Republic Of Iraq
Ministry of Higher Education and
Scientific Research
Tikrit University
Electrical Engineering Department
Model Predictive Speed Control of DC Motor
A graduation project is submitted to the Electrical Engineering
Department in partial fulfillment of the requirements for the degree of
Bachelor of Science in Electrical Engineering.
By
Abdul Hakim Jassim Muhammad
Malaak Samir Ibrahim
Supervisor
Assi. Prof. Dr. Thamer Hassan Attia
1443
2022
‫بسم اهلل الرمحن الرحيم‬
‫اَّلل اله ِذين آمنُوا ِم ْن ُكم واله ِذين أُوتُوا ال ِ‬
‫ْم‬
‫ل‬
‫ْع‬
‫يَ ْرفَ ِع هُ َ َ‬
‫َْ َ‬
‫َ‬
‫ٍ‬
‫ِ‬
‫ِ‬
‫ه‬
‫ي‬
‫ب‬
‫خ‬
‫ن‬
‫و‬
‫ل‬
‫م‬
‫ع‬
‫ت‬
‫ا‬
‫ِب‬
‫اَّلل‬
‫و‬
‫ات‬
‫ُ‬
‫َ‬
‫َ‬
‫َ‬
‫َ ر‬
‫َد َر َج َ ُ ْ َ‬
‫صدق اهلل العظيم‬
‫سورة المجادلة‬
‫اآلية (‪)11‬‬
‫‪1‬‬
Acknowledgment
First of all, I am thankful to the glory of Allah for all things.
I would like to express my deepest gratitude to my supervisor
Hassan Attia
Dr. Thamer
for his invaluable guidance, support, advice and, encouragement
during the preparation of this thesis (thank you for never giving up on me).
I also would like to acknowledge the staff of Electrical Engineering Department /
University of Tikrit and the people who helped me (thank you very much).
My sincere thanks go to my family for their help and encouragement.
2
CONTENTS
Page
Subject
CHAPTER ONE: INTRODUCTION
1.1
General
……………………….. 5
1.2
Classification of DC motor
……………………….. 6
1.3
Permanent Magnet DC Motor
……………………….. 6
1.4
Objectives
……………………….. 8
CHAPTER TWO: DC MOTOR
……………………….. 9
2.1
Dc Motor
2.2
Advantages of Permanent Magnet DC Motor or PMDC Motor ….…….13
2.3
Disadvantages of Permanent Magnet DC Motor or PMDC Motor ……..13
2.4
Modelling of the system
……………………….. 14
CHAPTER THREE: PREDICTIVE CONTROL
3.1 Predictive Control
………………………..16
3.2 Math Presentation
………………………..17
……………………..… 18
3.3 System Representation
………………………..23
3.4 Optimal Control Problem
CHAPTER FOUR: EXPERIMENTAL WORK
REFERENCES
3
List of Nomenclature
Symbol
Description
Unit
K
i
T
P
N
J
Torque Constant
The Current Of The Armature
The Torque
Power
Speed
Rotor Inertia
---mA
n.m
W
m.s
Kg.m2
List of Figure
Figure
No.
1.1
1.2
2.1
3.1
3.2
DC motor
Classification Of DC Motor
Examples of DC drives
System Representation
Interactive Algorithm
Page
No.
5
6
11
19
25
3.3
NonIneractive Algorithm
26
3.4
Parallel Algorithm
26
3.5
Description
The effect of add 𝐾𝑝 (𝐾𝑖, 𝑎𝑛𝑑 𝐾𝑑) held constant
4
27
CHAPTER ONE
INTRODUCTION
CHAPTER ONE
INTRODUCTION
CHAPTER ONE
INTRODUCTION
1.1. General
In a DC motor, an armature rotates inside a magnetic field. The basic
working principle of a DC motor is based on the fact that whenever a
current-carrying conductor is placed inside a magnetic field, there will
be mechanical force experienced by that conductor [1].
All kinds of DC
motors work under this principle. Hence for constructing a DC motor, it
is essential to
establish a magnetic field. The magnetic field
is
established by using a magnet. You can use different types of magnets –
it may be an electromagnet or it can be a permanent magnet. A
Permanent Magnet DC motor (PMDC motor) is a type of DC motor that
uses a permanent magnet to create the magnetic field required for the
operation of a DC motor, as shown figure (1.1).
figure (1.1): DC motor [A]
5
CHAPTER ONE
INTRODUCTION
1.2. Classification of DC motor
Based on the type of construction and electrical connection, DC motor
can be categorized into four major types. A brief chart (based on the
type of construction and electrical connection) is given below:
figure (1.2): Classification Of DC Motor
1.3 Permanent Magnet DC Motor
In these types of DC motor, the permanent magnet is used to create a
magnetic field. In this, not input current is consumed for excitation.
