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Transcript of CHAPTER 3 PERFORMANCE ANALYSIS WITH PI, ANFIS AND SLIDING...
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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
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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.
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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
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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
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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
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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.
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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.
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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)
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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)
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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.
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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
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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
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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.
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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.
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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
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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
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Figure 3.11 Membership Functions Obtained after Training for Change
in Speed Error
Figure 3.12 Architecture of ANFIS
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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.
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Figure 3.16 Comparison of speed response PI and SMC
Figure 3.17 Current, torque and back EMF PI Controller
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Figure 3.18 Current, torque and back EMF SMC Controller
Figure 3.19 Comparison between PI controller and SMC-load torque
step change
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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)
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Figure 3.22 Current, torque and back EMF -Line variation (SMC)
Figure 3.23 Comparison of speed response -Line variation (PI and SMC)
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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
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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
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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
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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
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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
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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
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(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
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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.