Control - Troubleshooting - Automatic

Objectives / Skills

Stochastic processes: understand the definition of a random signal and its basic properties learn the first and second order characterization tools (expectation, correlation functions) spectral analysis learn the properties of well-known stochastic processes (white noise, autoregressive processes)
Digital control systems: understand the basic concepts of designing a numerical control algorithm understand the principles of parametric model identification from measured input-output data discover the main model structures learn the principles of model validation
Fault detection and isolation: understand the concept and benefits of fault detection in aerospace applications acquire a basic knowledge on model-based fault detection and isolation methods acquire the methodological and mathematical tools for designing a fault detection algorithm via the parity space approach

Skills currently being developed

Integrate financial dimensions, legal and contractual aspects into engineering practice


Skills at mastery level

Have a global systemic approach Reason in a context of international regulatory constraints
Anticipate and decide in situations of uncertainty Be results-oriented (costs, lead-times, quality) and customer-oriented
Evaluate your own skills and steer your career path


Skills at mastery level

Mobilize a broad field of fundamental and technical sciences related to avionics and space systems, and have the associated capacity for analysis and synthesis
Identify on-board aircraft systems, control and measurement systems, and associated communication protocols
Identify radio-frequency systems communicating with aircraft, and the characteristics of the signals used
Design, dimension, carry out and test a repair/modification of an on-board system in an aircraft
Communicate and work as part of a team Manage and lead a work unit or a project group

Integrate into a professional environment in France or abroad Communicate orally and in writing in English

Good knowledge of transfer function, continuous time control and frequency response of dynamical systems is needed. Basic knowledge of multivariable control and working knowledge of Matlab/Simulink are also necessary

Contents
Stochastic processes
The objective of this course is to introduce stochastic processes and their properties. After recalling the tools to study random variables and vectors, we extend the latter to infinite collections of random variables, i.e. random signals. We then present how to analyze the time-evolution of these random signals by means of correlation functions. Building upon this notion, power spectral densities are presented for the frequency domain analysis. Finally, we focus on well-known stochastic processes such as white noises, colored noises and autoregressive processes
Digital control systems
The first part of this course introduces the basic elements of a computer-controlled system as the ones that can be found in the aerospace field and shows the negative effects that can appear if the specificities of these systems are not taken into account during the control law design. We then present the design of robust digital RST controllers with two degrees of freedom by sensitivity functions shaping in the frequency domain
The second part of the course presents the parametric model identification for dynamic systems. We start by introducing the concept of linear regression model to establish a relationship between a dependent variable and one or more explanatory variables. The Least Squares (LS) method is proposed to estimate the parameters of these models by minimizing a quadratic criterion. This method gives unbiased results under some conditions only in the case on systems disturbed by zero mean Gaussian disturbances (also known as white noise). To overcome this limitation, recursive identification methods are proposed for models in the ARMAX class. The last part of the course discusses the validation of the identified models
Fault detection and isolation
This class is intended to provide students with an overview of fault detection and isolation methods used in aerospace applications. A focus is provided regarding model-based approaches. The general idea is to compute a fault indicator signal (called residual signal) from the signals available in the flight control unit (measure and control signals). This residual signal is then evaluated in order to determine a fault occurrence, generate an alarm and localize the faulty component. Main method studied in the class is called the parity space approach
Teaching method

These courses are entirely taught in English
The lessons from these courses will be delivered in the form of integrated courses using Matlab-Simulink. The concepts studied during these courses will be put into practice during the pedagogic projects of semester 10
All course material will be available on the Moodle platform

Specialization: Aeronautical systems