Permanent magnet DC (PMDC) machines with brushes are being of less
importance today, and they are continuously replaced by permanent
magnet
synchronous
machines
(PMSM)
6
or
brushless
DC
(BLDC)
CHAPTER ONE
INTRODUCTION
machines. Despite this fact, PMDC machines still have their own field of
use in various types of applications, from machine tools and small home
appliances to photovoltaic, robotic, and medical applications. They are
widely used as auxiliary drives in automotive solutions due to the
presence of a DC grid in modern vehicles, and they are especially
suitable for battery-operated equipment. The biggest drawback of these
machines is a commutator, which needs regular maintenance and causes
sparkles, and, therefore, the machines cannot be used in an explosive
environment. On the other hand, linear speed-torque curve, high torque
at low speed, and the simplicity of torque/speed control are well-known
advantages of the conventional PMDC machines.
Coreless
PMDC
vibrations,
and
machines
have
smoother
motor
almost
no
running
cogging
at
low
torque,
speed
fewer
against
conventional PMDC machines. In order to work in all four quadrants,
these machines are often supplied by an H-bridge DC-DC converter,
which changes the mean value of the voltage on the machine terminals.
This converter uses pulse-width modulation (PWM) with a 2-level or 3level type of control [2].
The PMDC machines have been extensively studied and many advanced
control strategies have been presented in the past, but they are studied by
many researchers even today [3–6]. Among the new approaches, a new
and attractive alternative for the control of H-bridge supplied PMDC
machine is finite control set model predictive control (FCSMPC) [7]. A
framework for the analytical derivation of FCSMPC can be found in [8].
FCS-MPC has been applied to the control of several types of electrical
drives.
Techniques
for
reducing
a
steady-state
error
of
FCS-MPC
controlled H-bridge have been presented in [9]. Detailed description of
the algorithm design for the commutation torque ripple minimization
applied to a BLDC machine can be found in [10]. Direct speed control
7
CHAPTER ONE
INTRODUCTION
of a PMSM for a single-mass system has been developed in [11].
Predictive strategy for the speed control of a two-mass system driven by
PMSM has been proposed in [12], introducing reduced order extended
Kalman filter for mitigation of oscillations and compensation of load
torque disturbances. In authors’ opinion and supported by the literature
review, a FCS-MPC for the PMDC machine has not been reported yet.
1.4. Objectives
The objectives of this paper lie in the following:
1. For the first time, a predictive control strategy is proposed for the
combination of a DC-DC converter and a PMDC machine.
2. The proposed predictive control is compared to the conventional
approach based on PI controllers.
3. In addition, we have proposed a new cost function that is different
from the commonly used ones [8].
4. In
the
novel
cost
function,
two
current
components
are
introduced: a current component corresponding to a dynamic feed
forward torque, iF, and a current component corresponding to a
static load torque, iL
5. We will also show how these components affect the overall
control performance of the FCS-MPC controller.
8
CHAPTER TWO
DC MOTOR
CHAPTER TWO
DC MOTOR
CHAPTER TWO
DC MOTOR
2.1. DC MOTOR
DC motors have common use and affect industrial applications such as
lathes,
fans,
pumps,
discs,
and
band
saw
drives.
However,
the
controllability, lower cost, higher efficiency, and higher current load
capacity of static power transformers have brought a significant change
in the performance of electric drives. The spin-in motors spin the spin
because the current flowing through the coil produces a magnetic field
repulsed by a permanent magnet mounted on the rebar. When the spin
coil spin brushes make contact with the coil, the polarity voltage is
reversed, and the coil is alienated again [13].
