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Automatic Control (TSRT15): Lecture 1

Tianshi Chen*Division of Automatic ControlDept. of Electrical EngineeringEmail: tschen@isy.liu.sePhone: 13-282226Office: B-house extrance 25-27

* All lecture notes in this course are revised on the ones used before.

I sincerely appreciate Johan Löfberg for his permission to use them.

2Course plan

Lecture notes will (hopefully) be posted some days in advance

12 lectures

12 exercise sessions

3 mandatory laboratory sessions (all materials on homepage)Lab 1: PID-control (preparation questions in the PM)Lab 2: Control of double-tanks (preparation takes time!)Lab 3: Control of inverted pendulum (computer lab)Lablists will be sent out on email and be posted on-line

Exam: Course book, tables and formula collection allowed. Separate notes and other sheets not allowedStudy notes in book are allowed

3Outline

Automatic control in practice

Definition of basic principlesSignal, system, Control

Fundamental Principle of Control: Feedback

Linear Dynamic systems

Design of a cruise controllerOpen vs closed-loop control, P-control

4Automatic control

Makes ”impossible” problems solvable

Often called the ”hidden technology”

Central for Swedish technology companies

Many interesting applications!

A lot of interesting math

5Control examples

Mobile phones

Automatic control is used to control the power in radio signals between phone and base-station.

6Control examples

Head-phones

Active noise cancellation in head-phones use automatic control to transmit counteracting sound in anti-phase.

Similar technique for sound and vibration damping in airplanes, cars, snowboards and buildings.

7Control examples

Hard disks

The reading arm must be positioned at they right spot as fast as possible.

Without active control, the arm oscillates after movements, and prevents reading data until it has settled.

8Control examples

Segway

One of the most obvious consumer products,and it does not work without a control system.

9Control examples

Modern cars

Most acronyms hides a control system!

ABS (anti-lock braking system)ESC (electronic stability control)ACE (active cornering enhancement)TCS (traction control system)ACC (adaptive cruise control)ANC (active noise control)…

10Control examples

Heavy trucks

The aim is to utilize an on-board database with road topography information in combination with a positioning system in order to calculate fuel-optimal velocity trajectories and gear shifting schemes.

11Control examples

Modern fighters

Designed so that they are impossible to fly manually(to obtain better performance)

Requires a control system

If the control system has a design problem, it can go very wrong. This is what happened in the Gripencrashes in 89’ and 93’

12Control examples

Kite-Powered Cargo Ship

Has been tested in practice over the Atlantic

Reduced fuel consumption by 20%

Kite position controlled for maximalpower

13Control examples

Extremely large telescopes

We have reached the limit on mirror size

Large telescopes are built with many small mirrors whose position is continuously controlled to focus the image(called adaptive optics)

14Control examples

Industrial robots

Same as the hard disk

A robot arm is weak, and oscillates after movements

15Control examples

Automatic Anaesthesia

A control system replaces the nurse (still research)

The system controls the level of consciousness

16Control examples

Interest rates and Inflation

The Swedish bank uses state interest rate to control inflation

17Automatic control?

The ”thing” we control can be conceptually illustrated

u(t)

w(t)

y(t)Systemr(t)

Design the control u(t) so that the system (according to the outputy(t)) behaves as wanted (reference r(t)) despite disturbances w(t).

Here, u(t), y(t), r(t) and w(t) are functions of time and called signals.

18Control examples

System u(t) y(t) w(t) r(t)

Car Throttle,break speed Slope, air resistance

Desired speed

Anaesthesia Drugs consciousness Drug tolerance, weight

Less than dead

Economy Interest Inflation Politics Inflation goal 2%

Magnetelevation

Magnet strength

Elevation Wind Desired elevation

19Dynamical systems

Systems memory, current output depends on past inputs

Mathematically: System described by a differential equation

A description (often approximate) of a system is called a model

Opposite: Static system

Speed and position of a car (depends on past throttle)

Room temperature (depends on past heating and outside temperature)

Economics (depends on politics, investments past years)

20Linear systems

u(t) y(t)System

Linear system means superposition holds

21Linear systems

Linear ordinary differential equations fulfill this

We only work with systems described by linear ordinary differential equations

More (much more) about this next lecture

22Fundamental principle of control: Feedback

A fundamental principle in control is feedback, here illustrated on a distillation column

1. Formulate a control goal (reference signal)We want a temperature of 80º

2. Measure current temperature (measurement signal)It is now 60º

3. Apply action (control using the control signal)Increase heating!

Feedback!

23Fundamental principle of control: Feedback

Feedback system

u(t) y(t)System

w(t)

Controllerr(t)

Feedback!

24Control examples

Feedback system

speedthrottle

25Control examples

Feedback system

consciousnessDrugs

26Control examples

Feedback system

interest inflationSystem2%

27What we will learn?

In this course we ask

How do we describe the system to be controlled

How do we analyze the system to be controlled

How do we design a controller

How do we analyze the feedback system (what can go wrong)

28Design of cruise controller

φ

u(t): Driving/breaking force [N]y(t): Velocity of car [m/s]φ : Road slope [rad]m: Car weight [kg]α: Aerodynamic coefficient [Ns/m], αy(t): Drag force [N]

29Open loop control

Model: m = 1000kg, α = 200Ns/m, φ = 0

Newton

Open loop: Our goal is a reference speed r(t) = 25m/s for t ` 0.Assume y(0) = 0. We test the following control law

Solution:We reach the reference speed asymptotically

30Open loop control

u(t) y(t)

mg sin(φ)

200r(t)=25

31Open loop control

Non-nominal model:

Wind tunnel test wrong, in reality α = 150Ns/m

Under the assumption y(0) = 0, we use the same control law and obtain

The car achieves a too high speed

Cause: we have not feeded back the true velocity!

32Open loop control

33Closed-loop control

Feedback the velocity!

A reasonable strategy is to throttle more when too slow

This is called proportional control, P-control, and the constant K is the only design variable in the controller

The closed-loop system

34Closed-loop control

u(t) y(t)

mg sin(φ)

Kr(t)=25

-1

e(t)

35Closed-loop control

36Closed-loop control

37But what is a controller, really?

A controller is a computer in the car, measuring speed and desired speed, and sends command signals (desired torque) to the engine

program CruiseControl

repeatr = getReferenceMeasurementy = getSpeedMeasurementu = K*(r-y);sendCommandToEngine(u)

end

y

r

u

38Summary of this lecture

Automatic control is everywhere

We use differential equation to create models of systems

Open-loop control very sensitive to model parameters and disturbances

Feedback can reduce sensitivity significantly

Feedback u(t) = K(r(t)-y(t)) is called P-control

We still haven’t achieved perfect control, better design is needed

39Summary of this lecture

Automatic control: “Making things behave as we want”.

Signal: Functions of time with information

System: An object driven by input signals, generating output signals

Model: A simplified description of reality. In this course, a mathematical description of the system we study

Dynamical systems: Systems where the output signal depends on past inputs

Feedback: Feed back information about the current state to the controller. Automatic control is the theory about feedback systems

Important concepts