Automatic Control (TSRT15): Lecture 1

Transcription

1 Automatic Control (TSRT15): Lecture 1 Tianshi Chen* Division of Automatic Control Dept. of Electrical Engineering tschen@isy.liu.se Phone: Office: B-house extrance * All lecture notes in this course are revised on the ones used before. I sincerely appreciate Johan Löfberg for his permission to use them.

2 Course plan 2 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 and be posted on-line Exam: Course book, tables and formula collection allowed. Separate notes and other sheets not allowed Study notes in book are allowed

3 Outline 3 Automatic control in practice Definition of basic principles Signal, system, Control Fundamental Principle of Control: Feedback Linear Dynamic systems Design of a cruise controller Open vs closed-loop control, P-control

4 Automatic control 4 Makes impossible problems solvable Often called the hidden technology Central for Swedish technology companies Many interesting applications! A lot of interesting math

5 Control examples 5 Mobile phones Automatic control is used to control the power in radio signals between phone and base-station.

6 Control examples 6 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.

7 Control examples 7 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.

8 Control examples 8 Segway One of the most obvious consumer products, and it does not work without a control system.

9 Control examples 9 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)

10 Control examples 10 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.

11 Control examples 11 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 Gripen crashes in 89 and 93

12 Control examples 12 Kite-Powered Cargo Ship Has been tested in practice over the Atlantic Reduced fuel consumption by 20% Kite position controlled for maximal power

13 Control examples 13 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)

14 Control examples 14 Industrial robots Same as the hard disk A robot arm is weak, and oscillates after movements

15 Control examples 15 Automatic Anaesthesia A control system replaces the nurse (still research) The system controls the level of consciousness

16 Control examples 16 Interest rates and Inflation The Swedish bank uses state interest rate to control inflation

17 Automatic control? 17 The thing we control can be conceptually illustrated w(t) u(t) System y(t) r(t) Design the control u(t) so that the system (according to the output y(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.

18 Control examples 18 System u(t) y(t) w(t) r(t) Car Throttle,break speed Slope, air resistance Desired speed Anaesthesia Drugs consciousness Drug tolerance, Less than dead weight Economy Interest Inflation Politics Inflation goal 2% Magnet elevation Magnet strength Elevation Wind Desired elevation

19 Dynamical systems 19 Systems memory, current output depends on past inputs 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) Mathematically: System described by a differential equation A description (often approximate) of a system is called a model Opposite: Static system

20 Linear systems 20 u(t) System y(t) Linear system means superposition holds

21 Linear systems 21 Linear ordinary differential equations fulfill this We only work with systems described by linear ordinary differential equations More (much more) about this next lecture

22 Fundamental principle of control: Feedback 22 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!

23 Fundamental principle of control: Feedback 23 Feedback system w(t) r(t) Controller u(t) System y(t) Feedback!

24 Control examples 24 Feedback system throttle speed

25 Control examples 25 Feedback system Drugs consciousness

26 Control examples 26 Feedback system 2% interest System inflation

27 What we will learn? 27 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)

28 Design of cruise controller 28 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]

29 Open loop control 29 Newton Model: m = 1000kg, α = 200Ns/m, φ =0 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

30 Open loop control 30 mg sin(φ) r(t)= u(t) y(t)

31 Open loop control 31 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!

32 Open loop control 32

33 Closed-loop control 33 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

34 Closed-loop control 34 mg sin(φ) r(t)=25 e(t) K u(t) y(t) -1

35 Closed-loop control 35

36 Closed-loop control 36

37 But what is a controller, really? 37 A controller is a computer in the car, measuring speed and desired speed, and sends command signals (desired torque) to the engine y u r program CruiseControl repeat r = getreferencemeasurement y = getspeedmeasurement u = K*(r-y); sendcommandtoengine(u) end

38 Summary of this lecture 38 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

39 Summary of this lecture 39 Important concepts 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