Mauro Franceschelli

Fault Diagnosis and Estimation in Dynamical Systems

04 febbraio 2021

Video recordings of the lectures are available on Adobe Connect.

The recordings that you can find in the following links were not post-produced and are just the record of the lectures as they were given by the lecturer to the class.

The videos are available after each lecturers (might possible delays) on Adobe Connect only to the students enrolled, which are required to login using their User ID and password.

According to the currents laws (D.R. 341/2020 on 24/03/2020 (art. 4)): “It is forbidden to the users to register, copy, modify and share with any tool the teaching materials (registrations, slides, etc). Furthermore, it is forbidden to use the teaching material not for educational purposes as well as for any purpose not allowed by the copyright laws.”.

Teaching material updated for a.a. 2020/2021

March 2nd 2021 - Video - Lecture 1 - Introduction to the course

March 5th 2021 - Lecture 2 Slides - A brief review of analysis of continuous-time linear dynamical systems

March 5th 2021 - Video - Lecture 2 - Entrance test and brief review of analysis of continuous-time linear dynamical systems

March 9th 2021 - Lecture 3 Slides - review of analysis of continuous-time state variable linear dynamical systems

March 9th 2021 - Video -  Lecture 3 - review of analysis of continuous-time state variable linear dynamical systems

March 12th 2021 - Lecture 4  Slides - review of matrix algebra, state-space transformations, steady-state and transient behavior and introduction to Matlab.

March 12th 2021 - Lecture 4- Matlab scripts 

March 12th 2021 - Video - Lecture 4 - review of matrix algebra, state-space transformations, steady-state and transient behavior and introduction to Matlab.

March 16th 2021 - Lecture 5 Slides - Analysis of discrete-time dynamical systems and discretization of continuous-time systems

March 16th 2021 - Video - Lecture 5 - Analysis of discrete-time dynamical systems and discretization of continuous-time systems

March 19th 2021 - Lecture 6 Slides - Equilibrium and stability analysis for continuous-time and discrete-time linear systems

March 19th 2021 - Matlab Simulink files

March 19th 2021 - Video - Lecture 6 - Equilibrium points, Stability criteria for continuous-time and discrete-time systems, introduction to Simulink

March 23rd 2021 - Lecture 7 Slides - Analysis of nonlinear systems and first Lyapunov method (continuous and discrete-time)

March 23rd 2021 - Video - Lecture 7 - Analysis of nonlinear systems and first Lyapunov method (continuous and discrete-time)

March 30th 2021 - Video - Lecture 8 - Assignment 1

April 9th 2021 -  Lecture 9 Slides - Analysis of nonlinear systems and the second Lyapunov method (continuous and discrete-time)

April 9th 2021 - Video - Lecture 9 - Analysis of nonlinear systems and the second Lyapunov method (continuous and discrete-time)

April 13th 2021 - Video - Lecture 10 - Assignment 2

April 16th 2021 - Lecture 11 Slides - Introduction to Controllability and Observability and canonical forms

April 16th 2021 - Video - Lecture 11 - Properties of Controllability and Observability and canonical forms

April 20th 2021 - Lecture 12 Slides - Full State feedback design

April 20th 2021 - Lecture 12 Matlab and Simulink files

April 20th 2021 - Video - Lecture 12 - Full state feedback design

April 23rd 2021 - Lecture 13 Slides - The state estimation problem in dynamical systems and state observer design

April 23rd 2021 - Video - Lecture 13 - The state estimation problem in dynamical systems and design of state observers

April 23rd 2021 - Lecture 13 Matlab Simulink files

April 27th 2021 - Lecture 14 - Assignment 3

April 30th 2021 - Lecture 15 - Review of stochastic processes

 April 30th 2021 - Lecture 15 - The Kalman filter

 April 30th 2021 - Lecture 15 - Matlab script (Kalman filter)

April 30th 2021 - Video - Lecture 15 - Review of stochastic process and the Kalman filter

