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CHAPTER 3

PERFORMANCE ANALYSIS WITH PI, ANFIS AND

SLIDING MODE CONTROLLERS

3.1 INTRODUCTION

The Permanent Magnet Synchronous Motor (PMSM) has a

sinusoidal back emf and requires sinusoidal stator currents to produce

constant torque while the permanent magnet brushless dc (PMBLDC) motor

has a trapezoidal back emf and requires rectangular stator currents to

produce constant torque (Miller 1989). The system is becoming increasingly

attractive in high-performance variable-speed drives since it can produce

torque-speed characteristic similar to that of a permanent-magnet

conventional dc motor while avoiding the problems of failure of brushes and

mechanical commutation. The PMBLDC motor is becoming popular in

various applications because of its high efficiency, high power factor, high

torque, simple control and lower maintenance. BLDC motor is one type of

synchronous motor, which can be operated in hazardous atmospheric

condition and at high speeds due to the absence of brushes.

Pillay et al (1985) and Krishnan et al (1990) have investigated that

the PMSM a sinusoidal back emf and requires sinusoidal stator currents to

produce constant torque, while the BLDC motor has a trapezoidal back emf

and motor requires rectangular stator current to produce constant torque.

(Bhim singh et al 2002) have proposed a digital speed controller for BLDC

motor and implemented in a digital signal processor (DSP). Later in 1998, the

62

rotor position and the speed of permanent magnet have been estimated using

Extended Kalman filter (EKF) by Peter Vas et al (1998). Jadric et al (2001)

have proposed that the hall effect sensor are usually needed to sense the rotor

position which senses the position signal for every 60 degree electrical. The

mathematical model of the BLDC motor has been developed and validated in

MATLAB platform with proportional-integral (PI) speed controller

(Varatharaju et al 2011). Host of efforts has attempted and solved the problem

of non linearity and parameter variations of PMBLDC drive (Lajoie et al

1985, Sebastain et al 1989, Rubai et al 1992, Luk at al 1994 and Radwan et al

2005).

The draw-backs of Fuzzy Logic Control (FLC) and Artificial

Neural Network (NN) can be over come by the use of Adaptive Neuro-Fuzzy

Inference System (ANFIS) (Zhi Rui Huang et al 2006 and Uddin 2007).

ANFIS is one of the best tradeoff between neural and fuzzy systems,

providing: smooth control, due to the FLC interpolation and adaptability, due

to the NN back propagation. Some of advantages of ANFIS are model

compactness, require smaller size training set and faster convergence than

typical feed forward NN. Since both fuzzy and neural systems are universal

function approximators, their combination, the hybrid neuro-fuzzy system is

also a universal function approximator. The non-linear mapping in a neuro-

fuzzy network is obtained by using a fuzzy membership function based neural

network.

Using the developed model of the BLDC motor, a detailed

simulation and analysis of a BLDC motor speed servo drive is obtained.

Closed loop control of PMBLDC motor drive consisting of PI speed

controller and hysteresis current controller is simulated. In addition, the

ANFIS controller and SMC also designed.

63

3.2 PI CONTROLLER

To accurately control the speed of drive without extensive operator

involvement, a speed control system that relies upon a controller is essential.

The speed control system accepts the actual motor speed through a speed

sensor such as a Tacho generator or Hall sensors, encoders etc as input. It

compares the actual speed to the desired control speed otherwise called set

point, and provides an output, which adjusts the duty cycle of PWM pulses

applied to the IGBT based VSI fed BLDC drive. The controller is one part of

the entire control system and the whole system should be analyzed in

selecting the proper controller. The following factors should be considered

when selecting a controller:

(i) Type of input sensor (Hall sensors/encoders/Tacho generator/

Revolvers) and speed range

(ii) Type of output required (electromechanical relay, solid state

relay, analog output or digital output)

(iii) Control algorithm needed (On/Off, Proportional, PI, PID)

(iv) Type of outputs required for forward/reverse motoring with

controlled current mode of operations

Only very moderate control of speed can be achieved by causing

motor power to be simply switched ON and OFF according to an under or

over speed condition respectively. Ultimately, the motor power will be

regulated to achieve a desired system speed but refinement can be employed

to enhance the control accuracy.

