Parcours Electrical Engineering and Control Systems / MISCIT 2è année

Feedback control design, diagnostic/supervision and process optimization typically require a specific modeling approach, which aims to capture the essential dynamics of the system while being computationally efficient. The first part of the class details the guiding principles that can be inferred from different physical domains and how multi-physics models can be obtained for complex dynamical systems while satisfying the principle of energy conservation. This leads to algebro-differential mathematical models that need to be computed with stability and computational efficiency constraints. System identification constitutes the second part of the class, to include knowledge inferred from experimental data in the input/output map set by the model. It provides methods to evaluate the model performance, to estimate parameters, to design "sufficiently informative" experiments and to build recursive algorithms for online estimation.

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This five months project (in parallel with the theoretical classes) investigates new automation solutions for real-time feedback operation, the minimization of energy consumption in key industrial processes and the analysis and optimization of complex dynamical systems. This automation is based on distributed sensing capabilities, networked sensors, physical modeling for the process automation design and real-time feedback control. The design project is structured into two parts: from September to December with meetings every other week in Design Project 1, and in January with meetings multiple times per week in Design Project 2.

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This set of courses proposes an overview of recent techniques for the identification, observation, simulation and control of distributed parameter systems. This class of systems is widely used in physics and considered in many applications (such as in environment dynamics, airflow control, structural mechanics, and adaptive optics) having a large or an infinite number of degrees of freedom. A Partial Differential Equation (PDE) usually models them. Their mathematical study asks for a special care to analyze the dynamics behavior and to describe their control properties. Different aspects of this description are considered in this Teaching Unit, by emphasizing the practical methods allowing for some real applications. 

This Teaching Unit is composed by three different courses:

Analysis and control (13.5 h)

Modeling and Inverse problems (13.5h)

Distributed optimization  (13.5h)

Prerequisites: basic mathematical background, control theory of finite dimensional systems (control and observation theory for linear ODEs, in particular optimal LQ regulation).

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Security of Network and Applications

The objective of this class is to introduce security principles, on the theoretical, organizational and technical aspects. The points which are more specifically developed are: detection errors, firewall technics, network architecture, cryptology and VPN, anti-virus strategy. Are also discussed how to implement a security strategy, and some elements for the definition of a security policy. Some elements about safe networks, or networks for safety or critical applications, are also studied.

Distributed Algorithms and Network Systems

Objectives Distributed algorithms aim at obtaining a global goal by exploiting a large number of simple devices (``agents''), and their local interactions. These algorithms can be for the purposes of estimation in a wireless sensor network, or control e.g. of a self-organized robotic fleet. This introductory class will first review the necessary tools from graph theory and Markov chains, and then present consensus: a prototypical example of distributed algorithm, as well as a building block for more complex algorithms. Theory will be accompanied by implementation on a real-world sensor network: FIT/IoT LAB.Class schedule 

1. Introduction: network systems 
2. Graphs: fundamentals of algebraic graph theory
3. Markov chains: convergence to invariant measure, Perron-Frobenius theorem 
4. Consensus (time-invariant graph) 
5. Consensus (gossip: randomly varying graph) 
6. Consensus-based algorithms: using consensus as a building block of other algorithms (e.g., localisation from relative measurements, least-squares regression, gradient descent minimization, distributed Kalman filter, counting nodes in an anonymous network) 
7. Labs (3): implementation of distributed algorithms on real sensor network, remotely using FIT/IoT LAB. Programming language: C.

Programmable Sockets

This two-sessions lab aims at establishing a communication with a PLC-like computer controlling a levitating ball. The work is related to the IP (TCP and UDP) libraries on Python, and to some more high-level protocols or technologies (HTTP, GRPCio for security constraints, etc.).

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Non linear control (20 h)

1. Introduction to nonlinear systems: representation and specific features 
2. Nonlinear systems analysis: stability, tangent linearization, Lyapunov methods 
3. State feedback control of nonlinear systems: approximate linearization, exact linearization, backstepping, sliding modes 
4. State observers for nonlinear systems: Extended Kalman Filter, Output injection, High gain designs 
5. Observer-controller schemes: adaptive methods, output feedback control 

 Predictive control (14 h)

• Predictive control 
  • Introduction to constraints
  • Finite horizon predictive control
  • Stability conditions
  • Examples
• Predictive control of nonlinear systems
  • Closed loop stability
  • Control parametrization
  • Optimization tools
  • Examples
• Complete case study

List of examples from Mechatronics: Inverted pendulum, tiliting trains, elastic crane, Boeing aircraft, chain of masses linked through springs, automate-manual transmission (AMT), etc.

Prerequisites: State space and transfer approaches for linear systems, optimisation

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Project management (10.5 h)

The objectives of this class are to supply the bases of the project management as well as to present the good practices in industries. The quality management according to the standards ISO and the piloting by process are presented through industrial projects. 

