MECE 3350
Control Systems
Lecture 1
Introduction to Linear Control Systems
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Lecture 1
Videos in this lecture
Lecture 1: https://youtu.be/TyJSMVarQZQ
Exercise 1: https://youtu.be/xHRKLbFdjvw
Exercise 2: https://youtu.be/Up_FpeS5zUI
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Lecture 1
Applications of Control System
Autonomous robots
https://www.youtube.com/watch?v=fRj34o4hN4I
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Lecture 1
Applications of Control System
Autonomous cars
https://www.youtube.com/watch?v=cdgQpa1pUUE
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Lecture 1
Applications of Control System
Control of quadcopters
https://www.youtube.com/watch?v=w2itwFJCgFQ
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Lecture 1
Applications of Control System
Self-balancing robots
https://www.youtube.com/watch?v=n_6p-1J551Y
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Lecture 1
Applications of Control System
Robotic surgery
https://www.youtube.com/watch?v=-5lzGk7dgCQ
Anything else?
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Lecture 1
More applications
→ Automatic assembly line
→ Machine tool control
→ Space technology and satellite control
→ Power Systems
→ Micro electro mechanical systems (MEMS)
→ Smart transportation systems
→ Ship stabilization systems
→ Temperature control systems
→ Missile launching systems
→ Voltage stabilizer systems
→ Sun tracking control of solar collectors
→ ...
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Lecture 1
Control engineering
The first step in control engineering is to understand the system we want to
control.
Then, we design a secondary system that controls the behaviour of the first
system
This is called open-loop control.
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Lecture 1
Control engineering
A closed-loop control system uses a measurement of the output and feedback
of this signal to compare it with the desired output.
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Lecture 1
Control engineering
A closed-loop control system uses a measurement of the output and feedback
of this signal to compare it with the desired output.
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Lecture 1
A simple feedback system
The variable being controlled is measured by a sensor and fed back to the
controller to influence the controlled variable.
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Lecture 1
Example - cruise control
From measurements, we determined that:
→ A 1◦ change in the throttle angle causes a 10 km/h change in speed.
→ When the road grade changes by 1%, the speed changes by 5 km/h
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Lecture 1
Example - cruise control
Step 1 - Model the system to be controlled
→ A 1◦ change in the throttle angle causes a 10 km/h change in speed.
→ When the road grade changes by 1%, the speed changes by 5 km/h
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Lecture 1
Example - cruise control
Step 2 - Find a suitable controller
→ A 1◦ change in the throttle angle causes a 10 km/h change in speed.
→ When the road grade changes by 1%, the speed changes by 5 km/h
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Lecture 1
Example - cruise control
Step 2 - Find a suitable controller
→ A 1◦ change in the throttle angle causes a 10 km/h change in speed.
→ When the road grade changes by 1%, the speed changes by 5 km/h
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Lecture 1
Example - cruise control
y = 10(u − 0.5w )
u=
Combining the equations:
y=
100
5
r−
w
101
101
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Lecture 1
Linear systems
A linear system satisfies the properties of superposition and homogeneity
Superposition: xi provides a response yi , thus:
Homogeneity: x1 provides a response y1 , the response to αx1 is:
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Lecture 1
Linear systems
Are these systems linear ?
Linear approximations
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Lecture 1
Pendulum example
Torque vs angle θ
τ (t) = mg` sin(θ)
Is this system linear?
Taylor’s series around θ = 0:
sin θ = θ −
θ3
θ5
θ7
+
−
+ ...
3!
5!
7!
For θ ≈ 0, we have:
τ (t) ≈
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Lecture 1
Exercise 1
Sketch a block diagram fro a manual steering system of an automobile.
Indicate the location of the following elements and signals:
The process
The desired output signal
The sensor
The actuator
The actuator output signal
The controller
The controller output signal
The reference signal
The error signal
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Lecture 1
Exercise 1 - continued
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Lecture 1
Exercise 2
Sketch a block diagram fro a manual steering system of a water level controlled
by a float and valve. Indicate the location of the following elements and signals:
The process
The desired output signal
The sensor
The actuator
The actuator output signal
The controller
The controller output signal
The reference signal
The error signal
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Lecture 1
Exercise 2 - continued
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Lecture 1
Next episode...
• Dynamic models
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Lecture 1