Such refinement is available in the form of Proportional (P),

Integral (I) and Derivative (D) functions applied to the control loop. These

functions, referred to as control terms can be used in combination according

64

to system requirements. The proposed scheme uses combination of P and I

controller to achieve precise speed control.

To achieve optimum speed control, irrespective of the technique

employed, one should ensure:

(a) Adequate motor power is available

(b) The hall sensor or encoder that acts as a speed sensor, is

located in a suitable place so as to measure actual shaft speed

such that it will respond for dynamic changes occurring in the

motor shaft.

(c) Adequate Sensor Measuring Range in the system to

optimize the measuring sensitivity under varying load or speed

conditions.

Proportional Integral controller is most preferable controller in

industries for servo drives for closed loop control that requires analytical

model and transfer function of the system. Tuning of PI parameters over

entire range of control is difficult and time consuming task. The proposed

scheme eliminates that PI tuning difficulties. PI controller implementation is

done in varies digital controllers.

Tuning a PID controller, involves setting the Proportional gain KP,

Integral gain KI, and Derivative gain KD values to get the best possible

control for a particular process. If the controller does not include an auto tune

algorithm, then the unit must be tuned using trial and error. Tuning of the PID

settings is quite a subjective procedure, relying heavily on the knowledge and

skill of the control or design engineer. Although tuning guidelines are

available, the process of controller tuning can still be time consuming with the

result that many plant control loops are often poorly tuned and full potential

65

of the control system is not achieved. The effect of change is gain of P, I and

D controller upon the system response are highlighted in Fig 3.1 to 3.3.

Figure 3.1 Effect of changes in KP

Figure 3.2 Effect of changes in KI

66

Figure 3.3 Effect of changes in KD

PI controller is widely used in industry due to its ease in design and

simple structure. The rotor speed r(n) is compared with the reference speed

r*(n) and the resulting error is estimated at the nth sampling instant as :

*

e r r(n) (n) (n) (3.1)

The new value of torque reference is given by:

(n) (n 1) p e e 1 eT T K ( (n) (n 1) K ( (n) (3.2)

Where e (n 1) is the speed error of previous interval, and e(n) is the speed

error of the working interval. Kp and K1 are the gains of PI speed controller.

By using Ziegler Nichols method the Kp and KI values are determined. Figure

3.4 show the block diagram of typical closed loop control of BLDC motor

drive.

67

Speed PI

Regulator

PWM

Technique

Voltage

source

3- phase

Inverter

Rectifier

3-Phase

BLDC

Motor

Speed by

Hall

Sensors

PWM 1~6

*

r*

s

rr

r

slip

r

Figure 3.4 Closed Loop arrangement with motor and sensors

3.3 ANFIS CONTROLLER

In this section basics of ANFIS and development of ANFIS

controller are given. ANFIS uses the neural networks ability to classify data

and find patterns. It then develops a fuzzy expert system that is more

transparent to the user and also less likely to produce memorization error than

a neural network. ANFIS keeps the advantages of a fuzzy expert system,

while removing (or at least reducing) the need for an expert. The problem

with ANFIS design is that large amounts of training data require developing

an accurate system. The ANFIS, first introduced by Jang (1993), is a

universal approximator and, as such, is capable of approximating any real

continuous function on a compact set to any degree of accuracy (Jain et al

1999, Jang et al 1993 and Jang et al 1997). ANFIS is a method for tuning an

existing rule base with a learning algorithm based on a collection of training

data. This allows the rule base to adapt.