It is substantial to know how the DC engine can accelerate the
manipulates of robot. The voltage applied on the DC motors effects
the speed of DC motors,
on
the characteristics of the engine, and the load
on the wheels. Find out the shape of the wheel acceleration curve
without sliding it is useful for the shape of the cyclic wheel acceleration
curve without slide is useful for the implementation of controllers that
provide traction control. Traditionally, DC models have developed close
loop control systems associated with their use to propel them using
classical control theory techniques, based on the transfer functions. The
techniques of designing a control and system analysis are widely
repressed and very valid to be utilized in real time development. In some
cases we
can be find the solution by advanced hardware technology and
by the advanced use of software, the control system is easily analyzed
and details. DC motors can be used in different applications and can be
used in different sizes and rates. The processor calculates the real actual
speed of the motor by sensing the voltage of the terminal. Then
9
CHAPTER TWO
DC MOTOR
compares the actual speed of the motor with the signal speed and it
generates
the
comfortable
control
signal
that
is
entered
into
the
triggering unit.[14].
We pay attention DC motors with permanent magnets. The power
provided by the engines is torque. The torque stall included in the DC
motor information from data sheet and is the extreme
torque produced
by the engine when the torque is not grasped and prevents rotating.[15]
The spin-in motors spin because the current flowing through the coil will
make a magnetic field repulsed by the permanent magnet
and it will be
mounted in the coil producing a magnetic field repulsed by a permanent
magnet mounted in the voltage polarity in a manner that the coil is
repulsed back, etc. and so on.
When the engine is rotating, the V voltage applied to the engine
dwindles from the E voltage produced by the rotor. The rotor spin faster,
the greater the value of E.[16]
Due to their high reliability, flexibility and cheapness, the DC
motors as shown in Fig. 1 are commonly used in industrial applications,
robot maneuvers and household appliances where the speed and position
of the engine is required [17].
DC machines are distinguished by their variety. Through different
combinations of series- shunt, and individually-encased field coils they
can be designed to display a wide range of volt-amp or torque-speed
properties for a dynamic and steady-state operation. Due to of the ease
with which the control systems of DC machines can be used frequently
in many applications that require a wide range of engine speeds and
precise control of engine output.
outstanding to that of A.C. motor. Therefore, it is not astonishing to note
that industrial drives. [18]. DC engines are rarely used in normal
applications because all companies of electrical supply offer AC power.
10
CHAPTER TWO
DC MOTOR
However, for exceptional applications such as steel mills , crane tools,
and electric trains, it is useful to convert AC to direct current to use DC
motors. The cause of the relationship between
speed and torque
characteristics of dc, the engines are far
Fig (2.1). Examples of DC drives
In the control of closed loop system, DC is an industrial applications
and researches are very common. The torsion tester is often used to
provide a quick feedback to control movement [19, 20]. In the
involvement of flexibility in the system, for example, shaft loader for
compatible vehicles or flexible coupling, the process in the servo
control becomes fully contained because the limited shaft hardness
provides resonance and shaft. These are strongly unwanted effects that
can be discarded by proper controller design. To be able to obtain a
model,
estimation,
and
exclude
these
high
frequency
resonance
problems, it is necessary to have an estimation model of the complete
system including sensors.
11
CHAPTER TWO
DC MOTOR
In DC motor, the position with and without velocity control by using
tachometer feedback, the familiar tachometer model [21, 22] It is
sufficient for less exigent motion control exercises, but is unavailing to
supply high-speed and high-accuracy movement control. In fact, when
this mathematical model was used to estimate the frequency response
of a system with multiple shaft elasticity, it resulted in faulty results
that did not conform to empirical measurements. This led to an
achievement leading to a more accurate and accurate model of the
torsion tester. A comprehensive analysis of a modeling has been
conducted
It was found that the reciprocal induction between the windings of the
motor and the tachometer, however, leads to the term magnetic
coupling in the expression of the output voltage of the tachometer. This
effect is quantified and extracted in this paper, and the improved
tachometer model is acquired using the mail rules of electromagnetic.
After that, this model is then used to analyze and calculate the
tachometer of a DC motor. It turns out that the new analytical
estimations are in perfect agreement with empirical measurements.
The result of these dynamics shows the tachometer on the response
system more than everything. It is seen that the dynamics of the
tachometer affect the transfer function of the system in a systemdependent manner. This is illustrated in the following sections. We find
that the dynamics of the tachometer contribute to some additional zeros
to the system transfer function in general. The number of these
additional zeros depends on the system itself. These zeros are located
in the s-plane by the relative orientation of the static field of the
tachometer with respect to the static field of the motor. Having proved
the model experience, we later integrated it into the feedback control
design to control the motion of the engine ds, which is the ultimate
12
CHAPTER TWO
DC MOTOR
goal of the whole process. The importance and impact of these
additional zeros are discussed in terms of the design of the controller in
detail.
