Control Systems
Module: Introduction to Control Systems
About me
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M.S. & Ph.D., Department of Electrical Engineering, IIT Madras
Researcher, Mobile Robotics, Addverb Technologies, Noida
Operations Research Analyst, Solverminds Solutions & Tech, Chennai
Research Interests:
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Game theory
Robotics
Control & Optimization (IP/LP/MILP/Convex/Non-linear)
Multi-agent Path Finding
Operations Research
Course Outline
Module 1: Introduction to Control Systems
Module 2: Mathematical Modeling of a System
Module 3: Block Diagram Reduction
Module 4: Time Response Analysis
Module 5: Stability Analysis
Module 6: Steady-State Errors
Module 7: Design via State Space
Module 8: Root Locus Techniques and Design via Root Locus
Module 9: Frequency Response Techniques and Design via Frequency Response
Module 10: Digital Control Systems
Text and Reference Books
Text Books:
• Norman S. Nise, Control System Engineering, 7th Edition, Wiley.
• Katsuhiko Ogata, Modern Control Engineering, 5th Edition, Prentice Hall.
Reference Books:
• Benjamin C. Kuo, Automatic Control Systems, Prentice Hall.
• Richard C. Dorf and Robert H. Bishop, Modern Control Systems, Pearson.
• Gene Franklin, J.D. Powell, and Abbas Emami-Naeini, Feedback Control of Dynamic Systems,
Prentice Hall.
• Eronini I. Umez-Eronini, System Dynamics and Control, Thomson Engineering.
Assessment
Assignments + Classroom Quizzes: 30%
Mid-Sem Exam: 30%
End-Sem Exam: 40%
Outline
Introduction to Control Systems:
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System & Control System
Open loop and Closed loop Control systems
Examples of Control Systems
A brief history of Control Systems
Future evolution of Control Systems
Control Systems Design
System/Plant/Process
• A system is a collection of interrelated and interacting components that work together to achieve a
particular objective or purpose.
• A system generates an output (response) in response to an input (excitation).
Input/ Excitation
Sy
Plant
Output/ Response
• A system may comprise multiple subsystems within its structure.
Automobile and its subsystems:
• Engine System: Responsible for generating power.
• Braking System: Manages the vehicle's deceleration and stopping.
• Electrical System: Controls lighting, instrumentation, and other electrical components.
• Transmission System: Facilitates the transfer of power from the engine to the wheels.
• Fuel System: Manages the storage and delivery of fuel to the engine.
Examples
Air conditioner
•Input – Electrical energy (Voltage)
•Output – Heat energy (Changes the ambient temperature)
Human body infected with a virus
•Input – Drug administration
•Output – Drug distribution & effect on the body
Vehicle
•Input – Acceleration or Deceleration
•Output – Vehicle displacement
Motor
•Input – Electrical energy (Voltage)
•Output – Mechanical energy (Torque / Rotation)
Control System
Control system: a mechanism that alters the future state of the system.
Control theory: a branch of applied mathematics that provides a strategy to select an
appropriate input
A control system is necessary to regulate or manage the behavior of a system or process.
A control system consists of subsystems and processes (or plants) assembled for the purpose
of obtaining a desired output with desired performance.
Types of Control Systems
Process to be Controlled:
An open-loop control
system utilizes an actuating
device to control the
process directly without
• No feedback
using feedback.
• Cannot Tolerate Disturbances
Ex. Ceiling Fan,
• Lower cost and Complexity
Oven, toasters.
A closed-loop control
system uses a
measurement of the
output and feedback of
this signal to compare it
with the desired output
(reference or command).
Ex. Air Conditioner
An actuator physically performs
the action, while a controller
directs and regulates the action.
• Feedback for corrective action​
• Robust to Disturbances​
• Higher cost and Complexity​
Examples of control systems
Manual Closed loop Control system:
Student–teacher learning process:
Desired output: Fluid level
Actuator: Valve + Human Hands
Controller: Brain
Sensors: Human Eyes
Process: Tank
Examples of Control systems
Input: Reference cleanliness
Control variable: Amount of time
Output: Actual cleanliness after washing
Disturbances: Variable cleanliness of the cloths
Open loop control systems cannot correct for
any disturbances.