68

The section presents a methodology for developing adaptive speed

controllers in a BLDC motor drive system. A PI controller is employed in

order to obtain the controller parameters at each selected load. The resulting

data from PI controller are used to train ANFIS that could deduce the

controller parameters at any other loading condition within the same region of

operation. The ANFIS controller is tested at numerous operating conditions

with hysteresis current controlled position determination. The section also

provides comparison of PI controller with ANFIS controller. The BLDC

motor drive system with PI controller exhibits higher overshoot and settling

time when compared to the designed ANFIS controller.

3.3.1 Rules

As a simple example, a fuzzy inference system with two inputs x

and y and one output z is assumed. The first-order Sugeno fuzzy model, a

typical rule set with two fuzzy IfThen rules can be expressed as:

Rule 1: If x is A1 and y is B1, then f1=p1x+q1y+r1 (3.3)

Rule 2: If x is A2 and y is B2, then f2=p2x+q2y+r2 (3.4)

The resulting Sugeno fuzzy reasoning system is shown in

Figure 3.5. Here, the output z is the weighted average of the individual rules

outputs and is itself a crisp value.

3.3.2 ANFIS Architecture

The ANFIS architecture is shown in Figure.3.6. If the firing

strengths of the rules are w1 and w2, respectively, for the particular values of

the inputs Ai and integral of Bi, then the output is computed as weighted

average,

1 1 2 2

1 2

w f w ff

w w (3.5)

69

Let the membership functions of fuzzy sets Ai and Bi, are Ai and Bi.

Layer 1: Each neuron i in layer 1 is adaptive with a parametric

activation function. Its output is the grade of membership function; an

example is the generalized bell shape function.

2b

1(x)

x c1

a

(3.6)

Where [a, b, c] is the parameter set. As the values of the parameters change,

the shape of the bell-shape function varies.

Layer 2: .Every node in layer 2 is a fixed node, whose output is the

product of all incoming signals.

wi = Ai(x) Bi(y), i=1,2 (3.7)

Layer 3: This layer normalizes each input with respect to the

others (The ith

node output is the ith

input divided the sum of all the other

inputs).

ii

1 2

ww

w w (3.8)

Layer 4: This layers ith

node output is a linear function of the third

layers ith

node output and the ANFIS input signals.

i ii i i iw f w (p x q y r ) (3.9)

Layer 5: This layer sums all the incoming signals.

1 21 2f w f w f (3.10)

70

X

X

1A1B

2A 2B

Y

Yx y

1w

2w

1 1 1 1f p x q y r

2 2 2f p x q y r

weighted

average

1 1 2 2

1 2

w f w ff

w w

Main (or)

Pr oduct

Figure 3.5 Two-input first-order Sugeno fuzzy model with two rules

Layer 1

Layer 2 Layer 3Layer 4

Layer 51

A

2A

1B

2B

N

N

y

yx

x

1

2

1

2

1 1f

2 2f

f

Figure 3.6 Equivalent ANFIS architecture

3.4 SLIDING MODE CONTROLLER

Sliding mode control is an important robust control approach. For

the class of systems to which it applies, sliding mode controller design

provides a systematic approach to the problem of maintaining stability and

consistent performance in the face of modelling imprecision.

71

This section investigates variable structure control (VSC) as a high-

speed switched feedback control resulting in sliding mode. For example, the

gains in each feedback path switch between two values according to a rule

that depends on the value of the state at each instant. The purpose of the

switching control law is to drive the nonlinear plants state trajectory onto a

prespecified (user-chosen) surface in the state space and to maintain the

plants state trajectory on this surface for subsequent time. The surface is

called a switching surface. When the plant state trajectory is above the

surface, a feedback path has one gain and a different gain if the trajectory

drops below the surface. This surface defines the rule for proper switching.

This surface is also called a sliding surface (sliding manifold). Ideally, once

intercepted, the switched control maintains the plants state trajectory on the

surface for all subsequent time and the plants state trajectory slides along this

surface.

The most important task is to design a switched control that will

drive the plant state to the switching surface and maintain it on the surface

upon interception. A Lyapunov approach is uesd to characterize this task.