2.2. Advantages of Permanent Magnet DC Motor or PMDC Motor
The advantages of a PMDC motor are:
1. No need of field excitation arrangement.
2. No input power in consumed for excitation which improve efficiency
of DC motor.
3. No field coil hence space for field coil is saved which reduces the
overall size of the motor.
4. Cheaper and economical for fractional kW rated applications.
2.3. Disadvantages of Permanent Magnet DC Motor or PMDC Motor
The disadvantages of a PMDC motor are:
1. The armature reaction of DC motor cannot be compensated hence the
magnetic strength of the field may get weak due to the demagnetizing
effect of the armature reaction.
2. There is a chance of getting the poles permanently demagnetized
(partial) due to excessive armature current during the starting, reversal,
and overloading conditions of the motor.
3. The field in the air gap is fixed and limited – it cannot be controlled
externally. This makes it difficult for this type of motor to achieve
efficient speed control of DC motor in this type of motor is difficult.
2.4. Modelling of the system
A model based on the motor specifications needs to be obtained.
Figure-1 shows the DC motor circuit with torque and rotor angle
consideration
The torque T of the motor is related to the current of the armature, i , by
a torque constant K;
13
CHAPTER TWO
DC MOTOR
𝑇= 𝐾𝑖
(1)
The produced voltage, Ea , is proportional to angular velocity by
𝐸𝑎 = 𝐾𝑤𝑚
𝐾=
(2)
𝑑ѳ
(3)
𝑑𝑡
By using Newton’s law and Kirchhoff’s law in Fig 1. and we can get the
following equations.
b
𝑑𝜃
𝑑𝑡
𝑅𝑖 + L
+J
𝑑𝑖
𝑑𝑡
𝑑𝜃 2
𝑑𝑡
=Ki
= 𝑉 (𝑠) − k
(4)
𝑑𝜃
𝑑𝑡
(5)
Using the Laplace transform, equations (3) and (4) can be written a
𝑏𝑠 Ѳ(𝑠) + 𝐽𝑠 Ѳ(𝑠) = 𝐾 𝑖(𝑠)
𝐾 𝐼 ( 𝑠) + 𝐿𝑠 𝐼 (𝑠) = 𝑉 (𝑠) − 𝐾𝑠 Ѳ(𝑠)
(6)
(7)
The Laplace 𝑠 operator. From (7) we can find I(s)
I(s) =
𝑉(𝑠)−𝐾𝑠𝜃(𝑠)
𝑅+𝐿(𝑆)
(8)
and substitute it in (5) to
bs θ(s) = Js θ(s) =
𝐾(𝑉(𝑠)−𝐾𝑆𝜃(𝑠))
𝑅+𝐿(𝑠)
(9)
we can find the transfer function of the output angle θ to the input
voltage V(s) as follow
14
CHAPTER TWO
DC MOTOR
Ga(s) =
𝜃(𝑠)
𝑉(𝑠)
=
𝐾
{𝑆[(𝑗𝑠+𝑏)(𝑅+𝐿𝑠)+𝑘 2 ]}
(10)
It is simple to see that the transfer function of relationship between the
input voltage V(s) with the angular velocity is ;
𝐾
Ga(s) =
{𝑆[(𝑗𝑠+𝑏)(𝑅+𝐿𝑠)+𝑘 2 ]}
By using m-file of the model , we can
(11)
To represent the model with m-
file, we can implement the Fig. 2 data as follows
By put the values of Power P, Speed N , Rotor Inertia J with Supply
voltage , we can calculate the torque constant K
Wᵐ =
𝑣𝑡
𝑘
=
2𝜋𝑛
60
(12)
K=14
By using equation (3) of
𝑘𝑖 =
𝑑𝑤
𝑑𝑡
+ 𝑏𝜔
(13)
The values of I and ω are stabilized at the steady state ;
𝑑𝜔
𝑑𝑡
T=
b=
𝑘𝑖
𝜔
𝑃
𝑊
=
=
370
157
1.4∗2.3
157
=0
= 2.35 𝑁. 𝑚
(14)
= 0.02 N.m /rpm
(15)
By applying all parameters to be used for desired DC Motor model.
