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MECE 3350Control Systems

Lecture 1Introduction to Linear Control Systems

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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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Applications of Control System

Autonomous robots

https://www.youtube.com/watch?v=fRj34o4hN4I

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Applications of Control System

Autonomous cars

https://www.youtube.com/watch?v=cdgQpa1pUUE

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Applications of Control System

Control of quadcopters

https://www.youtube.com/watch?v=w2itwFJCgFQ

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Applications of Control System

Self-balancing robots

https://www.youtube.com/watch?v=n_6p-1J551Y

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Applications of Control System

Robotic surgery

https://www.youtube.com/watch?v=-5lzGk7dgCQ

Anything else?

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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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Control engineering

The first step in control engineering is to understand the system we want tocontrol.

Then, we design a secondary system that controls the behaviour of the firstsystem

This is called open-loop control.

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Control engineering

A closed-loop control system uses a measurement of the output and feedbackof this signal to compare it with the desired output.

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Control engineering

A closed-loop control system uses a measurement of the output and feedbackof this signal to compare it with the desired output.

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A simple feedback systemThe variable being controlled is measured by a sensor and fed back to thecontroller to influence the controlled variable.

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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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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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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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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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Example - cruise control

y = 10(u − 0.5w)u =

Combining the equations:

y = 100101 r − 5

101w

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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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Linear systems

Are these systems linear ?

Linear approximations

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Pendulum exampleTorque vs angle θ

τ(t) = mg` sin(θ)

Is this system linear?

Taylor’s series around θ = 0:

sin θ = θ − θ3

3! + θ5

5! −θ7

7! + . . .

For θ ≈ 0, we have:

τ(t) ≈

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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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Exercise 1 - continued

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Exercise 2

Sketch a block diagram fro a manual steering system of a water level controlledby 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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Exercise 2 - continued

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Next episode...

• Dynamic models

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