Lyapunov method is usually used to determine the stability properties of an

equlibrium point without solving the state equation. Let V(x) be a

continuously differentiable scalar function defined in a domain D that

contains the origin. A function V(x) is said to be positive definite if V(0)=0

and V(x)>0 for x. It is said to be negative definite if V(0)=0 and V(x)>0 for x.

Lyapunov method is to assure that the function is positive definite when it is

negative and function is negative definite if it is positive. In that way the

stability is assured.

A generalized Lyapunov function, that characterizes the motion of

the state trajectory to the sliding surface, is defined in terms of the surface.

For each chosen switched control structure, one chooses the gains so that

72

the derivative of this Lyapunov function is negative definite, thus

guaranteeing motion of the state trajectory to the surface. After proper design

of the surface, a switched controller is constructed so that the tangent vectors

of the state trajectory point towards the surface such that the state is driven to

and maintained on the sliding surface as shown in Figure 3.7. Such controllers

result in discontinuous closed-loop systems.

Let a single input nonlinear system be defined as

(n)x f (x, t) b(x, t)u(t) (3.11)

Here, x (t) is the state vector, u(t) is the control input (in our case braking

torque or pressure on the pedal) and x is the output state of the interest (in our

case, wheel slip). The other states in the state vector are the higher order

derivatives of x up to the (n-1)th

order. The superscript n on x(t) shows the

order of differentiation. f(x ,t) and b(x,t) are generally nonlinear functions of

time and states. The function f(x) is not exactly known, but the extent of the

imprecision on f(x) is upper bounded by a known, continuous function of x;

similarly, the control gain b(x) is not exactly known, but is of known sign and

is bounded by known, continuous functions of x . The control problem is to

get the state x to track a specific time-varying state x d in the presence of

model imprecision on f(x) and b(x). A time varying surface s(t) is defined in

the state space R(n)

by equating the variable s(x; t ), defined below, to zero.

n 1ds(x, t) ( ) x(t)dt

(3.12)

Here, is a strict positive constant, taken to be the bandwidth of the system,

and dx(t) x(t) x (t) is the error in the output state where xd(t) is the desired

state. The problem of tracking the n-dimensional vector xd(t ) can be replaced

by a first-order stabilization problem in s. s(x; t ) verifying (3.12) is referred

73

to as a sliding surface, and the systems behaviour once on the surface is

called sliding mode or sliding regime. From (3.12) the expression of s

contains(n 1)

x , differentiating s once will make the input u to appear.

Furthermore, bounds on s can be directly translated into bounds on the

tracking error vector x , and therefore the scalar s represents a true measure of

tracking performance. The corresponding transformations of performance

measures assuming (0) 0x is:

0, ( ) 0, ( ) (2 )i i

t s t t x t (3.13)

where /n 1

. In this way, an nth-order tracking problem can be replaced

by a 1st-order stabilization problem.

21 ds s

2 dt (3.14)

The simplified, 1st-order problem of keeping the scalar s at zero

can now be achieved by choosing the control law u of (3.11) such that outside

of S(t) where is a strictly positive constant. Condition (3.14) states that the

squared distance to the surface, as measured by s2, decreases along all

system trajectories. Thus, it constrains trajectories to point towards the surface

s(t). In particular, once on the surface, the system trajectories remain on the

surface. In other words, satisfying the sliding condition makes the surface an

invariant set (a set for which any trajectory starting from an initial condition

within the set remains in the set for all future and past times). Furthermore,

equation (3.14) also implies that some disturbances or dynamic uncertainties

can be tolerated while still keeping the surface an invariant set.

74

dx (t)

x

s 0x

Sliding mode

exponential convergence

finite-timereaching phase

Figure 3.7 Graphical interpretation of equations (3.12) and (3.14) (n=2)

Finally, satisfying (3.12) guarantees that if x(t=0) is actually off

xd(t=0), the surface S(t) will be reached in a finite time smaller than |s(t=0)|/ .

