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Welcome to TSRT15 ReglerteknikLecture 1
Johan LöfbergAvdelningen för reglerteknikInstitutionen för systemteknik
E-mail: [email protected]: 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