Control is a multi-disciplinary area, involving theoretical, numerical and hardware tools, finalized at modifying the behavior of real-world systems. Due to its nature, control is nowadays fundamental in most fields of science and technology, ranging from the "classical" aerospace, automotive, robotics and energy fields, to less "traditional" fields, e.g., related to biomedical, data analytics, communication and network applications. Starting from the observation that the majority of real-world dynamic systems are nonlinear, the first objective of the course is to provide the basic methodologies for analyzing the properties of a nonlinear system and for designing effective control algorithms, aimed at obtaining the desired behavior for the system variables of interest. The second objective of the course is to show how these methodologies can be applied to aerospace systems, allowing the accomplishment of the most challenging missions.

The knowledge acquired during the course will regard the following subjects: properties of nonlinear systems; properties of feedback systems; modern control design methods for nonlinear systems; coordinate reference systems, rotations and translations; spacecraft/aircraft attitude kinematics and dynamics; spacecraft orbital dynamics; spacecraft/aircraft control design. The skills acquired during the course will be the following: understanding and analyzing the behavior of a dynamic system; developing advanced control algorithms for nonlinear systems; understanding and analyzing the behavior of a spacecraft/aircraft; developing advanced control algorithms for spacecraft/aircraft systems; developing simulation and control software in Matlab/Simulink. The student will learn how to use in a comprehensive way the acquired knowledge and skills in order to deal with new problems, without being limited to a small set of applications/case studies.

Strong background in differential and integral calculus of vector valued functions and in linear algebra. Basic concepts of physics, mechanics, complex numbers, real rational functions. Basic notions on dynamic systems and automatic control.

Nonlinear system analysis: basic notions on dynamic systems; state equations; basic stability concepts; Lyapunov stability. Control design for nonlinear systems. Overview on different approaches: linearization and gain scheduling; feedback linearization; embedded model control; sliding-mode control; nonlinear model predictive control. Observer design for nonlinear systems: extended Kalman filter. Aerospace topics: coordinate reference systems; rotations and translations; rigid body attitude kinematics and dynamics; orbital dynamics. Aerospace applications/case studies will be about spacecraft orbit/trajectory control; spacecraft attitude control; aircraft flight control.

Lectures will be concerned with theoretical topics, numerical examples and solved problems. LAB exercises will also be carried out, based on the Matlab/Simulink software. The LAB sessions will be focused on the development of academic and applicative examples, some of which are taken from the aerospace field.

[1] C. Novara, Nonlinear Control and Aerospace Applications: lecture notes. Politecnico di Torino, 2017. [2] J-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991. [3] S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer, 1999. [4] M. H. Kaplan, Modern Spacecraft Dynamics and Control, I. John Wiley and Sons, 1976. [5] B. Wie, Space Vehicle Dynamics and Control. Aiaa, 1998. [6] F. Markley and J. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control. Cambridge University Press, 2014. [7] D. G. Hull, Fundamentals of Airplane Flight Mechanics, Springer, 2007. [8] A. Tewari, Atmospheric and Space Flight Dynamics: Modeling and Simulation with Matlab and Simulink, Birkhauser, 2007. [9] E. Canuto, C. Novara, L. Massotti, C. Perez Montenegro and D. Carlucci, Spacecraft dynamics and control. The embedded model control approach, Butterworth-Heinemann (Elsevier), 2018.

Modalità di esame: Test informatizzato in laboratorio;

Exam: Computer lab-based test;

... Written examination (carried out in lab with the help of the PC and the Matlab/Simulink software) with multiple choice questions and design problems. The number of questions will range between 7 and 11, depending on the average difficulty. A (small) negative score will be assigned to wrong answers. The duration of the exam will be 2.30 hours. The following material will be available during the exam: lecture slides (without students' notes), Matlab libraries. No other material will be allowed (in particular, no solved exercises). No oral examinations will be held.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Modalità di esame: Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