Assume for instance that s(t=0)>0, and let treach be the time required to hit the

surface s=0.

Integrating (2.14) between t=0 and treach leads to

0-s(t=0)=s(t=treach)-s(t=0) - (treach-0)

Which implies that treach s(t=0)/ Starting from any initial condition, the state

trajectory reaches the time-varying surface in a finite time smaller than

|s(t=0)|/ , and then slides along the surface towards xd(t) exponentially, with

a time-constant equal to 1/ .

In summary, the idea is to use a well-behaved function of the

tracking error, s, according to (3.12), and then select the feedback control law

u in (3.11) such that s2 remains characteristic of a closed-loop system, despite

the presence of model imprecision and of disturbances.

75

3.5 SIMULATION RESULTS

3.5.1 PI Controller

The set of equations representing the model of the drive system

developed in chapter 2 and simulated with PI Speed controller. The results are

observed for the 3 phase, 2.0 hp, 4- pole 1500 rpm, 4 A motor (Refer table

2.2). Figure 3.8 and 3.9 show the simulated results for the steady state and

transient responses respectively.

Figure 3.8 Torque and Speed Waveforms when moment of inertia

= 0.013 kg-m2

Figure 3.9 Torque and speed waveforms for Step Change in Moment of

Inertia at 0.5 sec

76

In Figure 3.8 shows the Torque and Speed variations for moment of

inertia 0.013kg-m2. It reaches the steady state torque and speed suddenly at

time 0.03seconds. From these figures it is inferred that increasing the moment

of inertia ploys an important role in settling time.

3.5.2 ANFIS Controllers

Fuzzy membership functions can take many forms, but simple

straight-line functions are often preferred. Triangular membership functions

are often selected for practical applications and different membership

functions are tried for the minimum mean root square errors (MRSE). A set of

modified membership functions are derived through training the ANFIS by

using data obtained from PI controller as illustrated in Figure.3.10 and

Figure.3.11. ANFIS controller is designed with two inputs (speed error and

change in speed error) and one output and shown in Figure.3.12. Figure3.13

shows the stator currents while Figure.3.14 and Figure.3.15 show the torque

and speed responses respectively for ANSFIS controller.

Figure 3.10 Membership Functions Obtained after Training for Speed

Error

77

Figure 3.11 Membership Functions Obtained after Training for Change

in Speed Error

Figure 3.12 Architecture of ANFIS

78

Figure 3.13 Stator Current ANFIS controller

Figure 3.14 Torque Response -ANFIS Controller

Figure 3.15 Speed Response ANFIS Controller

3.5.3 SMC

The performance comparison of SMC and the PI controller is

provided in this section. Both load and line variations are obtained. The load

torque is varied at time 2S from 11 N-m to 15 N-m. Figure 3.16 show the

speed response for both the controllers. Figure 3.17 and 3.18 show the stator

current, torque and back EMF respectively for PI controller and SMC. Speed

response results are illustrated for reduction of load torque from 11N-m to

5N-m in Figure 3.19.

79

Figure 3.16 Comparison of speed response PI and SMC

Figure 3.17 Current, torque and back EMF PI Controller

80

Figure 3.18 Current, torque and back EMF SMC Controller

Figure 3.19 Comparison between PI controller and SMC-load torque

step change

81

The study of line voltage variation is done by changing the dc bus

voltage from 400V to 600V and again to 400V. The results are provided from

Figure 3.20 to 3.23.

Figure 3.20 Comparison between PI controller and SMC-Line variation

Figure 3.21 Current, torque and back EMF -Line variation (PI)

82

Figure 3.22 Current, torque and back EMF -Line variation (SMC)

Figure 3.23 Comparison of speed response -Line variation (PI and SMC)

83

3.6 HARDWARE IMPLEMENTATION

When system engineers implement BLDC speed control with a

digital signal processor, coding the control algorithm will be the first step.