Closed loop control systems correct for any disturbances by
measuring the output response, feeding that measurement back
through a feedback path, and comparing the response to the input.
Closed loop system
Disturbance
Control Input
Control system
Reference
Plant
Feedback : Measured temperature
Air conditioner maintaining desired temperature as a Closed-loop System:
Traffic conditions
Control system
Control Input
Reference
Output
Plant
Feedback
Human steering an automobile as a Closed-loop System
Output
Parallel Parking Problem
To find the path a car must take to parallel park into a
parking space.
Inverted Pendulum
Objective: Keep the pendulum in the
upright position, that is to keep θ = 0, in the
presence of disturbances.
A Brief History of Automatic Control
Feedback control is an engineering discipline. As such, its progress is closely tied to the practical
problems that needed to be solved during any phase of human history.
• Ancient Greek and Arabic culture (from ~300 BC to AD ~1200): Accurate track of time
• Industrial Revolution in Europe (the 1700s, but trends started in around 1600),
• Emergence of Telecommunications and advancements during 1st & 2nd World wars (1910–1945)
• Appearance of computers & the start of space research (1957–Till now)
Water Clock
Openloop control
systems
Egypt around 1500 BC
Greek water clock measured time through a gradual flow of water, in which constant flow rate at E was
obtained by overflowing water at D.
Disadvantage: Large quantity of water wasted by overflow, due to which the clock was named Clepsydra
(“water thief” in Greek).
Water Clocks
• Ctesibius (Greek) (250BC) invented a float regulator for a water
clock for accurate determination of time.
• First feedback control systems invented by human
• Philo (Byzantium (Greek city)) (250 BC), Heron of Alexandria (AD
1st century), Arabic engineers (AD 800-1200) also used a float
regulator to control the oil level in an oil lamp, automatic
dispensing of wine, etc.
• Invention of mechanical
became obsolete.
clocks,
float
controlled
clocks
• Arabic engineers discovered On-Off controllers, which reappeared
in minimum-time problems (1950's).
Temperature control uses On/Off control where system receives
full power until it reaches the desired setpoint. Once the setpoint
is surpassed, the heater is completely turned off.
Industrial Revolution
• Development of grain mills and furnaces in the 1600s laid the groundwork for industrial advancements. T.
Newcomen's steam engine in 1712, but it was energy inefficient, limiting industrial applications.
• Industrial Revolution is James Watt's flyball speed governor (1769), a device that regulated steam flow to a
steam engine to maintain constant engine speed.
• If actual speed increases beyond the desired value, increase in
centrifugal force of spinning flyball governor causes closing of
steam valve, resulting in the supply of less steam,
and speed of the steam engine decreases. If the engine speed
drops below the desired value, the opposite action occurs.
• A variety of control devices was invented, including float
regulators (used in a steam engine for pumping water),
temperature regulators, pressure regulators (steam-pressure
regulation in the boiler, for the steam that drives the engine
should be at a constant pressure).
Feedback control system
Transition from trial-and-error
• Design of feedback control systems up through the Industrial Revolution was by trial-and-error together
with a great deal of engineering intuition: More of an art than a science.
• Controlling the speed of every Steam engine was plagued by problems of instability and inaccuracy.
• James Clerk Maxwell (1868): stability criterion of "Flyball governor" for a third-order system based on the
coefficients of the differential equation. He linearized the differential equations of motion to find
the characteristic equation of the system.
• He studied the effect of the system parameters on stability and showed that the system is stable if the
roots of the characteristic equation have negative real parts.
• In 1874, Edward John Routh, extended the stability criterion to fifth-order systems.
• Lyapunov extended the work of Routh to nonlinear systems in 1892.
Ship control & Frequency domain Analysis
• In 1922, E A Sperry invented Gyroscope (a sensor used for measuring orientation), which he used in
the stabilization and steering of ships, and later in aircraft control. --- Automatic steering system
• Theoretical development of Nicholas Minorsky was applied to the automatic steering of ships that led
to what we call today proportional-plus-integral-plus-derivative (PID) controllers.