15
CHAPTER THREE
PREDICTIVE CONTROL
CHAPTER THREE
PREDICTIVE CONTROL
CHAPTER THREE
PREDICTIVE CONTROL
3.1. Predictive Control
Predictive control or Model Predictive Control is a method of
controlling and adapting systems, also known as receding horizon or
moving horizon control [13-15]. The characteristic of this method is
that it enters the future changes of the target inputs (that is, changing
the value we want for the system outputs) in the calculation of the
controller’s outputs, which makes this method used in problems of the
Trajectory Tracking type. The method works as follows:
1. We have the function or path that we want to follow.
2. We take this path in a field called the Prediction Horizon field.
3. In this field, an ideal control problem is calculated or solved, i.e. an
improvement is performed (usually based on an integration sign
that contains certain properties as the controller output where We
don't want our controllers to put a lot of effort into the system. The
integration also usually contains the difference or error between the
desired path and the real path). In this area, the significance is
minimized.
4. The
forward-looking
controller
method
that
works
on
digital
computers later takes the value obtained in the above process and
uses it in the next time step. Although it can take this result for a
longer period (the domain of prediction), it does not take this result
until in the next time step and at each step, it returns the algorithm
again. Therefore, there are many advantages, thus it is achieved
that the calculations are always in the light of new or immediate
data, i.e. new values of the sensors.
16
CHAPTER THREE
PREDICTIVE CONTROL
3.2. Math Presentation
The orientalist control principle is based on trying to calculate the
least value of an arithmetic criterion or a (functional) parameter in each
operation of the model. This criterion as this equation is the discrete
form of the arithmetic criterion. This is done by using Nu number of
future control entries where N1 is the minimum forecast horizon and
N2 is the maximum forecast horizon. As for ρ, it is an equilibrium
criterion for controlling the value of the fine resulting from the second
part of the equation over the amount of the total arithmetic criterion.
For non-linear systems, the equation must be optimized for each
sample, which leads to predicting a set of future values for the
controller input (here we have referred to a set of our consideration
values for our focus on the discontinuous form of the figure in the
continuous
mathematical
formula,
a
mathematical
function
is
obtained), from this set is entered The first value (in the connected
formula the first part of the function and the length of the part is the
length of time between two optimizations) to the system. As for the
linear systems, the optimization is achieved in advance and the control
is transferred from an oriental to a linear instantaneous control.
For non-linear systems, the equation must be optimized for each
sample, which leads to predicting a set of future values for the
controller input (here we have referred to a set of our consideration
values for our focus on the discontinuous form of the figure in the
continuous
mathematical
formula,
obtained), from this set is entered
a
mathematical
function
is
The first value (in the connected
formula the first part of the function and the length of the part is the
length of time between two optimizations) to the system.
17
CHAPTER THREE
PREDICTIVE CONTROL
As for the linear systems, the optimization is achieved in advance and
the control is transferred from an oriental to a linear instantaneous
control.
Model predictive control (MPC) has gained interest both in academia
and industry over the past few decades compared to other control
methods, such as PID or PWM control. This is true mainly because
MPC can be applied in many different processes, can implement
constraints, and is easy to be understood, since its basic concepts can
be explained intuitively.[23] The basic idea of model predictive control
is to predict and optimize future system behaviour using the system
model. The basic elements of MPC are:
1. The system model, describes the plant’s behaviour over time.
2. The control problem, where an objective function is formulated
with regard to the system model to calculate the optimal control
sequence for a specific number of future instances (prediction
horizon)
3. Receding horizon policy, The following sections explain these
elements in detail.
3.3. System Representation
Modeling is a very important part of the MPC algorithms since
different
models
produce
algorithms
with
different
complexity
influencing the time needed to find the optimal solution to the control
problem.[24] as shown in figure (3.1).
18
CHAPTER THREE
PREDICTIVE CONTROL
figure (3.1). System Representation
Many different forms of modeling can be used in MPC, but for the
purposes of this research, the state space representation will be used.
The use of microprocessors makes MPC a discrete-time controller, thus
the state-space representation in discrete-time is in order for the system
model:
x(k + 1) = f(x(k),u(k))
(3.1)
y(k) = g(x(k))
(3.2)
Where:
x(k) ∈ R n is the state vector of the system at time instant kTs,
u(k) ∈ R m is the input vector at time instant kTs,
y(k) ∈ R p is the output vector at time instant kTs,
the functions f and g are the state-update and output functions,
respectively, which can be linear or nonlinear, and
Ts is the sampling interval.