May 4th 2021 - Video - Lecture 16 - Assignment 4

May 7th 2021 - Lecture 17 - The high gain observer

May 7th 2021 - Video - Lecture 17 - High Gain observer and Assignment 5

May 11th 2021 - Lecture 18 - Introduction to model-based fault diagnosis

May 11th 2021 - Video - Lecture 18 - Introduction to model-based fault diagnosis

May 14th 2021 - Lecture 19 - Residual generation, Unknown Input Observer and FDI scheme

May 14th 2021 - Video - Lecture 19 - Residual generation, Unknown Input Observer and FDI scheme

May 18th 2021 - Lecture 20 - Parameter estimation methods

May 18th 2021 - Lecture 20 - Additional Matlab material

May 18th 2021 - Video - Lecture 20 - Parameter estimation methods 

May 25th 2021 - Video - Lecture 21 - Assignment 6

Assignments for a.y. 2020/2021

Assignment 1    -      Assignment 1 solution

Assignment 2    -      Assignment 2 solution    -     Additional simulink material

Assignment 3    -      Assignment 3 solution

Assignment 4    -      Assignment 4 solution

Assignment 5    -      Assignment 5 solution      

Assignment 6    -      Assignment 6 solution

Training for the oral examination

Examples of typical exam questions for a.y. 2020/2021

 


Teaching material adopted during a.y. 2019/2021

Part of the study material of FDE consists in the slides presented during the lectures and the Matlab scripts developed during both the lectures and the exercitations:

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7 – Matlab scripts

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 12 – Matlab scripts

Lecture 13

Lecture 13 – Matlab Simulink and script

Lecture 14

Lecture 15

Lecture 15 – Matlab Simulink and script

Lecture 16

Lecture 17

Lecture 17 – Matlab script

Lecture 18

Lecture 18 – Matlab Simulink file

Lecture 18 part II

Lecture 19

Lecture 20

Lecture 21

Lecture 21 – Matlab scripts

Suggested books and other material:

Material on continuous time linear systems, stability, observability and controllability, Lyapunov methods, state feedback, and  state observers in Italian, is found in:

  • Alessandro GIUA, Carla SEATZU, Analisi dei sistemi dinamici- 2a edizione, Springer-Verlag Italia, Milano, 2009.  (Chapter 4, 8, 11)

Material on discrete-time and continuous time linear systems, stability, observability and controllability, state feedback,  Lyapunov methods Luenberger observers,  is found in:

  • Katsuhiko Ogata, “Discrete-time control systems” second edition, Prentice Hall International editions, 1995  (Part of chapter 1, 5, 6)

Material on Fault diagnosis and Estimation is found in:

  • Silvio Simani, Cesare Fantuzzi and Ron J. Patton “Model-based fault diagnosis in dynamic systems using identification techniques” Springer-Verlag 2002. (Part of chapters 1,2,3,4)

Material on high gain observers (and Lyapunov methods) is found in:

  • Hassan K. Khalil “Nonlinear systems” third edition, Pearson Eduction Limited 2014.  (Part of chapter 14)

Additional material on nonlinear analysis, Lyapunov methods  is found in

  • Jean-Jacques E. Slotine, Weiping Li “Applied Nonlinear Control” Prentice-Hall, 1991.  (Part of chapter 3)

Suggested readings:

Tutorial on Kalman filters:

  • Matthew B. Rhudy, Roger A. Salguero and Keaton Holapp, “A Kalman filtering tutorial for undergraduate students” International Journal of Computer Science & Engineering Survey (IJCSES) Vol.8, No.1, February 2017.

Tutorials on High-Gain Observers:

  • Ahmed Mohammed Dabroom and Hassan K. Khalil, “Output Feedback Sampled-Data Control of Nonlinear Systems Using High-Gain Observers” IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 46, NO. 11, NOVEMBER 2001
  • Hassan K. Khalil “High-Gain Observers in Nonlinear Feedback Control” International Conference on Control, Automation and Systems 2008, Oct. 14-17, 2008 in COEX, Seoul, Korea

Other sources and papers will be provided during the lectures.