• Frequency domain approaches developed by Laplace, Fourier, Cauchy and others were explored and
used in communication systems.
• Major problem with the development of a mass communication system extending over long distances
is the need to periodically amplify the voice signal in long telephone lines. (Noise Amplification)
• To design of suitable repeater amplifiers with no distortion, H.S. Black (1927) demonstrated the
usefulness of negative feedback introducing a phase shift at the correct frequencies in the system.
• In the late 1920s and early 1930s, Bode (GM & PM) and Nyquist (Nyquist stability criterion) at Bell
Telephone Laboratories developed the analysis of feedback amplifiers.
• Walter R. Evans (1948), working in the aircraft industry, developed Root locus technique plotting roots
of a characteristic equation of feedback system whose parameters changed over a particular range. --Direct way to determine the closed-loop pole locations in the s-plane.
Control Systems Timeline
1940-1960s​​
​Operational amplifiers Frequency domain methods​​
Nyquist plots Bode plots​​
Root locus methods​​
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PID controllers​
1960s Onwards​
State space methods: (Kalman-1960) Describes a given system using a
system of linear differential equations, manipulated using matrix
operations and used to relate state variables to the system input, output.
Multivariable control: variable interacts strongly, MIMO Systems.
Optimal control​: Finding a control law for a given system such that a
certain optimality criterion is achieved. Send a rocket to the moon with
minimal fuel consumption, Produce a given amount of chemical in
minimal time .
Adaptive control​: The controller parameters are adjusted automatically
to compensate for changing process conditions
Stochastic control: Existence of uncertainty either in observations or in
the noise that drives the evolution of the system
Nonlinear control​: All physical systems are nonlinear to some extent
Robust control: To ensure precise and accurate system performance
despite uncertainties and disturbances
Applications:
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Guidance, navigation, and control of missiles and spacecraft.
Industrial Robots, Medical equipment.
Process control, Factories, mills, and manufacturing facilities.
Traffic control systems, Railway signaling, Autopilot systems.
Missile defense systems, Drones, and Radar systems.
Control of Power Generation & distribution systems
Embedded control systems in automobiles to control engine,
transmission, brakes, and suspension.
Journals/Conferences in Control Systems
IEEE Transactions on Control Systems Technology (TCST)
IEEE Transactions on Automatic Control (TAC)
IEEE Transactions on Robotics
IEEE Transactions on Control of Network Systems (TCNS)
IEEE Transactions on Industrial Informatics
IET Control Theory and Applications
International Journal of Robust and Nonlinear Control
IEEE Transactions on Cybernetics
Jobs:
American Control Conference ACC
Conference on Decision and Control CDC
European Control Conference ECC
Mediterranean Conference on Control and Automation
IFAC Symposium on System Identification
IEEE Conference on Control Technology and Applications (CCTA)
IEEE International Conference on Robotics and Automation (ICRA)
IEEE International Conference on Intelligent Robots and Systems (IROS)
The Design Steps of a Control System
Step 1: Determine a physical system and specifications from requirements.
Step 2: Draw a functional block diagram.
Step 3: Represent the physical system as a schematic.
Step 4: Use the schematic to obtain a mathematical model, such as a block diagram, signal flow
diagram, state-space representation.
Step 5: Reduce the block diagram to single block or closed loop system.
Step 6: Analyze, design and test the system to meet specified requirements and specifications (for
ex. stability, transient response, and steady-state performance).
References
• Norman S. Nise, Control System Engineering, 7th Edition, Wiley.
• Katsuhiko Ogata, Modern Control Engineering, 5th Edition, Prentice Hall.
• Richard C. Dorf and Robert H. Bishop, Modern Control Systems, Pearson.
• Gene Franklin, J.D. Powell, and Abbas Emami-Naeini, Feedback Control of Dynamic
Systems, Prentice Hall.
• Eronini I. Umez-Eronini, System Dynamics and Control, Thomson Engineering.
See pg 4 for extra book