Table of Content
[Task 1]
Examine basic concepts of control systems using block diagram representation and simplifications
....................................................................................................................................................... 5
[Task 2]
Design open loop control model system on MATLAB simulation program where :- The input signal
(unit step) and the system consists of control with parameter(1/s+1) and Transfer Function with
parameter (1/s^2 +2s+1) , show on the osc (input ,output signals) in the same time........................ 10
Explain how can convert this model to closed loop control model on MATLAB simulation program 11
[Task 3]
1- Explore the main building blocks for electrical and mechanical control systems ....................... 12
2- Apply Laplace transforms to electrical control system .............................................................. 14
3- Apply advanced modelling techniques using MATLAB program for mechanical control system .. 16
4- Develop the block diagram of a closed loop mechanical system for the position control of DC
motor using a PID controller .......................................................................................................... 18
5- Evaluate the performance of a PID controller in point (4) ............................................................ 20
Working of PID controller .............................................................................................................. 22
Advantages of using a PID controller in control systems ................................................................ 22
6- Analyse all control systems in fig (1),(2),(3) using appropriate mathematical models and computer
simulation..................................................................................................................................... 25
7- Perform high level self-tuning control system techniques for Electro-Mechanical system using
mathematical modelling and computer simulation ....................................................................... 33
Computer simulation .................................................................................................................... 34
Advantages of Using the Saturation Block...................................................................................... 38
Reference ..................................................................................................................................... 40
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Table of Figure
Figure 1. control system ........................................................................................ 5
Figure 2. Open-loop control system ........................................................................ 5
Figure 3. Closed-loop control systems .................................................................... 6
Figure 4. Continuous & Discrete Control Systems ................................................... 6
Figure 5. Linear control systems ............................................................................. 7
Figure 6. Nonlinear control systems ....................................................................... 7
Figure 7. Time-varying & Time-invariant control systems ......................................... 8
Figure 8. Single-input single-output (SISO) control systems ..................................... 8
Figure 9. When Simulation is Run ......................................................................... 10
Figure 10. open loop control model system ........................................................... 10
Figure 11. When Simulation is Run ....................................................................... 11
Figure 12. When I convert this model to closed loop control model ........................ 11
Figure 13. Electrical control system ...................................................................... 12
Figure 14. Mechanical control system................................................................... 13
Figure 15. Electrical control system ...................................................................... 14
Figure 16. Parameters of Motor & Arm ................................................................... 16
Figure 17. Desgin mechanical control system on Matlab ........................................ 16
Figure 18. Mechanical control system................................................................... 16
Figure 19. Signal of Output ................................................................................... 17
Figure 20. Parameters of Gain .............................................................................. 17
Figure 22. Design When i Add PID Controller ......................................................... 18
Figure 21. Signal of PID Controller ........................................................................ 18
Figure 23. Output Signal After PID Controller......................................................... 19
Figure 24. Controller Parameters of PID Controller ................................................ 19
Figure 25. PID Controller Block diagram ................................................................ 21
Figure 26. PID Controller Signals .......................................................................... 23
Figure 27. mathematical model of Electrical Control System ................................. 25
Figure 28. Electrical Control System ..................................................................... 25
Figure 30. Design on Computer Simulation ........................................................... 26
Figure 29. Output Signal on Computer Simulation of Electrical Control System ....... 26
Figure 31. mathematical model of Mechanical Control System .............................. 27
Figure 32. Mechanical Control System .................................................................. 27
Figure 34. Design of Mechanical Control System on Computer Simulation .............. 28
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Figure 33. Output Signal on Computer Simulation of Mechanical Control System .... 28
Figure 35. mathematical model of Electro Mechanical Control System ................... 30