The exam is held through the LockDownBrowser, Responsus and Exam systems. The VLAIB modality is used, allowing students to work on a LAIB virtual machine, equipped with Matlab/Simulink. Students are reccomended to 1) Watch the video https://youtu.be/XuX8WoeAycs 2) Read the document https://didattica.polito.it/pdf/InstructionsVLAIB_stud.pdf 3) Read the quiz guide https://docs.moodle.org/30/en/Quiz_quick_guide 4) Try an exam simulation using the link available on their own portal page 5) Read the Code of Ethical Conduct: https://didattica.polito.it/regolamenti/pdf/Code_of_Ethical_Conduct.pdf Allowed exam material: The slides of the course; the Matlab/Simulink libraries used in the course. This material is downloadable from the EXAM platform during the exam. Any other material is forbidded. Topics to study: All the topics treated in the slides, except those presented in the slides with a light blue background; all the topics treated during the Lab sessions. What discussed during the experimental lab session is not required. The exam consists of multiple choice questions. Answers are given directly on the Exam platform. The number of questions ranges between 7 and 11, depending on the average difficulty. A (small) negative score is assigned to wrong answers. The duration is 2:15 hours + 30 minutes (accounting for possible technical problems). Allowed software: Matlab/Simulink, pdf reader. Any other software is forbidden. Navigation is forbidden. Taking photos and screenshots is forbidden. White paper sheets for handwritten calculations are allowed. A small number of separated sheets should be used. Paper notebooks of any kind are not allowed. Suggestion: Besides indicating the answers on the Exam platform, write them on a paper sheet and show them to the camera. Write only the numbers of the questions and the corresponding answers as clearly as possible. Do not show the procedures and/or calculations needed to get the answers. WARNING: In VLAIB modality, you will use a LAIB virtual machine and so you will work initially with an Italian keyboard. Consider that it will be possible to change the keyboard setting. WARNING: Students are recommended to use just one browser, open a single session and login only once. The exam may be not recorded correctly if these indications are not followed. IMPORTANT: It may happen that, for technical reasons (typically external to Politecnico), some students cannot (or have difficulties to) take the exam. These students will participate, of necessity, to the subsequent exam. We are all working in this emergency situation due to the covid-19 epidemic. Students must understand that the technical staff of Politecnico are doing their best (and even more) to make all teaching and exam activities work properly. In any case, there may be technical problems independent of the Politecnico staff.

Modalità di esame: Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

The exam is held through the LockDownBrowser, Responsus and Exam systems. The VLAIB modality is used, allowing students to work on a LAIB virtual machine, equipped with Matlab/Simulink. Students are reccomended to 1) Watch the video https://youtu.be/XuX8WoeAycs 2) Read the document https://didattica.polito.it/pdf/InstructionsVLAIB_stud.pdf 3) Read the quiz guide https://docs.moodle.org/30/en/Quiz_quick_guide 4) Try an exam simulation using the link available on their own portal page 5) Read the Code of Ethical Conduct: https://didattica.polito.it/regolamenti/pdf/Code_of_Ethical_Conduct.pdf Allowed exam material: The slides of the course; the Matlab/Simulink libraries used in the course. This material is downloadable from the EXAM platform during the exam. Any other material is forbidded. Topics to study: All the topics treated in the slides, except those presented in the slides with a light blue background; all the topics treated during the Lab sessions. What discussed during the experimental lab session is not required. The exam consists of multiple choice questions. Answers are given directly on the Exam platform. The number of questions ranges between 7 and 11, depending on the average difficulty. A (small) negative score is assigned to wrong answers. The duration is 2:15 hours + 30 minutes (accounting for possible technical problems). Allowed software: Matlab/Simulink, pdf reader. Any other software is forbidden. Navigation is forbidden. Taking photos and screenshots is forbidden. White paper sheets for handwritten calculations are allowed. A small number of separated sheets should be used. Paper notebooks of any kind are not allowed. Suggestion: Besides indicating the answers on the Exam platform, write them on a paper sheet and show them to the camera. Write only the numbers of the questions and the corresponding answers as clearly as possible. Do not show the procedures and/or calculations needed to get the answers. WARNING: In VLAIB modality, you will use a LAIB virtual machine and so you will work initially with an Italian keyboard. Consider that it will be possible to change the keyboard setting. WARNING: Students are recommended to use just one browser, open a single session and login only once. The exam may be not recorded correctly if these indications are not followed. IMPORTANT: It may happen that, for technical reasons (typically external to Politecnico), some students cannot (or have difficulties to) take the exam. These students will participate, of necessity, to the subsequent exam. We are all working in this emergency situation due to the covid-19 epidemic. Students must understand that the technical staff of Politecnico are doing their best (and even more) to make all teaching and exam activities work properly. In any case, there may be technical problems independent of the Politecnico staff.