The DSP must provide sufficient resources, particularly enough computing

bandwidth to run the control algorithm, interface to sensors, and drive the

power switches that supply current to the motors windings. A system

engineer implementing a design that uses a BLDC motor must choose the best

combination of control algorithm and DSP, given the applications

performance requirements and cost budget. This can be a challenge. The

information presented in this thesis is intended to aid the process of finding

optimum solutions.

Carefully studied BLDC applications and applicable speed control

algorithms in the light of MCU resource requirements, particularly the

analysis also covered DSP resource needs, such as analog-to-digital

converters (ADCs), PWM outputs, special timers, pin counts, and on-chip

RAM and flash ROM. This accumulated knowledge is applicable to a wide

range of BLDC applications. DSP chips characterized by the execution of

most instructions in one instruction cycle, complicated control algorithms can

be executed with fast speed, making very high sampling rate possible for

digitally-controlled inverters than microprocessors.

Shih-Liang Jung et al (1998) proposed a DSP TMS32OC14 based

repetitive control scheme to obtain high power factor at low switching

frequency. Their control scheme consists of two parts: ac current loop and dc

voltage loop. Current loop employs a repetitive controller so that the inherent

periodic error caused by low switching frequency can be suppressed. As to

the voltage loop, a digital PI controller with load current compensation is

designed to regulate the dc-link voltage such that the ripple can be minimized.

Recently, direct torque control of multi-phase induction motor using

84

TMS320F2407 DSP was developed (Mythili and Thyagarajah 2005). By

using DSP different controllers are designed in the areas of active filter,

power factor correction methods etc. A model layout of DSP control in motor

control is highlighted in Figure 3.24. The thesis utilizes DSP

TMS320LF2407.

Figure 3.24 BLDC Motor Control in application

3.6.1 Motor Control Features

High-Performance

16-bit CPU core with hardware multiplier

Up to three 16-bit timers with 40MHz clock

3.3us ADC conversion with timer-trigger start option

85

Advanced Motor-tuned Timers

Up to 6-ch complimentary PWM signals with independent

compare registers

Programmable Dead-Time Control (16-bit)

Selectable buffer operation for fast timer reload

PWM signal shut-off using external trigger

Safety Mechanism for UL Compliance

Watchdog with dedicated on-chip oscillator

Power-on Reset, Voltage Detection Circuits

Outstanding Development Support

Multiple motor control algorithms

Free Compiler for up to 64KB code and peripheral code

generator

3.6.2 Description of DSP Resources

In this configuration, the DSP has six output pins, of which a

minimum of three pins must have PWM output capability. The remaining pins

are in the high/low or on/off state. Its worth noting that even though only

three PWM output pins are required, in many cases six PWM output pins are

preferred. A timer or set of timers is required to create the necessary PWM

outputs for each phase. The timer creates the PWM output waveforms with a

selected carrier frequency and appropriate PWM duty ratio.

The PWM duty cycle is determined in various ways. For some

applications, the duty cycle is kept constant and Hall sensor signals are used

only for commutation switching. In such cases, neither speed nor current

86

measurement is required. In other applications, a timer is used to measure the

time between two Hall sensor signals. The time measurement is then

converted to a speed measurement and a proportional integration (PI) speed

loop is executed to determine the PWM duty cycle. Speed loop execution is

asynchronous to the carrier frequency, however, which makes tuning the gain

of the PI loop difficult and reduces performance. Furthermore, the frequency

of the speed loop is directly related to the speed of the motor. At lower

speeds, the loop rate is lower resulting in poor performance, while at faster

speeds, the loop rate is higher, resulting in comparatively better performance.

Nevertheless, overall performance is adequate only for some applications.

This control method generally does not handle what is known as torque

control. For applications requiring torque control, current must be measured.

Torque is directly proportional to current. Thus, current measurement allows a

system engineer to decipher the torque-speed point of the motor. Based on

this point, the load can be estimated and the motor operated at a proper speed

for high efficiency. Current measurements have to be synchronous to the

carrier frequency, and the speed loop must be synchronous to the current loop.