19
CHAPTER THREE
PREDICTIVE CONTROL
Starting from the current state x(k), this model is used for the
calculation of the state and the output future values over a finite
number N of planed control actions
{u(k),u(k + 1), . . . ,u(k + N)}.
starting from the step k + 1 for the state it holds:
x(k + 1) = f(x(k),u(k))
x(k + 2) = f(x(k + 1),u(k + 1)) = f(f(x(k),u(k)),u(k + 1))
(3.3)
x(k + N) = f(x(k + N − 1),u(k + N − 1))
= f(f . . .(f(x(k),u(k)),u(k + 1)), ...u(k + N − 1))
Thus the output over N steps is:
y(k + 1) = g(f(x(k),u(k)))
y(k + 2) = g(f(x(k + 1),u(k + 1))) = g(f(f(x(k),u(k)),u(k + 1)))
(3.4)
y(k + N) = g(f(x(k + N − 1),u(k + N − 1)))
= g(f(f . . .(f(x(k),u(k)),u(k + 1)), ...u(k + N − 1)))
Linear
model
For
a
linear
model
the
discrete
time
state-space
representation is:
x(k + 1) = Ax(k) + Bu(k)
y(k) = C x(k)
(3.5)
(3.6)
where A, B and C are the system matrices.
Following the same procedure as in (3.3) and (3.4), the state over a
finite number of planed actions N is:
20
CHAPTER THREE
PREDICTIVE CONTROL
Or in a matrix form:
Using the last applied control action u(k − 1) (which is known) it is possible to
write the future control actions u(k),u(k + 1), . . . ,u(k + N − 1) in the form:
u(k) = u(k) − u(k − 1) + u(k − 1)
= ∆u(k) + u(k − 1)
u(k + 1) = ∆u(k + 1) + ∆u(k) + u(k − 1)
u(k + N − 1) = ∆u(k + N − 1) + • • • + ∆u(k) + u(k − 1)
where
∆u(k + l − 1) = u(k + l − 1) − u(k + l − 2), l = 1, . . . , N.
Combining (3.7) and (3.9) we get:
21
(3.9)
CHAPTER THREE
The equations
PREDICTIVE CONTROL
describing the state evolution over
a prediction
horizon N are of course equivalent and for the system’s output in
both representations it holds
22
CHAPTER THREE
PREDICTIVE CONTROL
3.4. Optimal Control Problem
In order to obtain the control law a cost function is needed. In general,
the cost function is formulated in regard to the output difference to a
specific reference signal and the required control effort. Such a
function is of the form:
The most commonly used norms in MPC are p = 1 , p = ∞, which
produce a linear function, and p = 2, which produces a quadratic
function.
The aim of the optimization problem is, using the formulated cost
function J, to find the control sequence U(k) that results in the best
performance of the system:
23
CHAPTER FOUR
EXPERIMENTAL WORK
CHAPTER FOUR
EXPERIMENTAL WORK
CHAPTER FOUR
EXPERIMENTAL WORK
CHAPTER FOUR
EXPERIMENTAL WORK
SIMULINK
30
CHAPTER FOUR
EXPERIMENTAL WORK
MATLAB 1
clear all
clc
R=4.88;% resistance of the Motor (Ohm)
L=0.0384;%inductance of the Motor (Henry)
F=0.0131;%friction coefficient
J=0.0091;%moment of inertia
K=0.9533;%Torque Constant
num1=K;
den=[J*L J*R F*L (F*R+K^2)];
sys1=tf(num1,den);
[A1,B1,C1,D1] = tf2ss(num1,den)
Ts=0.001;
MV=struct('Min',-inf,'Max',Inf,'RateMin',-inf,'RateMax',inf);
OV=struct('Min',-inf,'Max',100); % range of output signal
p=50; % Prediction Horizon
m=4; % Control Horizon
mpccon=mpc(ss(A1,B1,C1,D1),Ts,p,m,[],MV,OV);
Tstop=5;
xo=[0 0 0]';
outc=sim('MPC_for_DC_Motor_V1');
save SIM_speed_change_step.mat outc
figure (1)
plot(T(1:10:end,1),r(1:10:end,1),'--k',T(1:10:end,1),W(1:10:end,1),'b','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g',...
'MarkerSize',16)
title('Reference Speed & Motor Speed Versus Time')
xlabel('Time in Sec')
ylabel('Speed (rad/Sec)')
ylim([0 100])
legend('Refernce Speed','Motor Speed')
31
CHAPTER FOUR
EXPERIMENTAL WORK
MATLAB 2
p=40; % Prediction Horizon
m=4; % Control Horizon
MATLAB 3
p=70; % Prediction Horizon
m=4; % Control Horizon
32
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27