Control Engineering Instructional Module Lectures

Control Engineering
Instructional Module
Lectures
1. Chapter 1: Introduction to Control Engineering

- System
- Block Diagram
- Open loop System
- Close loop System
2. Chapter 2: Transfer Function
- Overall transfer function
- Block Diagram Simplification
3. Chapter 3: LTI, Time and Frequency Domain, Laplace Transform
4. Chapter 4: Modelling Control system
- Modelling Mechanical System
- Spring and dampers
- Fluid and Thermal System
5. Chapter 5: Controller
- PID Controller
6. Chapter 6: Controlling modelled system
- Controlling First Order Plants
Chapter 1: Introduction to Control System
Learning Objectives:
 Explain the function of an automatic control system.

 Identify a block diagram representation of a physical system
 Explain the difference between an open loop and closed loop control system
Control System
System is a combination of physical components that able to convert an input into a desired output.
Wherein an input is an external source applied to a system in order to produce an output which is
the response obtained from the system (See figure 1). Meanwhile, a control system Is a
combination of physical components that able to regulate, maintain, direct itself to achieve certain
objective.
figure 1. System block diagram
Block Diagrams
Block diagram is a graphical representation of a control system. It shows the interrelationship of

systems and how signals flow between them. In another word block diagram are simplified
drawings that remove all of the stuff that is not needed so that the user can focus on the concept
being described. With block diagrams, we focus on how systems are connected and the signals
that flow between them. We omit the other engineering information that would just clutter up the
diagram. For example, block diagrams don’t show the physical location and drawings of the
hardware. In figure 2, an illustration of blocks is shown. An arrow represents the signal flow (note:
In control system signal flow is not reversible), a rectangular block represents the systems and
other components and Circle represents summation of signals .
figure 2. symbols of block diagrams
Open Loop Control System
Open loop control system modifies output based on predetermined control values. Wherein there
is no actual measurement of controlled quantity. In an example shown in figure 3. A tank level, h,
is dependent on the volume of water leaving the system, Q out, which is control by a predefined
valve opening. In this kind of control, h, will only maintain its level when Q in = Qout as Qout has a
constant value. Therefore, if any disturbances occur such as increasing or decreasing Q in , the level
of tank will not be under control.
figure 3. Open loop system: Tank water level problem
Close Loop System
Closed loop control modifies output based on measured values of the control variable. Measured
value compared to desired value and used to maintain desired value when disturbances occur.
Closed loop control uses feedback of output to input. In this control system, electronic sensors are
used to monitor the state of changes in the system. It sends feedback to the controller which then
manipulated the control elements depending on the error sent to it. Since this is an automatic
control system, changes in Qin and any disturbances that may affect the system will be resolved
through Error detection. For the block diagram of a close loop control system see figure 4.
figure 4. Close loop control system: Tank water level problem

Chapter 2: Transfer Function
 Identify overall transfer function of a control system

 Explain the difference between linear and non-linear response
 Simplify control system block diagram
Transfer function
Transfer function is the ratio of the output to the input of a control system component. Generally,
a function of frequency and time. It also the Laplace transform of the impulse response of a linear,
time-invariant system with a single input and single output when you set the initial conditions to
zero. They allow us to connect several systems in series by performing convolution through simple
multiplication. A block diagram of a transfer function was shown in figure 5.
figure 5. Block Gain transfer function
Examples:
figure 6. Components block diagram

Overall transfer function
The overall transfer function summarizes the whole transfer function of a complex system into a
single block diagram. By computing the overall transfer function, the complexity of the system
was minimized, wherein the value of output will be determined by the given gain of each
subsystem. An example of finding the overall transfer function was given below
figure 7. Block Diagram of Servo Control

Block Diagram simplification
Finding the overall transfer function of the system simplifies the block diagram.
the as a convolutional rule, block in series can be simplifies by just multiplying its gain.
Chapter 3: LTI, Time, Frequency Domain and Laplace Transform
 Have an understanding with linear-time invariant system

 Have an understanding between time domain and frequency domain
 Convert differential equation into frequency domain using laplace transform
Linear Time Invariant system

According to our formal definition, transfer functions require that you have a linear and time-invariant
(LTI) system. LTI system have the following properties; homogeneity, superposition, and time-
invariance. These properties are what cause the system to behave in predictable ways
Homogeneity means that if you scale the input, x(t), by factor, a, then the output, y(t), will also
be scaled by a. So in the example below, a step input of height A produces an oscillating step to
height B. Since h(x) is a linear system then a step input that is doubled to 2A will produce an
output that is exactly doubled as well.
Superposition, or you might also hear it called additivity, means that if you sum two separate
inputs together, the response through a linear system will be the summed outputs of each individual
input. In the example below the step input, A, produces output, a, and the ramp input, B, produces
output, b. Superposition states that if we sum inputs A+B then the resulting output is the sum a+b.
Time invariance, refers to a system behaving the same regardless of when in time the action
takes place. Given y(t) = h(x(t)), if we shift the input, x(t), by a fixed time, T, then the output,
y(t), is also shifted by that fixed time. We can write this as y(t −T) = h(x(t −T)). Sometimes this
is also referred to as translation invariance which covers translation through space as well as
time. Here’s an example of how shifting the input results in a shifted output in a time-invariant
system
Watch this video:

Control Systems Lectures - LTI
Systemhttps://www.youtube.com/watch?v=3eDDTFcSC_Y&t=388s
Time Domain and Frequency Domain
Watch these Videos:
1. Control Systems Lectures - Time and Frequency Domain-
https://www.youtube.com/watch?v=noycLIZbK_k
2. Introduction to the Fourier Transform (Part 1) -
https://www.youtube.com/watch?v=1JnayXHhjlg
3. Introduction to the Fourier Transform (Part 2) –
https://www.youtube.com/watch?v=kKu6JDqNma8
Laplace Transform
Watch these videos
1. The Laplace Transform and the Important Role it Plays-
https://www.youtube.com/watch?v=VJ9phDRys_I
2. The Laplace Transform - A Graphical Approach
https://www.youtube.com/watch?v=ZGPtPkTft8g&t=288s
References:
Brian Douglas (2019) :“An Engineer’s Guide to The Fundamental of Control Theory”

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Control Engineering

1. Chapter 1: Introduction to Control Engineering

 Explain the function of an automatic control system.

figure 1. System block diagram

Block diagram is a graphical representation of a control system. It shows the interrelationship of

figure 2. symbols of block diagrams

Open Loop Control System

Close Loop System

figure 4. Close loop control system: Tank water level problem

 Identify overall transfer function of a control system

figure 5. Block Gain transfer function

figure 6. Components block diagram

figure 7. Block Diagram of Servo Control

 Have an understanding with linear-time invariant system

Linear Time Invariant system

Watch this video:

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