Figure 36. Electro Mechanical Control System ...................................................... 29
Figure 37. Controller Parameters of Electro Mechanical Control System ................. 31
Figure 38. Design of Electro Mechanical Control System on Computer Simulation .. 31
Figure 40. Signal of PID Controller ........................................................................ 32
Figure 39. Output Signal on Computer Simulation of Electro Mechanical Control
System ............................................................................................................... 32
Figure 41. Electro-Mechanical system .................................................................. 33
Figure 42. mathematical model of Improve for Electro Mechanical Control System . 33
Figure 43. Steps of Improve for Electro Mechanical Control System on Computer
Simulation .......................................................................................................... 34
Figure 44. Design When Add Saturation ................................................................ 35
Figure 45. Output Signal....................................................................................... 35
Figure 46. Values of Saturation ............................................................................. 36
Figure 47. Design Electro Mechanical Control System After improve ...................... 36
Figure 48. Output Signal After Improve.................................................................. 37
Figure 49. Curve of Saturaion ............................................................................... 39
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Table of Table
Table 1. Explore the main building blocks ............................................... 12
Table 2. Explore the main building blocks of Mechanical Control System 13
Table 3. Explain of Electro Mechanical Control System ........................... 29
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[Task 1]
Examine basic concepts of control systems using block diagram
representation and simplifications
A control system is a system that is used to control the behavior of a device or
process. It is made up of three main components: a sensor, a controller, and an
actuator. The sensor detects a physical quantity such as temperature, pressure, or
position and converts it into an electrical signal. The controller processes this signal
and generates an output signal that is used to control the actuator. The actuator is a
device that translates the output signal from the controller into a physical action,
such as opening or closing a valve, turning a motor on or off, or adjusting the speed of
a motor.
Figure 1. control system
Control System Types
Open-loop control systems: These systems do not use feedback, which means that
the output is not influenced by the actual performance of the system. Instead, the
input to the system is predetermined based on a set of predetermined rules or
instructions. This can make open-loop control systems less precise and less
responsive to changes in the system or the environment.
Figure 2. Open-loop control system
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Closed-loop control systems: These systems use feedback to compare the desired
output of the system to the actual output, and adjust the input to the system based
on the difference between these two signals (called the error). The goal of a closed-
loop control system is to reduce or eliminate the error by adjusting the input to the
system in a way that drives the output towards the desired value. This can make
closed-loop control systems more precise and more responsive to changes in the
system or the environment.
Figure 3. Closed-loop control systems
Continuous control systems: These systems operate over a continuous range of time
and/or output values. They may use analog or digital signals to represent the input
and output of the system. Continuous control systems are often used in applications
where a continuous output is required (such as in a temperature control system).
Discrete control systems: These systems operate at discrete points in time, and the
input and output are typically represented by digital signals. Discrete control
systems are often used in applications where the output is only required at specific
points in time (such as in a machine control system).
Figure 4. Continuous & Discrete Control Systems
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Linear control systems: These systems can be represented by linear differential
equations, which means that the system dynamics are proportional to the input and
can be described using linear mathematical operations. Linear control systems have
certain properties (such as superposition) that make them relatively easy to analyze
and control.
Figure 5. Linear control systems
Nonlinear control systems: These systems cannot be represented by linear
differential equations, and may exhibit complex behaviors such as bifurcations and
chaos. Nonlinear control systems can be more challenging to analyze and control
than linear systems and may require specialized techniques or algorithms.
Figure 6. Nonlinear control systems
Time-invariant control systems: These systems have the same input-output
relationship at all times, which means that the system dynamics do not change over
time. Time-invariant systems are often used in applications where the system
parameters are not expected to vary significantly over time.
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Time-varying control systems: These systems have a time-varying input-output
relationship, which may be caused by changes in the system dynamics or external
factors. Time-varying systems can be more challenging to analyze and control than
time-invariant systems, as the system dynamics may change over time.
Figure 7. Time-varying & Time-invariant control systems
Single-input single-output (SISO) control systems: These systems have a single input
and a single output, which means that there is only one degree of freedom in the
system. SISO systems are relatively simple to analyze and control and are often used
in basic control systems.
