automatic control and system theory

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C. Melchiorri (DEI) Automatic Control & System Theory 1

AUTOMATIC CONTROL AND SYSTEM THEORY

Claudio Melchiorri

Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione (DEI) Università di Bologna

Email: [email protected]

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Automatic Control and System Theory

Monday Tuesday Wednesday Thursday Friday

09-10 5.5 L 5.2 L

10-11 5.5 L 5.2 L

11-12 5.5 E 5.2 E

14-15 1.4 L

15-16 1.4 L

16-17 1.4 E

Validity: 23/09/13 – 20/12/13

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Validity: 23/09/13 – 20/12/13

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The course deals primarily with the design of advanced control systems. Main topics: •  Analysis of SISO / MIMO dynamic systems expressed in state-space •  Structural (geometrical) properties of dynamic systems •  Control synthesis for dynamic systems expressed in state space •  Optimal Control •  Non linear systems

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Practical activities: •  Matlab/Simulink •  RTAI-Linux Exam: •  Report on the practical part •  Oral discussion Pre-requisites: •  Basic courses on automatic control (continuous- & discrete-time domains) •  Basic knowledge of geometry, mathematics, physics, electronics

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Suggested books:

•  Notes available @ http://www-lar.deis.unibo.it/people/cmelchiorri/

•  G. Marro, Controlled and Conditioned Invariants in Linear System Theory •  R. Carloni, C. Melchiorri, G. Palli, Esercizi di controlli automatici e teoria dei

sistemi, Esculapio Ed. Bologna, 2008.

•  G. Strang, Linear Algebra and its Applications, Books and Matlab Toolbox of Prof. Marro available at: http://www3.deis.unibo.it/Staff/FullProf/GiovanniMarro/gm_books.htm

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The course is composed by two modules Prof. Claudio Melchiorri:

•  http://www-lar.deis.unibo.it/~cmelchiorri/

•  Mail: [email protected] Dr. Gianluca Palli:

•  http://www-lar.deis.unibo.it/~gpalli/

•  Mail: [email protected]

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Contents 1.  The state space. Basic concepts and definitions; Examples of dynamic systems

expressed in SS; Numerical solution of differential equations; Control and Observation; Main problems of System Theory and Automatic Control.

2.  Linear Systems. Linear non stationary and stationary continuous-time systems; Extension to discrete-time systems; Sampled systems in state space.

3.  Properties of linear stationary systems. Controllability and Observability; Equivalent systems and Realizations; Canonical realizations; SS vs Transfer matrices; Physical meaning of zeros in the SS

4.  State feedback. Eigenvalues placement by state feedback; State observers; Eigenvalues placement by output feedback.

5.  Stability analysis. Lyapunov’s First (indirect) Method; Lyapunov’s Direct Method; Definite Positive functions and Lyapunov functions; Limit cycles; Stability for time-varying linear systems.

6.  Optimal control. Sylvester and Lyapunov matrix equation. Definitions of norms for signals and systems; Optimal feedback control; Infinite horizon optimal regulation and tracking; Stability margins; Regulation with frequency specifications; Integral control; Finite horizon optimal control.

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GOAL: control of complex dynamic systems Control:

Action on the system (machine, plant, process, …) to modify (improve) its behavior according to desired requirements

Necessity of:

•  Devices for measurement and actuation (sensors, motors, …) •  Elaboration system (DSP, PLC, …) “real-time” with a proper computing

power •  Control laws to “decide” the proper actions to be applied to the system

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Control … everywhere!

•  Engineering applications •  Chemical plants, machines and mechanical plants; Robotics;

Aeronautics; Space; … •  Production plants & processes; Power generation and distribution; •  Traffic control and management •  Electronics, Electro-mechanics, Telecommunication, Mechatronic

devices •  Transportation systems (trains, automobiles, …), Domotics, …...

•  Other sectors •  Economy and Finance •  Social and Political systems •  Environment and Ecology •  Medicine and Biology •  …

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•  Energy generation and distribution

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•  Process control

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•  Manufacturing industry

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•  Vehicle control

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•  Consumer Electronics

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•  Medical applications

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•  Robotics

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•  Science

Adaptive optics Atomic Microscope

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•  Biology “Feedback is a central feature of life. The process of feedback governs how we grow, respond to stress and challenge, and regulate factors such as body temperature, blood pressure and cholesterol level. The mechanisms operate at every level, from the interaction of proteins in cells to the interaction of organisms in complex ecologies.” M.B. Hoagland, B. Dodson,

“The Way Life Works”, Times Book, 1995

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A VERY short control history

•  The origins •  Mankind has always attempted to improve the behaviour of

(dynamic) systems by means of control •  Only after the mid of the XIX century a structured (scientific)

approach has been followed

tem

po

Water Clock Ktesibios 300 B.C.

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• Famous example: J.Watt and the automatic control of the speed of a steam motor (1798 ca)

Device for the automatic control of the speed

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The origin of “Automatic control”

•  In the second part of the XIX century, J.C. Maxwell and I.A. Vyshnegradskii independently developed the first methodological approaches to control (control theory) based on models described by differential equations

•  During the first half of the XX century, Control Theory has been developed

both in the western countries and in the ex-URSS, based on •  Engineering motivations in the West •  Mathematical interests in the East

•  The electronic amplifier with negative feedback (Black, 1927) was an important engineering achievement in Control Theory

•  Theoretical developments on stability analysis by •  Nyquist (1932) •  Bode (1940)

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Automatic Control become an engineering discipline in the 40’s Reasons:

•  Second World War •  Plane autopilots, cannon pointing systems, radar, …

•  Development of electronic computers (beginning of the 50’s) •  They allowed the implementation of complex theoretical results

•  Space race (60’s and 70’s) •  Possible because of the availability of “sophisticated” control systems

•  Development of microprocessors (second part of the 70’s) and of DSPs (second part of the 80’s)

•  Wide use of automation “concepts” in industries •  Application of control devices in a multitude of systems also in non-

industrial contests

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Bode Diagram

Frequency

Phas

e

Mag

nitu

de

-40 -30 -20 -10 0

10

10 0 10 1 10 2 -180 -135 -90 -45 0


•  “Frequency” control techniques (based on Laplace Transform, Bode Diagrams, etc.) had a large diffusion during and immediately after the 2nd World War.

• These techniques are suitable for SISO linear time-invariant systems (“classical” control theory).

Re

Im

-

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• On the other hand, e.g. with nonlinear or MIMO systems, these techniques show important limitations, and their applicability is greatly limited

•  Starting in the late 50’s – beginning of the 60’s, different techniques have been developed for analysis and control design of MIMO systems (Sputnik - 1957).

•  ”Modern” control theory

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Current situation and perspectives

Sophisticated control systems are normally used in civil, industrial, miitary devices (hidden technology)

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• Applications in engineering (non industrial) fields •  Automobiles

•  “modern” cars could not work without many control loops •  autobrake, ABS, asset control, injection control, …..

•  Consumer electronics •  Photo/Video-cameras, cell phones, PC, … •  Washing machines, fridges, cooling/heating,

•  Domotics •  Remote control of domestic apparatus •  …

•  Energy •  Wind/Solar generation, …

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Other areas of interest:

•  Biomedical devices •  Biological systems •  Environment •  Socio-Economic systems •  Financial markets •  Management • …

automatic control and system theory

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