This class contains a method to establish a CV as well as simulations of real recruitment interview.Class schedule 

Industrial seminars (27 h for IPA)

• Climate change & sustainable engineering. P. Martinerie, CNRS.
• Semi-active damper design and regulation. B. TALON, SOBEN.
• Mobile robots in everyday life. V. TALON, TwinswHeel.
• Case study on warm compression station for cryogenics. B. BRADU, CERN . 
• Keys and social issues to enter the industrial life. M. PRUNIER, Schneider.

Research seminars (15 h for CST)

Each year, MiSCIT and GIPSA-lab invite keynote speakers to give a short class on their research topic. The lectures (typically 15h) are given in the Control Systems Department of GIPSA-lab. They focus on the latest results in a specific topic of control and systems theory, and may include some labs to illustrate specific aspects. The attendance is composed as Master and Ph.D. students, as well as engineers, researchers and professors. A basic knowledge in dynamical systems, linear algebra and control theory is expected.

Linear Matrix Inequalities and Sum-of-Squares Optimization in Systems and Controls Theory: A Practical and Theoretical Overview (2013) 

By Mattew M. Peet, Professor of Aerospace Engineering, Arizona State University (USA)

Abstract: The topic of this course will be the use of LMI methods for optimal control of linear, nonlinear and infinite-dimensional systems. We will start by posing all major finite-dimensional optimal control problems as LMIs. This includes both output and full-state feedback control for both the H_\infty and H_2 (LQG) system norms. We will also give a brief introduction to the popular SDP solver SeDuMi. Next, we will give a background on the use of LMIs for optimization of polynomial variables such as in the Sum-of-Squares framework - including the use of the Matlab toolbox SOSTOOLS. We will discuss several theoretical tools for the optimization of polynomials such as various versions of the Positivstellensatz. Finally, we will discuss how LMIs and polynomial optimization have been use to resolve long-standing problems in analysis of nonlinear systems and systems with delay, and how these results have been extended to synthesize optimal controllers for systems with delay and certain classes of partial-differential equations.

Syllabus:

• Day 1: Convex optimization; Semidefinite programming; Linear state-space systems theory; Optimal H_2 and H_\infty dynamic output-feedback controller synthesis. 
• Day 2: Polynomial optimization, Sum-of-Squares; Polya's lemma; Ideals, Varieties; The Positivstellensatz; Robust controller synthesis 
• Day 3: Nonlinear stability analysis; Analysis and control of linear delayed systems; Analysis and control of linear partial-differential equations; Stability Analysis of nonlinear delayed and partial-differential equations. 

Model Reduction (Approximation) of Large-Scale Systems (2012) 

By Charles Poussot-Vassal, Researcher at Onera - The French Aerospace Lab.

Abstract: In the engineering area (e.g. aerospace, automotive, biology, circuits), dynamical systems are the basic framework used for modelling, controlling and analysing a large variety of systems and phenomena. Due to the increasing use of dedicated computer-based modelling design software, numerical simulation turns to be more and more used to simulate a complex system or phenomenon and shorten both development time and cost. However, the need of an enhanced model accuracy inevitably leads to an increasing number of variables and resources to manage at the price of a high numerical cost. This counterpart is the justification for model reduction (see Figure 1). 
The objective of the lecture is to introduce the model reduction (or approximation) problem, within the linear framework only, and, in an increase complexity, some of the well established and modern techniques to solve this class of problem. The lecture is also coupled with two Matlab-based labs, in order to emphasize the numerical difficulties and to provide the participant an insight of the existing tools.

Syllabus:

• Day 1: Introduction, motivating examples and model reduction problem; Overview of the approximation methods and linear algebra tools; Gramian and SVD based techniques; Moment matching and Krylov subspace based techniques.
• Day 2: Lab 1, Application of the SVD techniques and the Arnoldi procedure; H2 first order optimality conditions, generalized Krylov subspace and Tangential techniques; Advanced techniques (Mixed and Sylvester approaches / Multi-LTI and LPV problems / Tools).
• Day 3: Lab 2, Krylov based techniques and MORE Toolbox (developed within Onera by C. Poussot-Vassal).

Design Project 2

This project is the direct continuation of Design Project 1.

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The five months internship can be carried out on various topics and in different industries or research labs. The topics are mostly centered on modeling and control applications, with some contributions in supervision, algorithms and integrated process design. The network aspects, while not directly reflected in the internships titles, appear implicitly as necessary issues in the automation setups. The control implementations range from classical PID or logical setups in industrial automata to advanced model-based optimal or robust feedback strategies.

It can be noted that most students find internships in large industries but a significant number are enrolled in SME and research labs. This motivates the importance of entrepreneurial and research skills in addition to the classical industrial ones. The collaborative internships between academic research labs and industries contribute to the transfer of knowledge between university and industry and is thus strongly encouraged. The variety of industrial markets addressed appears to be a direct consequence of the need for automation in all high-tech processes with strong efficiency needs. From the education point of view, it highlights the importance of a multidisciplinary approach to engineering problems in the process modeling and control design phases.

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