Systems control command (09_O-CCM)

• Coefficient : 6
• Hourly Volume: 150h (including 72h supervised)
  CTD : 19.5h supervised
  Labo : 52.5h supervised (and 12h unsupervised)
  Out-of-schedule personal work : 66h
• Including project : 18h supervised and 36h unsupervised project

AATs Lists

Description

1. Control of linear systems (state representation, stability, controllability, observability, control by state feedback, observer, state estimator.
2. Stability in the sense of Lyapunov (concepts of equilibrium stabilities, Lyapunov linearization method, direct Lyapunov method)
3. Introduction to the identification of controlled systems.
4. Introduction to the estimation of parameters and noisy signals using algebraic methods.
5. Introduction to robust control based on singular disturbances.
6. Introduction to nonlinear control (linearization, sliding modes, Lyapunov, flatness).

Learning Outcomes AAv (AAv)

• AAV1 [heures : 12, B2, B3]: At the end of this course, the student will be able to describe and model a controlled system in state representation, for applications in the fields of mechatronics, instrumentation or energy production. The dynamic system may be of varied nature: linear or non-linear, possibly non-stationary, continuous time or discrete time, single-input/single-output (SISO) or multi-input/multi-output (MIMO).

• AAV2 [heures : 8, B2, B3]: At the end of this course, the student will be able to simulate a controlled system in state representation using scientific calculation software and to operate transformations allowing access to various representations of the system (differential equations, state representation, transfer function, transfer matrix).

• AAV3 [heures : 12, B2, B3, B4, D2, D3, D4]: At the end of this course, the student will be able to build a state observer and synthesize a state feedback control observed on a SISO linear system meeting specifications (stability, precision, speed, robustness).

• AAV4 [heures : 12, B2, B3, B4, D2, D3, D4]: At the end of this course, the student will be able to model the uncertainties of modeling a discrete-time dynamic system and the uncertainties observation of the state of the system, with a view to an adaptive estimation of the state which it will carry out by Kalman filtering for the case of linear systems.

• AAV5 [heures : 20, B2, B3, B4, D2, D3, D4, E1, F1]: At the end of this course, the student will be able to linearize a dynamic process or an observation law in order to carry out an adaptive state estimation by extended Kalman filtering (EKF filter) and perform a comparison with an Unscented Kalman filter (UKF).

• AAV6 [heures : 16, B2, B3, B4, D2, D3, D4, E1, F1]: At the end of this course, the student will be able to control a linear system by feedback state according to a quadratic optimization criterion: LQR command or LQG command when the state is only partially observed

• AAV7 [heures : 12, B2, B3]: At the end of this course, the student will be able to identify the equilibrium points and analyze the local stability of a non-linear dynamic system, in the phase plane (for systems of order 2) and by Lyapunov methods

• AAV8 [heures : 42, B2, B3, B4, D2, D3, D4, E1, F1]: At the end of this course, the student will be able to implement, set up and adjust some system control solutions non-linear: linearizing control, control by flatness, control by Lyapunov function,…

Assessment methods

Average of several assessments

Key Words

state variables, modeling, stability, phase plane, Lyapunov, linear and nonlinear control, robustness, estimation, simulation.

Prerequisites

Analog and digital servos; usual linear algebra; analysis ; Differential equations ; programming concepts (Scilab).

Resources

B. Friedland. Control System Design. An introduction to State-Space Methods. Dover Publication. 1986.

J. Lévine Analysis of Nonlinear Systems. A Flatness-based Approach. Springer. 2009.

N. S. Nise, “Control Systems Engineering”, 4th Ed., Wiley, 2004.

H. Sira-Ramirez et S. K. Agrawal. Differentially Flat Systems. Marcel Dekker. 2004.

J. J. E Slotine et W. Li. Applied nonlinear control. Prentice-Hall, 1990.