Figure 8. Single-input single-output (SISO) control systems
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Control System Applications
Control systems are used in a wide variety of applications to automatically monitor
and control various processes and systems. Some examples of control system
applications include:
✓ Manufacturing and production processes: Control systems are used
to automate and optimize production processes in factories, mills,
and other manufacturing facilities.
✓ Building and home automation: Control systems are used to
automate and control various systems in buildings, such as lighting,
heating and air conditioning, and security.
✓ Transportation systems: Control systems are used to automate and
control various aspects of transportation systems, such as traffic
control systems, railway signaling systems, and aircraft autopilot
systems.
✓ Power generation and distribution: Control systems are used to
monitor and control power generation and distribution systems, such
as power plants and electric grids.
✓ Medical equipment: Control systems are used to automate and
control various types of medical equipment, such as dialysis
machines, ventilators, and X-ray machines.
✓ Agricultural and farming applications: Control systems are used to
automate and optimize various farming and agricultural processes,
such as irrigation, fertilization, and crop harvesting.
✓ Military and defense systems: Control systems are used to automate
and control various military and defense systems, such as missile
defense systems, drones, and radar systems.
✓ Robotics: Control systems are used to design and control the
movement and behavior of robots.
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[Task 2]
Design open loop control model system on MATLAB simulation program where :- The input
signal (unit step) and the system consists of control with parameter(1/s+1) and Transfer
Function with parameter (1/s^2 +2s+1) , show on the osc (input ,output signals) in the same
time.
Explain how can convert this model to closed loop control model on MATLAB
simulation program.
Figure 10. open loop control model system
Figure 9. When Simulation is Run
Page | 10
Explain how can convert this model to closed loop control
model on MATLAB simulation program
Figure 12. When I convert this model to closed loop control model
Figure 11. When Simulation is Run
Page | 11
[Task 3]
1- Explore the main building blocks for electrical and
mechanical control systems
Electrical control system
Figure 13. Electrical control system
Explore the main building blocks
Table 1. Explore the main building blocks
Component Symbol Function Value (from diagram)
Power 100 V,f=50 Hz100 \text{ V},
VsV_s Provides AC voltage to the circuit.
Supply f = 50 \text{ Hz}
Limits current and dissipates
Resistor RsR_s 50 Ω50 \, \Omega
energy as heat.
Stores energy in electric field;
Capacitor CC allows AC to pass depending on 1000 μF1000 \, \mu F
frequency.
Stores energy in magnetic field;
Inductor LL 0.1 H0.1 \, H
resists changes in current.
Not shown explicitly; in control
Control Not applicable in this
— systems includes sensors,
Path diagram
controllers, etc.
LL or Represents energy-consuming or Assumed part of the
Load
external processing element. inductor
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Mechanical control system
Figure 14. Mechanical control system
Explore the main building blocks
Table 2. Explore the main building blocks of Mechanical Control System
Block Description Role in System
Amplifies the error signal to Acts as the controller by
Amplifier (Kₐ) provide enough power to drive the generating the input
actuator. voltage.
Converts the input voltage into the Acts as the plant, modeled
Motor and by the transfer function:
physical movement of the read
Arm (G(s))
head.
Measures the actual head position Provides the feedback,
Sensor (H(s)) and provides feedback to the usually modeled as H(s) =
controller. 1.
Error Signal Difference between the desired Drives the control loop by
(E(s)) and actual head positions. indicating deviation.
