Dr. Engy Aly MaherWinter 2019

Dr. Engy Aly Maher

E-mail: engy.aly@guc.edu.eg

Office: C3-317

Office Hours: By appointment

Upon successful completion of this course, the student will be able to:

1. Understand basic concepts underlying the use of feedback control systems;

2. Analyze mechanical, electrical and electromechanical systems;

3. Integrate the concepts of feedback control systems with real-time simulation using MATLAB.

4. Design a stable feedback control system with one input and one output and optimized control

characteristics.

• Feedback Control of Dynamic Systems, by Franklin, Powell and Emami Naieni, 4th Edition,

Prentice Hall, 2002.

• Modern Control Engineering, 4th Edition, by K. Ogata, Prentice Hall, 2001

• Modern Control Systems, 9th Edition, by Dorf and Bishop, Prentice Hall, 2001.

• Automatic Control Systems, by B. Kuo, Prentice Hall, 1995.

Method Distribution Total

Quizzes 2 x 5% 10%

Assignments 2 x 5% 10%

Lab Quizzes

Lab Project

10%

20%

30%

MidTerm 15%

Final Exam 35%

1. Introduction to control systems analysis: open loop control

system, closed loop control system.

2. Transfer function, Block diagram, Block diagram reduction,

signal flow graph.

3. Mathematical modelling of dynamic systems: Mechanical,

Electrical, and Electromechanical systems.

4. Transient and steady-state response analysis. First and second-

order systems.

5. Stability analysis in the complex plane. Routh's stability.

6. Root Locus Analysis.

7. Proportional, integral and derivative Control (PID).

8. Bode diagram, Nyquist plot.

9. Nyquist stability criterion.

Introduction

Control is whenever some quantity, such as temperature, altitude, or speed must be made to behave

in some desirable way over time. In other words, control makes some object (called plant or

process) behave in some desirable manner.

A control system is a collection of components assembled to produce a desired response for a given

input. To make the system OUTPUT and the desired REFERENCE as close as possible, i.e., to

make the ERROR as small as possible.

Examples:

Controlled Variable – It is the quantity or condition that is measured and Controlled. Normally controlled

variable is the output of the control system.

Manipulated Variable – It is the quantity of the condition that is varied by the controller so as to affect the

value of controlled variable.

Control – Control means measuring the value of controlled variable of the system and applying the

manipulated variable to the system to correct or limit the deviation of the measured value from a desired

value.

Disturbances – A disturbance is a signal that tends to adversely affect the value of the

system. It is an unwanted input of the system.

If a disturbance is generated within the system, it is called internal disturbance. While an external

disturbance is generated outside the system.

Desired Response – the idealized instantaneous behavior that we would like from the system.

Transient Response – the gradual change in the system as it approaches its approximation of the desired

response.

Steady-State Response – the response of the system once it has finished changing and is now approximating

the desired response.

Steady-State Error – the difference between the steady-state response and the desired

response.

Natural vs. Man-made

Human body temperature \ Vehicles

Manual vs. Automatic

Room temp. via fan \ via A.C

Linear vs. Non Linear

Linear vs. Non Linear

Time invariant vs Time variant

Time invariant vs Time variant

Time invariant vs Time variant

When the characteristics of the system do not depend upon time itself then the system is said to time

invariant control system,

while Time varying control system is a system in which one or more parameters vary with time

Lumped parameter vs Distributed Parameter

Control system that can be described by ordinary differential equations are lumped-parameter

control systems.

Whereas the distributed parameter control systems are described by partial differential equations.

Continuous-data Vs Discrete-data System

In continuous data control system all system variables are function of a continuous time t.

A discrete time control system involves one or more variables that are known only at discrete time intervals.

Deterministic vs Stochastic Control System

A control System is deterministic if the response to input is predictable and repeatable.

If not, the control system is a stochastic control system

Open loop (OL) vs. Closed Loop (CL)\ Feedback (FB)

Open loop (OL) control systems: the output has no effect on the control action. In an open

loop control system the output is neither measured nor fed back for comparison with the

reference input.

As a general rule of thumb :

“Any control system working on a time basis is open loop.”

Advantages :

Simple in construction and design.

Economical.

Easy to maintain.

Generally stable.

Disadvantages:

They are unreliable.

Sensitive to disturbances

Disturbances cannot be corrected automatically.

In a Closed Loop or Feedback control system, the controlled output is measured and

compared with the reference input. The difference between the two, called error, is fed into

the controller which produces a control signal to reduce this error.

Electric Washing Machine Water Level Controller Electric Hand Drier Air Conditioner

Navigation Software Volume of Audio System Human crossing the roadLight Bulb

Actuator:- the device that causes the plant to provide the output. Or simply, It provides the

motive power to the plant.

Sensor:- the device that provides information about the output of the plant (not in every

control systems is present ).

Controller:- is the brain of the system. It may be a computer program, electrical or

mechanical device, etc.

Reference:- is the desired outcome of the control system.

Manual control system for regulating the level of the fluid in a tank

In this control system:

The reference is a desired level of fluid that operator is instructed to maintain.

The actuator is the valve that opens or closes the fluid flow out.

The sensor is visual.

The controller is the operator.

Mathematical Models

The control systems can be represented with a set of mathematical equations known as

mathematical model. These models are useful for analysis and design of control systems.

• Analysis of control system means finding the output when we know the input and

mathematical model.

• Design of control system means finding the mathematical model when we know the

input and the output.

Developing a mathematical model is to apply the fundamental physical laws of science and

engineering.

Electrical systems:

Kirchhoff's voltage law: The sum of voltages around a closed path equals zero.

Kirchhoff's current law: The sum of electric currents flowing from a node equals zero.

Developing a mathematical model is to apply the fundamental physical laws of science and

engineering.

Mechanical systems:

Newton's laws: The sum of forces on a body equals zero

The sum of moments on a body equals zero

The following mathematical models are mostly used.

• Differential equation model

• Transfer function model

• Block diagram

• State space model

Describe the relationship between the input and output of dynamic systems. One such

model is the linear, time-invariant differential equation

A system represented by a differential equation is difficult to model as a block diagram.

Thus, we now lay the groundwork for the Laplace transform, with which we can represent

the input, output, and system as separate entities.

The transfer function G(s) of a system is defined as the ratio of the Laplace transforms

output and input with zero initial conditions.