# Automatic Control: modeling and control

## Presentation

Programme (detailed contents):

v  Modeling and control of discrete event systems: modeling tools (finite state machines, Petri nets, State-charts) and implementation techniques.

v  Control in the state space: specifications, observability-controllability, state feedback control (pole placement), Observer based control. Controllability, algebraic based methods (1-DOF,2-DOF).

Organisation:

v  - lectures,

v  - tutorials in groups,

v  - lab-work in subgroups,

v  - small projects,

v  Documentations :

• Tutorial and lecture notes for "Control of Discrete Events Systems"
• Tutorial on “Control of linear systems”
• lab-work instructions with technical notes on equipment
• Specifications fro small projects

Main difficulties for students:

v  Models and analysis of time-invariant linear systems: the Prerequisites of linear algebra are, in general, not well understood .

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

v  The basic principles of the main modeling tools of Discrete Event Systems (Finite State Machines, State-charts Petri Nets)

v  Several techniques for the control of discrete event systems (FPGA, PLC, real time target)

v  The main methods of design of control laws for linear time-invariant systems described in the state space.

v  The basic principle of state observer design for linear time-invariant systems described in the state space

The student will be able to:

v  design and to build the control of a discrete event system

v  define the main characteristics of the control law from the specifications,

v  design the control law in the state space (pole placement).

design a state observer

## Needed prerequisite

- Classical control theory for continuous-time-invariant systems (frequential approaches)

- State space representation

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Bibliography

-"Contemporary Logic Design " R.H. Katz, The Benjamin/Cummings Publi.Comp. 1994

- "Réseaux de Petri : théorie et pratique" BRAMS, Tomes 1 et 2, 1983, Eds. MASSON

- "Du Grafcet aux réseaux de Petri" R. David, H. Alla, 1992, HERMES (Série Automatique)

-"On visual Formalism " D. harel, 1985, Communication of the ACM, vol. 31 n° 5l

-«Analyse et commande des systèmes linéaires » B. Pradin and G. Garcia. Presses Universitaires du Mirail, 2009

-”Mathematical Systems Theory I”. D. HINRICHSEN and A.J. PRITCHARD., Springer, Berlin Heidelberg, New-York, 2005

• ”Introduction to mathematical systems theory”J.W. POLDERMAN and J.C. WILLEMS, . Springer Verlag, New-York, 1998

•”Modern control engineering”, K. OGATA. Prentica Hall, Upper Saddle River, 2001, 4th Edition.

• ”Linear Systems”, P. ANTSAKLIS and A.N. MICHEL.. Mc

Graw-Hill, New-York, 1997