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2- Apply Laplace transforms to electrical control system
Figure 15. Electrical control system
Laplace transforms
1. Identify the components in the circuit
Given:
2. Laplace Transform of each component
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3. Write circuit equations in Laplace domain
4. Combine the equations
5. Substitute Is(s)I_s(s)Is(s) into the KVL equation
6. Rearrange the equation:
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3- Apply advanced modelling techniques using MATLAB
program for mechanical control system
Figure 18. Mechanical control system
Figure 17. Desgin mechanical control system on Matlab
Figure 16. Parameters of Motor & Arm
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Figure 20. Parameters of Gain
Figure 19. Signal of Output
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4- Develop the block diagram of a closed loop mechanical system for
the position control of DC motor using a PID controller
Figure 22. Design When i Add PID Controller
Figure 21. Signal of PID Controller
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Figure 24. Controller Parameters of PID Controller
Figure 23. Output Signal After PID Controller
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5- Evaluate the performance of a PID controller in point (4)
To evaluate the performance of the PID controller for the DC motor
position control
1. Overshoot
The plot shows some overshoot, which means the output initially exceeds the
desired value before settling. This is typical of underdamped systems and indicates
the system responds quickly but might require tuning for applications sensitive to
overshoot.
2. Settling Time
The response settles to the desired value relatively quickly. A good settling time
shows effective damping and responsiveness. From the graph, the system stabilizes
within a few seconds, indicating an acceptable settling time for many mechanical
systems.
3. Rise Time
The system rises to the desired value rapidly, suggesting that the proportional gain is
high enough to respond quickly to changes.
4. Steady-State Error
There is no steady-state error evident in the plot. The system reaches and stays at the
setpoint, which confirms that the integral action in the PID controller is functioning
correctly.
Notes
Strengths: Fast response, minimal steady-state error, acceptable
settling time.
Weaknesses: Some overshoot; derivative action might need slight
increase if smoother response is desired.
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Explanation of the three terms
1. Proportional Action
Role: The P term responds to the current error by generating a control action
proportional to the error magnitude.
Effect: It provides immediate corrective action to reduce the error. A higher
Proportional value results in a stronger and quicker response but may lead to
overshoot and oscillations.
2. Integral Action
Role : The I term or Integral term actuates the past error over time and
generates a control action to eliminate the accumulated steady-state error.
Effect : It ensures that even small errors are eventually corrected. It eliminates
offset but can lead to sluggish responses and overshooting if too aggressive.
3. Derivative Action
Role : The D term predicts the future error trend by the rate of change of the
error.
Effect : It adds a dumping effect, reducing oscillation and overshooting caused
by rapid changes in error.
Figure 25. PID Controller Block diagram
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Working of PID controller
To understand the working principals of PID controller, it is required to
understand what is happening inside the closed loop system. First a
setpoint or a target value is given to the PID controller. Then, it takes input
of the actuation device through the sensor and then it compares with the
setpoint and send feedback to the actuation device according to that. And
this loop continues until to get the most desired value. Shortly this is the
working principle of a PID controller.
Advantages of using a PID controller in control systems:
1. Simple Design and Implementation
Easy to understand and implement in both analog and digital
systems.
No need for a detailed mathematical model of the system.
2. Good Stability and Accuracy
The proportional term (P) reduces the error.
The integral term (I) eliminates steady-state error.
The derivative term (D) improves the system’s stability and damping.
3. Versatility
Suitable for a wide range of applications (mechanical, electrical,
thermal, etc.).
Can control both linear and some nonlinear systems.
4. Tunability
PID parameters can be tuned manually or using software tools to
optimize performance (e.g., response time, overshoot, stability).
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5. Robustness
Performs well even when system parameters vary slightly.
Offers reasonable performance under modeling uncertainties and
external disturbances.
6. Real-Time Control
Efficient in real-time applications where quick and responsive control
is needed (e.g., robotics, motor control, process automation).
7. Wide Industry Use
Standard controller in many industrial control systems due to its
reliability and proven track record.
Figure 26. PID Controller Signals
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6- Analyse all control systems in fig (1),(2),(3) using appropriate
mathematical models and computer simulation
Fig (1)
Figure 28. Electrical Control System
Figure 27. mathematical model of Electrical Control System
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Computer simulation
Figure 30. Design on Computer Simulation
Figure 29. Output Signal on Computer Simulation of Electrical Control System
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Fig (2)
Figure 32. Mechanical Control System
Figure 31. mathematical model of Mechanical Control System
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Computer simulation
Figure 34. Design of Mechanical Control System on Computer Simulation
Figure 33. Output Signal on Computer Simulation of Mechanical Control System
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Fig (3)
Figure 35. Electro Mechanical Control System
Table 3. Explain of Electro Mechanical Control System
input signal A desired angle by a control column
controller The controller generates ac control signal to fed an
electrohydraulices seryovalve by comparing
between desired angle and the actual angle of
elevator
process 1.Movement of the control column produces a signal
from the input angular sensor which is compared
with the measured elevator angle by the controller
which generates ac control signal proportional to the
error.