The output of the speed loop is a reference current that becomes an

input to the current loop. The output of the current loop is usually the voltage

necessary to drive the motor at that instant of time. This voltage is transferred

into the PWM duty cycle using binary arithmetic. Thus, three increasingly

complex scenarios are possible using Hall-sensor-based trapezoidal control:

the PWM duty cycle can be constant; a speed loop alone can be used to

determine the PWM duty cycle; or a combination of a speed loop and current

loop can be used to determine the PWM duty cycle.

3.6.3 Closed Loop Speed control of BLDC Motor

In Closed speed loop, a speed sensor is added and a speed loop

used to adjust the frequency and voltage of the applied sine wave. The reason

87

that a sensor is used to measure speed instead of a back-EMF signal is simple:

When all three phases are used to drive the motor, there is no free phase

through which a back-EMF signal can be detected. Even if such a signal could

be detected within a very short dead time, it would be inadequate for

determining rotor position. Thus, some type of sensor is needed on the motor

to give either speed information or rotor position data.

Figure 3.25 shows the schematic diagram of the hardware system,

where the system is controlled via a DSP controller TMS320LF2407A. DSP

commands are isolated and amplified via HCPL A316J gate drivers and the

phase currents are measured current transducers. Determination of the

voltage functions and making the virtual position signals are carried out via

hardware. Therefore, it is possible to employ the capabilities of the capture

unit in the event manager module of DSP.

Figure 3.25 Sensor-controlled BLDC Motor drive based on TMS320LF2407A

88

Hall sensors can provide accurate rotor position information and

are suitable for this motor control method. They can be used to determine

rotor angle and to synchronize the angle estimation for correct sine

computations. By using Hall sensors and a simple timer, a system engineer

can determine the motor speed, just as was done in the 6-step trapezoidal

method. Both sensor and timer functions can be added easily to the code. A

speed loop is executed at the proper time to increase or decrease the

frequency and voltage level of the sine wave. Because speed measurement is

asynchronous, frequency adjustments will also be asynchronous. Hall sensors

are expensive and require special mounting procedures. To reduce cost, it is

possible to use only one Hall sensor to measure speed instead of the usual

three sensors. The fabricated experiential setup is shown in Figure 3.26 while

representative gate pulses are given in Figure 3.27. The line and phase current

waveforms are shown in Figure 3.28 and 3.29.

Figure 3.26 Experimental setup

89

(a) (b)

(c) (d)

Figure 3.27 Gate Pulses for closed loop Six Switch Inverter control of

BLDC Motor

(a) Line (b) Phase

Figure 3.28 Current Waveforms using Digital scope

Figure 3.29 Phase Current using CRO

90

Table 3.1 Comparison of PI, ANFIS AND SMC Controllers

Controller PI ANFIS SMC

Peak overshoot 1518 rpm 1506rpm 1501rpm

Settling time 1.4 ms 0.7ms 0.2 ms

Steady state error 0.5 rpm 0.3rpm 0.1rpm

3.7 SUMMARY

The designed trapezoidal BLDC motor based drive system has the

closed-loop speed control, in which PI algorithm is adopted and the position

determination is done through hysteresis current control. The nonlinear

simulation model of the BLDC motors drive system with PI control based is

simulated in the MATLAB/Simulink platform. The simulated results in

electromagnetic torque and rotor speed are given for inertia change, load

variation and line variation.

ANFIS served as a basis for constructing a set of fuzzy if-then rules

with appropriate membership functions to generate the stipulated input-output

pairs. The performance of the developed MATLAB based speed controller of

the drive has revealed that the algorithms developed to analyze the behavior

of the PMBLDC motor drive system work satisfactorily in software

implementation. Using neuro-fuzzy controller error can be reduced and train

the membership functions to get the improved speed characteristics. It is

found that the ANFIS controller shows reduced overshoot and settling time in

both start-up and loaded change conditions and hence robust response.

Detailed steps involving implementing the PI controller based drive system is

discussed.