Students can download an academic version of the Matlab software by following the instructions (in Italian) at: https://www.unica.it/unica/en/studenti_s08_ss09.page

 

During the lectures, a total of six assignments with questions and exercises will be provided.

The final exam is oral and the students will be expected to understand, solve and discuss the provided assignments.

The final evaluation will be quantified by a mark representing a weighted average in the next areas:

  • Knowledge of the topics (40% final mark)
  • Application of the obtained knowledge to the design algorithms (30% final mark)
  • Autonomy in making judgments in regard to design choices (20% final mark)
  • Use of technical language (10% final mark)

Examples of typical exam questions can be found here

Vedemecum and where to study for a.a. 2019/2020

Course assignments a.a. 2019/2020

Assignment 1

Assignment 1 – solutionAssignment 2

Assignment 2 – Partial solution (ex. 1 and 3)

Assignment 3

Assignment 3 – solution

Assignment 4

Assignment 4 – solution

Assignment 5

Assignment 5 – solution

Assignment 6

Assignment 6 – solution

Course assignments a.a. 2018/2019

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6

Assorted Matlab scripts discussed during the lectures can be found here:

AssortedMatlabScripts

Short summary of course content  (a.a. 2018/2019)

Representation of dynamical systems:

State space representation of continuous time and discrete time dynamical systems. Analysis of continuous time linear systems, natural and forced response.  Analysis of discrete-time linear systems, natural and forced response. Discretization of dynamical systems.  Canonical forms of linear systems, continuous time and discrete time.

Where to study:

  • Lecture notes;
  • Katsuhiko Ogata, “Discrete-time control systems” Chapter 5, Sections 5.1,5.2,5.3,5.5.

Stability of dynamical systems:

Equilibrium points. Stability and Asymptotic stability of equilibrium points. Stability criteria for continuous time and discrete-time linear systems. Linearization of a nonlinear system around an equilibrium point. Stability of nonlinear systems: indirect (also called first) and direct (also called second) Lyapunov methods for  continuous time and discrete time dynamical systems.

Where to study:

  • Katsuhiko Ogata, “Discrete-time control systems” Chapter 5, Section 5.6.

Structural properties of dynamical systems and state feedback:

Controllability and Observability.  Controllable and observable canonical forms. Controllability and observability matrix. Full-state  feedback control by eigenvalue assignment. Design procedure.

Where to study:

Katsuhiko Ogata, “Discrete-time control systems” Chapter 6, sections 6.1,6.2,6.3,6.4,6.5.

Estimation in dynamical systems:

The state estimation problem, asymptotic (Luenberger) state observers. Full-order and reduced (minimum) order observers. Design procedure. Observer-state feedback and Separation principle. Kalman filter (Discrete-time) and Extended Kalman filters. Nonlinear systems and High-gain observers.

Where to study:

  • Katsuhiko Ogata, “Discrete-time control systems” Chapter 6, section 6.6;
  • Matthew B. Rhudy, Roger A. Salguero and Keaton Holapp, “A Kalman filtering tutorial for undergraduate students” International Journal of Computer Science & Engineering Survey (IJCSES) Vol.8, No.1, February 2017;
  • Hassan K. Khalil “Nonlinear systems” third edition, Pearson Eduction Limited 2014.  Chapter 14, section 14.5, 14.5.1, 14.5.2.

Fault diagnosis:

Introduction to Fault Detection and Identification (FDI). Methods for model based  fault diagnosis. Fault models.  The residual generation and evaluation problem. Unknown input observers. FDI by banks of unknown input observers. Parameter estimation for discrete-time linear systems. Residual generation by parameter estimation methods.

Where to study:

  • Silvio Simani, Cesare Fantuzzi and Ron J. Patton “Model-based fault diagnosis in dynamic systems using identification techniques” Springer-Verlag 2002.  Chapter 1, Sections 1.1, 1.2,1.3,1.4,1.5. Chapter 3, Sections 3.1,3.2,3.3.1. Chapter 4, Sections 4.1,4.2,4.3,4.4, 4.8.

Questionario e social

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