Expected skills and content of the exam

　　The examinee is expected to be able to analyze and solve an automation control problem and a problem involving several fields of physics (electrokinetics, mathematics for physics, wave physics, electromagnetism, thermodynamics, optics, and mechanics). The exam consists of two parts: an automation control problem which counts for 50 points, and a physics problem which counts for 100 points.

　　Engineering Science part (automation control)

　　I - Modeling of automation systems

　　1°) Forward chain control

　　2°) Feedback control

　　II - Hypotheses related to the study of linear time-invariant (LTI) systems

　　1°) Continuity

　　2°) Linearity

　　3°) Time invariance

　　III - Performances of LTI systems

　　1°) Steady-state performances

　　2°) Transient-state performances

　　IV - Mathematical tools for the study of LTI systems

　　1°) Laplace transform of a continuous signal

　　2°) Modeling by a block diagram

　　V - Time response

　　1°) First order systems

　　2°) Second order systems

　　3°) Higher order systems

　　VI - Frequency response

　　1°) Definition and methods

　　2°) Frequency plots

　　3°) Frequency response of some basic systems

　　4°) Frequency response of other systems

　　VII - Algebraic methods for the determination of the performances of a LTI system 1°) Stability

　　2°) Accuracy and robustness

　　3°) Swiftness and damping

　　VIII - Determination of the performances of a LTI system from the frequency response of its open- loop transfer function

　　1°) General methodology: Nyquist criterion

　　2°) Stability

　　3°) Damping: Nichols chart

　　4°) Accuracy/robustness and swiftness

　　IX - Compensation of control systems

　　1°) Types of controllers (serial, parallel, by anticipation)

　　2°) Classical controllers

　　Physics part

　　I - Electrokinetics

　　1°) General laws of electrokinetics

　　2°) Usual theorems of electrokinetics

　　3°) Transient regimes

　　4°) Linear circuits used with forced sinusoidal excitations

　　5°) Transfer function and filtering

　　6°) Filtering of periodic signals

　　II - Mathematics for physics presented through steady-state electromagnetism

　　1°) Charge distribution

　　2°) Electrostatic field

　　3°) Current distribution

　　4°) Magnetostatic field

　　5°) An electrostatic potential

　　6°) A vector potential

　　7°) The electrostatic dipole - The magnetic dipole

　　III - Wave physics

　　1°) 1-D d’Alembert equation

　　2°) Synchronous harmonic waves superposition: interferences and resonance 3°) Electromagnetic waves in vacuum

　　4°) Reflection of an electromagnetic wave off a perfectly conducting medium 5°) Linear propagation phenomenon - dispersion

　　6°) Propagation of an electromagnetic wave in a real conducting medium - absorption 7°) Reflection and refraction of an electromagnetic wave on a surface

　　IV - Electromagnetism

　　1°) Electromagnetism postulates

　　2°) Energy carried by an electromagnetic wave

　　3°) Conductive media

　　4°) Electric dipole radiation

　　5°) Quasi stationary state approximation

　　6°) Electromagnetic induction

　　V - Thermodynamics

　　1°) Temperature - Description of model fluids

　　2°) Thermodynamical system at the thermodynamical equilibrium

　　3°) First law of thermodynamics

　　4°) Second law of thermodynamics

　　5°) Heat engines

　　6°) Phase transition

　　7°) Transport phenomena: particles diffusion - heat conduction

　　VI - Optics

　　1°) Elements of geometrical optics

　　2°) Wave model of light

　　3°) Interference phenomena

　　4°) Spatial and temporal coherences

　　5°) Michelson interferometer

　　VII - Mechanics

　　1°) Newton’s laws of motion

　　2°) Work,potential energy and kinetic energy

　　3°) Angular momentum

　　4°) Linear systems used with forced sinusoidal excitations