Control Systems Theory (ME 332– GTU) Saeed Lotfan

Gebze Technical University

Dep. of Mechanical Engineering

Control Systems Theory (ME 332)

Lecture 1: Introduction
By Saeed Lotfan
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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Introduction
Examples of controlled systems:
Rockets fires: space shuttle lifts off to earth orbit; in splashing cooling water, a metallic part is
automatically machined.
human made
A self-guided vehicle delivering material to workstations in an aerospace assembly plant glides
along the floor seeking its destination.

Pancreas, which regulates our blood sugar. nature

in the

In time of “fight or flight,” our adrenaline increases along with our heart rate, causing more
oxygen to be delivered to our cells.
Non physical
The model with the input of student’s available study time, and the output of the grade.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Introduction
Examples of controlled systems:
Internet of Things (IoT) (efficient energy use in homes and businesses).

Manufacturing (3D printing).

Advantages of Control Systems

1. Power amplification

2. Remote control

3. Convenience of input form

4. Compensation for disturbances

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Control System Definition

System

Control

1. A control system consists of subsystems and processes (or plants) assembled for the purpose
of obtaining a desired output with desired performance, given a specified input.
2. A control system is an interconnection of components forming a system configuration that
will provide a desired system response.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Control System Definition 4th f

Example of an elevator:

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Control System Definition

A sensor is a device that provides a measurement of a desired external signal. For example,
resistance temperature detectors (RTDs) are sensors used to measure temperature.

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human human
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An actuator is a device employed by the control system to alter or adjust the environment. An
electric motor drive used to rotate a robotic manipulator is an example of a device transforming
electric energy to mechanical torque.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
Process to be controlled:

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Open-loop systems:

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
An open-loop control system utilizes an actuating device to control the process directly without
using feedback.

For example, the plant can be a furnace or air conditioning system, where the output variable
is temperature. The controller in a heating system consists of fuel valves and the electrical
system that operates the valves.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations

The distinguishing characteristic of an open-loop system is that it cannot compensate for any
disturbances that add to the controller’s driving signal.

For example, if the controller is an electronic amplifier and Disturbance 1 is noise, then any
additive amplifier noise at the first summing junction will also drive the process, corrupting the
output with the effect of the noise. The output of an open-loop system is corrupted not only by
signals that add to the controller’s commands but also by disturbances at the output. The
system cannot correct for these disturbances, either.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
Closed-Loop (Feedback Control) Systems:
In contrast to an open-loop control system, a closed-loop control system utilizes an additional
measure of the actual output to compare the actual output with the desired output response.
The measure of the output is called the feedback signal.

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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).

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
For example, if the controller uses electrical signals to operate the valves of a temperature
control system, the input position and the output temperature are converted to electrical
signals. The input position can be converted to a voltage by a potentiometer, a variable resistor,
and the output temperature can be converted to a voltage by a thermistor, a device whose
electrical resistance changes with temperature.

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v
Tempy

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
Closed-loop systems, then, have the obvious advantage of greater accuracy than open-loop
systems. They are less sensitive to noise, disturbances, and changes in the environment.
Transient response and steady-state error can be controlled more conveniently and with
greater flexibility in closed-loop systems, often by a simple adjustment of gain (amplification) in
the loop and sometimes by redesigning the controller. We refer to the redesign as
compensating the system and to the resulting hardware as a compensator.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
As the systems become more complex, the interrelationship of many controlled variables must
be considered in the control scheme.

Multi-loop feedback system:

so

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
As the systems become more complex, the interrelationship of many controlled variables must
be considered in the control scheme.

Multi-variable control system.:

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

System Configurations
A common example of an open-loop control system is a microwave oven set to operate for a
fixed time.

An example of a closed-loop control system is a person steering an automobile (assuming his or

her eyes are open) by looking at the auto’s location on the road and making the appropriate
adjustments.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Examples of Control Systems

The first automatic feedback controller used in an industrial process is generally agreed to be
James Watt’s flyball governor.
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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Examples of Control Systems

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Examples of Control Systems

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Examples of Control Systems

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Engineering Analysis and Design

Analysis is the process by which a system’s performance is determined. For example, we
evaluate its transient response and steady-state error to determine if they meet the desired
specifications.

Design is the process of conceiving or inventing the forms, parts, and details of a system to
achieve a specified purpose. Design is the process by which a system’s performance is created
or changed. For example, if a system’s transient response and steady-state error are analyzed
and found not to meet the specifications, then we change parameters or add additional
components to meet the specifications.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Engineering Analysis and Design

frequency domain Laplace Block diagram Analysis Design
time domain state spare representation Analysis Design

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Waveforms in Control

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Waveforms in Control

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Design Example
Rotating disk speed control:

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Design Example
Rotating disk speed control:

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
1. Study the Case Study of the main reference on page 11.
2. A variable resistor, called a potentiometer, is shown below. The resistance is varied by
moving a wiper arm along a fixed resistance. The resistance from A to C is fixed, but the
resistance from B to C varies with the position of the wiper arm. If it takes 10 turns to move
the wiper arm from A to C, draw a block diagram of the potentiometer showing the input
variable, the output variable, and (inside the block) the gain, which is a constant and is the
amount by which the input is multiplied to obtain the output.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
3. A temperature control system operates by sensing the difference between the thermostat
setting and the actual temperature and then opening a fuel valve an amount proportional to
this difference. Draw a functional closed-loop block diagram identifying the input and output
transducers, the controller, and the plant. Further, identify the input and output signals of all
subsystems previously described.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
4. Consider the inverted pendulum shown below. Sketch the block diagram of a feedback
control system. Identify the process, sensor, actuator, and controller. The objective is keep
the pendulum in the upright position, that is to keep θ = 0, in the presence of disturbances.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
5. Moored floating platforms are subject to external disturbances such as waves, wind, and
currents that cause them to drift. There are certain applications, such as diving support,
drilling pipe-laying, and tanking between ships in which precise positioning of moored
platforms is very important (Muñoz-Mansilla,2011). Figure on the next page illustrates a
tethered platform in which side thrusters are used for positioning. A control system is to be
designed in which the objective is to minimize the drift, Y, and an angular deviation from the
vertical axes, ϕ (not shown). The disturbances acting on the system’s outputs are the force,
F, and the torque, M, caused by the external environment. In this problem, the plant will have
one input, the force delivered by the thrusters (Fu) and two outputs, Y and ϕ. Note also that
this is a disturbance attenuation problem, so there is no command input. Draw a block
diagram of the system indicating the disturbances F and M, the control signal Fu, and the
outputs Y and ϕ. Your diagram should also have blocks for a controller, the one-input two-
output plant, and a block indicating how the disturbances affect each of the outputs.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
6. Given the electric network shown below.
a. Write the differential equation for the network if v(t) = u(t), a unit step.
b. Solve the differential equation for the current, i(t), if there is no initial energy in the
network.
c. Make a plot of your solution if R/L = 1.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
7. Small computers are used as part of a start-stop system in automobiles to control emissions
and obtain improved gas mileage. A computer-controlled start-stop system that
automatically stops and restarts an engine to reduce the time the engine idles could improve
gas mileage and reduce unwanted polluting emissions significantly. Sketch a block diagram
for such a system for an automobile.

8. Solve the following differential equations using classical methods. Assume zero initial
conditions.

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Control Systems Theory (ME 332– GTU) Saeed Lotfan

Practice at Home
9. Solve the following differential equations using classical methods and the given initial
conditions:

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