lecture 1 introduction to linear control systems

1/27

MECE 3350Control Systems

Lecture 1Introduction to Linear Control Systems

MECE 3350 - C. Rossa 1 / 27 Lecture 1

2/27

Videos in this lecture

Lecture 1: https://youtu.be/TyJSMVarQZQ

Exercise 1: https://youtu.be/xHRKLbFdjvw

Exercise 2: https://youtu.be/Up_FpeS5zUI

MECE 3350 - C. Rossa 2 / 27 Lecture 1

3/27

Applications of Control System

Autonomous robots

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

MECE 3350 - C. Rossa 3 / 27 Lecture 1

4/27

Applications of Control System

Autonomous cars

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

MECE 3350 - C. Rossa 4 / 27 Lecture 1

5/27

Applications of Control System

Control of quadcopters

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

MECE 3350 - C. Rossa 5 / 27 Lecture 1

6/27

Applications of Control System

Self-balancing robots

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

MECE 3350 - C. Rossa 6 / 27 Lecture 1

7/27

Applications of Control System

Robotic surgery

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

Anything else?

MECE 3350 - C. Rossa 7 / 27 Lecture 1

8/27

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

→ ...

MECE 3350 - C. Rossa 8 / 27 Lecture 1

9/27

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.

MECE 3350 - C. Rossa 9 / 27 Lecture 1

10/27

Control engineering

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

MECE 3350 - C. Rossa 10 / 27 Lecture 1

11/27

Control engineering

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

MECE 3350 - C. Rossa 11 / 27 Lecture 1

12/27

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

MECE 3350 - C. Rossa 12 / 27 Lecture 1

13/27

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

MECE 3350 - C. Rossa 13 / 27 Lecture 1

14/27

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

MECE 3350 - C. Rossa 14 / 27 Lecture 1

15/27

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

MECE 3350 - C. Rossa 15 / 27 Lecture 1

16/27

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

MECE 3350 - C. Rossa 16 / 27 Lecture 1

17/27

Example - cruise control

y = 10(u − 0.5w)u =

Combining the equations:

y = 100101 r − 5

101w

MECE 3350 - C. Rossa 17 / 27 Lecture 1

18/27

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:

MECE 3350 - C. Rossa 18 / 27 Lecture 1

19/27

Linear systems

Are these systems linear ?

Linear approximations

MECE 3350 - C. Rossa 19 / 27 Lecture 1

20/27

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) ≈

MECE 3350 - C. Rossa 20 / 27 Lecture 1

21/27

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

MECE 3350 - C. Rossa 21 / 27 Lecture 1

22/27

Exercise 1 - continued

MECE 3350 - C. Rossa 22 / 27 Lecture 1

23/27

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

MECE 3350 - C. Rossa 23 / 27 Lecture 1

24/27

Exercise 2 - continued

MECE 3350 - C. Rossa 24 / 27 Lecture 1

25/27

Next episode...

• Dynamic models

MECE 3350 - C. Rossa 25 / 27 Lecture 1