﬁer must be ﬁrst increased before

it can be used to drive the motor. The current ampliﬁcation

is accomplished by using a 40 V power transistor (TIP31A).

Additionally, when a sudden change in speed or direction

occurs, the back EMF produced by the motor can, sometimes,

cause large currents. Since the output stage of the integrated

circuit (UDN2936W-120) has transistors with a current rat-

ing of ±3 A, some limiting resistors were needed to prevent

damage. Figure 35.16 shows a snapshot of the laboratory

experiment.

Speed measurements were taken using a frequency to volt-

age converter LM2907. The LM2907 produces a voltage pro-

portional to the frequency of the pulses it receives at its input.

In this experiment, the pulses were sourced from the encoder

signal-A. The circuit was constructed such that the maximum

speed of the motor was corresponded to 5 V. This value was

the input to the microprocessor, via the on chip A/D con-

verter, as an 8-bit word. The direction of rotation was observed

using a D-ﬂip-ﬂop. This direction signal was used to indicate

the sign of the speed. The two signals, speed and direction,

were combined within the software environment to produce

an integer. Thus internally the speed could range from +256 to

–256. These limits represent +3000 and –3000 R.P.M. respec-

tively. Additionally, the digital output of the microprocessor

35 Fuzzy Logic in Electric Drives 1011

was limited to the resolution provided by seven bits. Therefore,

if the desired output voltage was 22 V, then the maximum byte

output was 127. Thus each increment in control signal, numer-

ically within the microprocessor, would produce a change of

0.17 V.

35.4.1 Experimental Results

A square-wave followed by sinusoidal reference track was con-

sidered. In this experiment, there is a weight attached to the

motor via a cable and pulley assembly. Figure 35.17 shows

the speed tracking performance of the fuzzy logic controller.

The motor is under constant load. The actual motor speed is

superimposed on the desired reference speed in order to com-

pare tracking accuracy. High tracking accuracy is observed at

Time (Sec)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Speed (Rad/Sec)

300

250

200

150

100

FIGURE 35.17 Fuzzy speed tracking under loading condition.

Time (Sec)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Position (Rad)

6.45

5.16

3.87

2.58

1.29

0.00

FIGURE 35.18 Fuzzy position tracking under loading condition.

all speeds. The corresponding position tracking performance is

displayed in Fig. 35.18. Reasonable position tracking accuracy

is displayed. One can see from these ﬁgures that the results

were very successful. For comparison purposes, Figs. 35.19

and 35.20 exhibit cases in which the fuzzy logic controller was

replaced by a bang–bang controller. However, when bang–

bang controller was applied, the controller could not maintain

tracking accuracy. That is, the response using the bang–bang

controller was unsatisfactory.

35.5 Conclusion

This chapter describes a fuzzy logic-based microprocessor

controller, which incorporates attractive features such as

1012 A. Rubaai

Time (Sec)

Speed (Rad/Sec)

300

250

200

150

100

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

FIGURE 35.19 Bang–bang speed tracking under loading condition.

Time (Sec)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Position (Rad)

6.45

5.16

3.87

2.58

1.29

0.00

5.0

FIGURE 35.20 Bang–bang position tracking with load.

simplicity, good performance, and automation while utiliz-

ing a low cost hardware and software implementation. The

test results indicate that the fuzzy logic-tracking controllers

follow the trajectories successfully. Additionally, experimental

results show that the effective smooth speed/position control

and tracking of brushless DC (BLDC) motors can be achieved

by the fuzzy logic controler (FLC), thus making it suitable

for high performance motor drive applications. The controller

design does not require explicit knowledge of the motor/load

dynamics. This is a useful feature when dealing with param-

eter and load uncertainties. The advantage of using a fuzzy

logic-tracking controller in this application is that it is well

suited to the control of unknown or ill-deﬁned non-linear

dynamics.

