## UE Modeling and system identification

Degrees incorporating this pedagocial element :

### Description

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.

Lesson Topic
Introduction to Modeling
Systems and models, examples of models, models for systems and signals.
PHYSICAL MODELING
Principles of Physical Modeling
The phases of modeling, the mining ventilation problem example, structuring the problem, setting up the basic equations, forming the state-space models, simplified models.
Some Basic Relationships in Physics
Electrical circuits, mechanical translation, mechanical rotation, flow systems, thermal systems, some observations.
Bond Graphs:
Physical domains and power conjugate variables, physical model structure and bond graphs, energy storage and physical state, free energy dissipation, ideal transformations and gyrations, ideal sources, KirchhoffÂ’s laws, junctions and the network structure, bond graph modeling of electrical networks, bond graph modeling of mechanical systems, examples.
SIMULATION
Computer-Aided Modeling
Computer algebra and its applications to modeling, analytical solutions, algebraic modeling, automatic translation of bond graphs to equations, numerical methods - a short glance.
Modeling and Simulation in Scilab
Types of models and simulation tools for: ordinary differential equations, boundary value problems, difference equations, differential algebraic equations, hybrid systems.
SYSTEM IDENTIFICATION
Experiment Design for System Identification:
Basics of system identification, from continuous dynamics to sampled signals, disturbance modeling, signal spectra, choice of sampling interval and presampling filters.
Non-parametric Identification:
Transient-response and correlation analysis, frequency-response/Fourier/spectral analysis, estimating the disturbance spectrum.
Parameter Estimation in Linear Models:
Linear models, basic principle of parameter estimation, minimizing prediction errors, linear regressions and least squares, properties of prediction error minimization estimates.
10 System Identification Principles and Model Validation
Experiments and data collection, informative experiments, input design for open-loop experiments, identification in closed-loop, choice of the model structure, model validation, residual analysis.
11 Nonlinear Black-box Identification
Nonlinear state-space models, nonlinear black-box models: basic principles, parameters estimation with Gauss-Newton stochastic gradient algorithm, temperature profile identification in tokamak plasmas
TOWARDS PROCESS SUPERVISION
12 Recursive Estimation Methods
Recursive least-squares algorithm, IV method, prediction-error methods and pseudolinear regressions, Choice of updating step
MODELING LABS
Lab 1-2 Vibration Isolation for Heavy Trucks
Lab 3 Modeling of a LEGO robot
Lab 4 Modeling and Simulation of a Thermonuclear Plant
Lab 5 Simulation and Control of an Inverted Pendulum Using Scilab
Lab 6 Identification of an Active Vibration Control Benchmark Using Matlab
Lab 7-8 Experiment design: Anthropogenic Impact on the Ozone Layer Depletion
Lab 9 Recursive identification of a LEGO robot

### Bibliography

• L. Ljung and T. Glad, "Modeling of Dynamic Systems", Prentice Hall PTR, 1994.
• S. Stramigioli, "Modeling and IPC Control of Interactive Mechanical Systems: A Coordinate-free Approach", Springer, LNCIS 266, 2001.
• S. Campbell, J-P. Chancelier and R. Nikoukhah, "Modeling and Simulation in Scilab/Scicos", Springer, 2005.
• L. Ljung, "System Identification: Theory for the User", 2nd Edition, Information and System Sciences, (Upper Saddle River, NJ: PTR Prentice Hall), 1999.
• O. Hinton, "Digital Signal Processing", Chapter 6 - Describing Random Sequences, EEE305 class material, 2003.