welcome to tsrt15 reglerteknik lecture 1 · welcome to tsrt15 reglerteknik lecture 1 johan löfberg...

Welcome to TSRT15 ReglerteknikLecture 1

Johan LöfbergAvdelningen för reglerteknikInstitutionen för systemteknik

E-mail: johanl@isy.liu.seTel: 284029Kontor: B-huset ingång 25-27

2Formalia

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

12 lectures

12 exercise sessions

3 mandatory laboratory sessionsLab 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

3Todays lecture

Automatic control in practice

Definition of basic principlesControl-, signal- and reference signal, system, modell

Feedback

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

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)…

6Control 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’

7Reglertekniska exempel

Kite-Powered Cargo Ship

Has been tested in practice over the Atlantic

Reduced fuel consumption by 20%

Kite position controlled for maximalpower

8Reglertekniska exempel

Modern bikes

Traction control now also on production bikes (2008 Ninja ZX-10R)

Used in MotoGP, and some say it has ruined the sport

”The electronics is so important now and this makes the rider less important. I would like that the rider controlled more the motorcycle but maybe with so powerful bikes now it would not be possible to ride these bikes without the electronics. For sure it is easier to ride them.”

Valentino Rossi

9Reglertekniska exempel

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)

10Reglertekniska exempel

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

11Reglertekniska exempel

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.

12Reglertekniska exempel

Mobile phones

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

13Reglertekniska exempel

Industrial robots

Same as the hard disk

A robot arm is weak, and oscillates after movements

14Reglertekniska exempel

Recognize them?

15Reglertekniska exempel

Inflation och ränta

The Swedish bank controls inflation using state interest

16Reglertekniska exempel

Segway

One of the most obvious consumer products

Does not work without a control system

17Reglertekniska exempel

Climb- and balance-chair (iBOT)

Equivalent to the Segway from an automatic control point of view

18Reglertekniska exempel

Automatic Anaesthesia

A control system replaces the nurse (still research)

The system controls the level of consciousness

19Det reglertekniska problemet

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

(we often use input instead of control, and output instead measurement)

20Det reglertekniska problemet

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

Cruise Throttle,break speed Desired speed Slope, air resistance

Anaesthesia Drugs consciousness Less than dead Drugtolerance, weight

Economi Interest Inflation Inflation goal 2%

Politics

Maglevtrain Magnet strength

Elevation Desired elevation

Wind

21Det reglertekniska problemet

We illustrate systems (the ”thing” we control) conceptually with block schemes

u(t) y(t)System

w(t)

In this course, we assume the system is dynamic and linear

22Dynamical systems

Systems memory, current state 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 on a car (depends on past throttle)

Room temperature (depends on past heating and outside temperature)

Economics (depends on politics, investments past years)

23Linear systems

u(t) y(t)System

Linear system means superposition holds

24Linjära system

Linear ordinary differential equations fulfill this

We only work with systems described by linear ordinary differential equations

More (much more) about this next lecture

25Det reglertekniska problemet

A fundamental princip in control is feedback, here illustrated on a destillation 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!

26Det reglertekniska problemet

Feedback system

u(t) y(t)System

w(t)

Regulatorr(t)

Feedback!

27Det reglertekniska problemet

Feedback system

speedthrottle

28Det reglertekniska problemet

Feedback system

interest inflationSystem2%

29Det reglertekniska problemet

Feedback system

consciousnessDrugs

30Det reglertekniska problemet

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)

31Design 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], Drag = αy(t) [N]

32Design av farthållare

Model: m=1000kg, α=200Ns/m, φ=0

Newton

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

Solution:We reach the reference speed asymptotically

33Design av farthållare

u(t) y(t)

mgsin(φ)

200r(t)=25

34Design av farthållare

Non-nominal model: Wind tunnel test wrong, in reality α=150Ns/m

We use the same control law and obtain

The car achieves a too high speed

Cause: we have not feed back the true velocity!

35Design av farthållare

36Design av farthållare

Closed-loop control: Feed back 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

37Design av farthållare

u(t) y(t)

mgsin(φ)

Kr(t)=25

-1

Σe(t)

38Design av farthållare

39Design av farthållare

40But 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

41Conclusion

Conclusion

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

42Conclusion

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

Signalser: Functions of time with information

System: An object driven by insignals, generating outsignals

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