35 Fuzzy Logic in Electric Drives 1013

Acknowledgments

The author would like to acknowledge the assistance of

Mr. Daniel O. Ricketts, a graduate student at Howard Univer-

sity in clarifying these concepts and obtaining the experimental

results. The author would also like to acknowledge the ﬁnan-

cial support by NASA Glenn Research Center, in the form of

grant no. NAG3-2287 technically monitored by Mr. Donald

F. Noga.

Further Reading

1. Ross, T. J., Fuzzy Logic with Engineering Applications, McGraw-Hill,

1995.

2. Mitra, S. and Pal. K. S., “Fuzzy Self-Organization, Inferencing, and

Rule Generation,” IEEE Trans. Syst., Man, Cybern.– Part A: Syst.

Humans, Vol. 26, No. 5, pp. 608–619, September 1996.

3. Jamshidi, M., Vadiee, N. and Ross, T. Fuzzy Logic and Control,

Prentice Hall, 1993.

4. Lee, C. C., “Fuzzy Logic in Control Systems: Fuzzy Logic Controller.

Part I,” IEEE Trans. Syst., Man, Cybern, Vol. 20, No. 2, pp. 404–418,

March/April 1990.

5. Lee, J., “On Methods for Improving Performance of PI-Type Fuzzy

Logic Controllers,” IEEE Trans. Fuzzy Systems, Vol. 1, No. 4,

November 1993.

7. Lofti, A. and Tsoi, A. C. “Learning Fuzzy Inference Systems Using and

Adaptive Membership Function Scheme,” IEEE Trans. Syst., Man,

Cybern., Vol. 26, No. 2, pp. 326–331, April 1996.

8. Lofti, A., Andersen, H. C., and Tsoi, A. C. “Matrix Formulation of

Fuzzy Rule-Based Systems,” IEEE Trans. Syst., Man, Cybern., Vol. 26

No. 2, pp. 332–339, April 1996.

9. Motorola, MC68HC11E9 Technical Data Manual, 1990.

10. Rubaai, A., Kotaru, R. and David Kankam, M. “A Continually

Online-Trained Neural Network Controller for Brushless DC Motor

Drives,” IEEE Trans. Ind. Appl., Vol. 36, No. 2, pp. 475–483,

March/April 2000.

11. Ross, T. J., Fuzzy Logic with Engineering Applications, McGraw-Hill,

1995.

12. Rubaai, A. and Kotaru, R. “Neural Net-Based Robust Controller

Design for Brushless DC Motor Drives,” IEEE Trans. Syst., Man,

Cybern., Part C: Applications and Review, Vol. 29, No. 3,

pp. 460–474, August 1999.

13. Allegro, UDN2936W-120 Technical Data Manual, 1993.

14. Marks II, R. J. (Editor), Fuzzy Logic Technology and Applications,

IEEE Press, 1994.

15. Zadeh, L. “Outline of a New Approach to the Analysis of Complex

Systems and Decision Processes,” IEEE Trans. Syst., Man, Cybern.,

Vol. 3, No. 1, pp. 28–44, January 1973.

Artiﬁcial Neural Network

Applications in Power Electronics

and Electrical Drives

B. Karanayil, Ph.D. and

M.F. Rahman, Ph.D.

School of Electrical Engineering and

Telecommunications,

The University of New South

Wales, Sydney, New South Wales

2052, Australia

36.1 Introduction ........................................................................................ 1015

36.2 Conventional and Neural Function Approximators..................................... 1016

36.2.1 Conventional Approximator • 36.2.2 Neural Function Approximator

36.3 ANN-based Estimation in Induction Motor Drives ..................................... 1017

36.3.1 Speed Estimation • 36.3.2 Flux and Torque Estimation • 36.3.3 Rotor Resistance

Identiﬁcation Using ANN • 36.3.4 Stator Resistance Estimation Using ANN

36.4 ANN-based Controls in Motor Drives ...................................................... 1025

36.4.1 Induction Motor Current Control • 36.4.2 Induction Motor Control

• 36.4.3 Efﬁciency Optimization in Electric Drives

36.5 ANN-based Controls in Power Converters ................................................ 1029

Further Reading ................................................................................... 1030