2.This is fed to an electrohydraulices seryovalve
which generates a spool-valve movement that is
proportional to the control signal, thus allowing high-
pressure fluid to enter the hydraulic cylinder.
3.The pressure difference across the piston provides
the actuating force to operate the elevator.
Feed back The system use the measured angle by angular
sensor as negative feedback to allow controller to
compare between actual angle and desired angle
Output Movements with speed to reach specific positions
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Figure 36. mathematical model of Electro Mechanical Control System
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Computer simulation
Figure 38. Design of Electro Mechanical Control System on Computer Simulation
Figure 37. Controller Parameters of Electro Mechanical Control System
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Figure 40. Signal of PID Controller
Figure 39. Output Signal on Computer Simulation of Electro Mechanical Control System
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7- Perform high level self-tuning control system techniques for Electro-
Mechanical system using mathematical modelling and computer
simulation
Electro-Mechanical system
Figure 41. Electro-Mechanical system
Figure 42. mathematical model of Improve for Electro Mechanical Control System
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Computer simulation
Figure 43. Steps of Improve for Electro Mechanical Control System on Computer Simulation
Page | 34
Figure 45. Output Signal
Figure 44. Design When Add Saturation
Page | 35
Figure 47. Design Electro Mechanical Control System After improve
Figure 46. Values of Saturation
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Figure 48. Output Signal After Improve
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Advantages of Using the Saturation Block
Protects System Components
Prevents sending signals outside the operational limits of actuators,
sensors, or other hardware.
Avoids potential damage or instability caused by overdriving
components.
Ensures Stability and Safety
Prevents controller outputs (e.g., from a PID controller) from
becoming excessively large, which might lead to system instability.
Avoids numerical issues by keeping values within simulation-friendly
ranges.
Simplifies Nonlinear Behavior Modeling
Helps in modeling real-world systems that have natural physical
constraints (like saturation in motors, amplifiers, valves, etc.).
Accurately represents systems that behave linearly up to a point and
then saturate.
Improves Simulation Robustness
Prevents simulation errors caused by unrealistic signal values (e.g.,
integrator windup when the output exceeds limits).
Facilitates more predictable and controlled simulation behavior.
Supports Anti-Windup Techniques
Works effectively with controllers that have anti-windup logic,
avoiding integrator accumulation when outputs are saturated.
Ease of Use
Simple to configure via upper and lower limit parameters.
Page | 38
Figure 49. Curve of Saturaion
Page | 39
Reference
✓ GeeksforGeeks. (2022, October 17). Proportional Integral
Derivative Controller in Control System.
https://www.geeksforgeeks.org/proportional-integral-derivative-
controller-in-control-system/
✓ Taha, T. (n.d.). EE 5143: Linear Systems and Controls.
Vanderbilt University.
https://lab.vanderbilt.edu/taha/teaching/ee-5143-linear-
systems-and-controls/
✓ The Engineering Projects. (2020, April 13). Introduction to
Control Systems.
https://www.theengineeringprojects.com/2020/04/introduction-
to-control-systems.html/?amp=1
✓ GeeksforGeeks. (2022, October 17). Components of Control
Systems. https://www.geeksforgeeks.org/components-of-
control-systems/
✓ GeeksforGeeks. (2022, October 17). Control System.
https://www.geeksforgeeks.org/control-system/
✓ TechTarget. (n.d.). Control system. TechTarget.
https://www.techtarget.com/whatis/definition/control-system
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