36.1 Introduction

In classical control systems, knowledge of the controlled sys-

tem (plant) is required in the form of a set of algebraic and

differential equations, which analytically relate inputs and out-

puts. However, these models can become complex, rely on

many assumptions, may contain parameters which are difﬁcult

to measure or may change signiﬁcantly during operation as in

the case of the rotor ﬂux oriented control (RFOC) induction

motor drive. Classical control theory suffers from some limita-

tions due to the assumptions made for the control system such

as linearity, time-invariance, etc. These problems can be over-

come by using artiﬁcial intelligence-based control techniques,

and these techniques can be used, even when the analytical

models are not known. Such control systems can also be less

sensitive to parameter variation than classical control systems.

The main advantages of using artiﬁcial intelligence-based

controllers and estimators are:

• Their design does not require a mathematical model of

the plant.

• They can lead to improved performance, when properly

tuned.

• They can be designed exclusively on the basis of linguistic

information available from experts or by using clustering

or other techniques.

• They may require less tuning effort than conventional

controllers.

• They may be designed on the basis of data from a real

system or a plant in the absence of necessary expert

knowledge.

• They can be designed using a combination of linguistic

and response-based information.

Generally, the following two types of intelligence-based

systems are used for estimation and control of drives, namely:

(a) Artiﬁcial Neural Networks (ANNs)

(b) Fuzzy Logic Systems (FLSs)

In different applications in power electronics and electrical

drives, there are occasions where an output y has to be esti-

mated for an input x. This is generally accomplished with the

help of mathematical equations of the system under consider-

ation. Sometimes it may not be possible to have an accurate

mathematical model, or there is no conventional model at

all which can be used. In these circumstances, model-free

1015

1016 B. Karanayil and M. F. Rahman

estimators required which can be either using ANNs or fuzzy

logic systems. A mathematical model-based system can operate

smoothly when there is no noise in the inputs but they might

fail when the input has noise or if the inputs themselves are

uncertain. Also, depending on the complexity of the mathe-

matical model, the computation times can be excessive leading

to difﬁculties for practical implementation.

A conventional function approximator, a neural function

estimator, and how these estimators are arrived at are discussed

brieﬂy in Section 36.2. It will be shown how neural estimators

are used in the estimation of speed, ﬂux, torque, etc. for an

induction motor. Some of these estimators are brieﬂy reviewed

in Section 36.3. Also, the ANNs have been used for identiﬁca-

tion and control of stator current in induction motor drives

and these are brieﬂy described in Section 36.4. In addition to

their applications to motor drives, they are also used in control

of power converters. Some of these applications are discussed

in Section 36.5.

36.2 Conventional and Neural Function

Approximators

36.2.1 Conventional Approximator

A conventional function approximator should give a good pre-

diction of output data, when a system is presented with a

new input data. A conventional function approximator uses

a mathematical model of the system as shown in Fig. 36.1a.

Sometimes it is not possible to have an accurate mathematical

model of the system, in such a case; mathematical model free

approximators are required, as shown in Fig. 36.1b. A con-

ventional function approximator can easily be replaced by a

neural network-based function approximator.

36.2.2 Neural Function Approximator

The function y = f (x

, x

, ..., x

) is the function to

be approximated and x

, x

, ... x

are the n variables

(n inputs) and the approximator uses the sum of non-linear

functions g

, g

, ...g

, where each of the g are non-linear

Mathematical

Function

Approximator

[Mathematical Model

For y = f (x)]

Neural Network

Based Function

Approximator

[ No Mathematical

Model ]

(a) (b)

FIGURE 36.1 Conventional and neural network-based function

approximators.

functions of a single variable. Thus

y = f (x

, x

, ..., x

) = g

+···+g

2n+1



2n+1

i=1

(36.1)

where g

is a real and continuous non-linear function which

depends only on a single variable z

. The output y can also be

represented as;

y =



j=1

= w

+···w

(36.2)

These equations can be represented by a network shown in

Fig. 36.2. There are n input nodes in the input layer, M hidden

nodes in the hidden layer.

Figure 36.3 shows the schematic diagram of a neural approx-

imation and Fig. 36.4 shows the technique of its training.

The error (e) between the desired non-linear function (y) and

the non-linear function (ˆy) obtained by the neural estimator

Input

Layer

Output

Layer

Hidden

Layer

FIGURE 36.2 Artiﬁcial neural network to generate the required

function.

Neural Function

Approximator

FIGURE 36.3 Schematic of a neural function approximator.

Desired Non-linear

Function

Neural Estimator

error

y = f (x)

Learning

Algorithm

FIGURE 36.4 Training of a neural function approximator.

36 ANN Applications in Power Electronics and Electrical Drives 1017

−10 −8 −6 −4 −20 2

810

−1

−0.5

0.5

1.5

−10 −8 −6 −4 −20246810

0.2

0.4

0.6

0.8

1.2

1.4

−10 −8 −6 −4 −202468

−10

−5

f (x)

xxx

logsigmoid tansigmoid purelin

FIGURE 36.5 Logsigmoid, tansigmoid, and purelin activation functions.

is the input to the learning algorithm for the artiﬁcial neural

estimator. This type of learning is known as back propagation.

The output of a single neuron can be represented as

= f









j=1

(t) + b







(36.3)

where f

is the activation function and b

is the bias. Figure 36.5

shows a number of possible activation functions in a neuron.

The simplest of all is the linear activation function, where the

output varies linearly with the input but saturates at ±1as

shown with a large magnitude of the input. The most com-

monly used activation functions are non-linear, continuously

varying types between two asymptotic values 0 and 1 or −1

and +1. These are respectively, the sigmoidal function also

called logsigmoid and the hyperbolic tan function also called

tansigmoid.

The learning process of an ANN is based on the training

process. One of the most widely used training techniques is

the error back-propagation technique; a scheme which is illus-

trated in Fig. 36.4. When this technique is employed, the ANN

is provided with input and output training data and the ANN

conﬁgures its weights. The training process is then followed by

supplying with the real input data and the ANN then produces

the required output data.

The total network error (sum of squared errors) can be

expressed as

E =



k=1



j=1



−o



(36.4)

where E is the total error, P is the number of patterns in the

training data, k is the number of outputs in the network, d

the target (desired ) output for the pattern K and o

(= y

)is

the jth output of the kth pattern. The minimization of the error

can be arranged with different algorithms such as the gradi-

ent descent with momentum, Levenberg–Marquardt, reduced

memory Levenberg–Marquardt, Bayesian regularization, etc.

36.3 ANN-based Estimation in Induction

Motor Drives

Artiﬁcial neural networks have found widespread use in func-

tion approximation. It has been shown that, theoretically,

a three layer ANN can approximate arbitrarily closely, any

non-linear function, provided it is non-singular. Some of the

ANN-based estimators reported in the literature for rotor ﬂux,

torque and rotor speed of induction motor drive are discussed

in the following section.

36.3.1 Speed Estimation

In general, steady-state and transient analysis of induction

motors is done using space vector theory, with the mathemat-

ical model having the parameters of the motor. To estimate

the various machine quantities such as stator and rotor

ﬂux linkages, rotor speed, electromagnetic torque, etc., the

above mathematical model is normally used. However, these

machine quantities could be estimated without the mathemat-

ical model by using an ANN. Here no assumptions have to be

made about any type of non-linearity.

As an example, the rotor speed of an induction motor can be

estimated from the direct and quadrature axis stator voltages

and currents in the stationary reference frame, as shown in

Fig. 36.6. A three layer feedforward neural network structure

with 8 × 7 × 1 (8 input, 7 hidden, and 1 output) is used

in this case. The input nodes were selected as equal to the

number of input signals and the output nodes as equal to

the number of output signals. The number of hidden layer

neurons is generally taken as the mean of the input and output