Dynamic systems
Course objectives
GENERAL GOALS: The course on systems theory is focused on methodologies for the mathematical representation of physical and artificial phenomena.The main objective of the course is to provide the student with the main tools for the quantitive analysis of the behaviour of a process in the engineering context or a natural phenomenon, as well as to highlight the problems connected to the non istantaneous dependence of the cause-effect relations in the representation. SPECIFIC OUTCOMES: The course provides the methodologies for the comprehension and investigation of the properties of linear continuous time and discrete time systems. KNOWLEDGE AND UNDERSTANDING: The comprehension of the generality of the mathematical model with respect to the behaviour of systems in different contexts (mechanical, electrical, demographic,...) will allow the student to study, starting from the model, the physical properties of the particular process under investigation CAPABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: At the end of the course the student will be able to associate a mathematical model to a continuous time or discrete time process and investigate its properties COMMUNICATION SKILLS: At the end of the course the student will be able to motivate his/her own design choices MAKING AUTONOMOUS JUDGEMENTS: The student will be able to choose between different methodologies, in order to solve the given problem in the best way.
Channel 1
PAOLO DI GIAMBERARDINO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to dynamical systems and their state space representations; linear, time invariant, finite dimensional, representations, implicit and explicit forms. Free and forced evolutions; from the transition matrix to the impulse response and their properties.
Analysis in the time domain: natural modes, temporal laws and trajectories, natural modes in the free and forced evolution. The cases of continuous time and discrete time systems.
Analysis in the transformed domain: the Laplace transform and its use in the analysis of continuous time systems; the Z transform and its use in the analysis of discrete time systems. Steady state and transient behaviours; steady state with respect to canonical inputs.
Frequency analysis: harmonic response, Bode diagrams, characteristic parameters of the harmonic response and the unit-step response.
Matrix transfert functions and their realisations; state space representations from input-output maps. Interconnected systems resulting from multiple elementary interconnections: cascade, parallel and feedback connections; their representations and properties.
Elements of stability theory: from definitions to conditions and criteria. Internal stability of linear systems; Routh and Jury criteria. Input-output stability: conditions and relation to internal stability.
Structural properties of the state space: reachability and observability; characterisation and decompositions with respect to them, Kalman scomposition and the system's internal structure. Properties.
Prerequisites
Knowledge of Mathematical Analysis:
functions of one and more variables in the real and complex domain and their graphic representations;
basic knowledge on calculus;
Knowledge of Geometry:
fundamentals of linear Algebra, linear operators, vector spaces.
Knowledge of Physics:
basic knowledge in the various fields of physics, sufficient to understand the application examples used.
Books
S. Monaco, C.Califano, P. Di Giamberardino, M. Mattioni, Teoria dei Sistemi. Lineari, stazionari a dimensione finita, Esculapio, 2021, 9788893852685
Frequency
Lessons in presence in classroom, mainly using a blackboard.
On line remote connections in case of COVID-19 related problems
Exam mode
Weighted average of the results of the two tests
Lesson mode
Lessons for the theoretical aspects, numerical exercitations for practical implementations.
PAOLO DI GIAMBERARDINO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to dynamical systems and their state space representations; linear, time invariant, finite dimensional, representations, implicit and explicit forms. Free and forced evolutions; from the transition matrix to the impulse response and their properties.
Analysis in the time domain: natural modes, temporal laws and trajectories, natural modes in the free and forced evolution. The cases of continuous time and discrete time systems.
Analysis in the transformed domain: the Laplace transform and its use in the analysis of continuous time systems; the Z transform and its use in the analysis of discrete time systems. Steady state and transient behaviours; steady state with respect to canonical inputs.
Frequency analysis: harmonic response, Bode diagrams, characteristic parameters of the harmonic response and the unit-step response.
Matrix transfert functions and their realisations; state space representations from input-output maps. Interconnected systems resulting from multiple elementary interconnections: cascade, parallel and feedback connections; their representations and properties.
Elements of stability theory: from definitions to conditions and criteria. Internal stability of linear systems; Routh and Jury criteria. Input-output stability: conditions and relation to internal stability.
Structural properties of the state space: reachability and observability; characterisation and decompositions with respect to them, Kalman scomposition and the system's internal structure. Properties.
Prerequisites
Knowledge of Mathematical Analysis:
functions of one and more variables in the real and complex domain and their graphic representations;
basic knowledge on calculus;
Knowledge of Geometry:
fundamentals of linear Algebra, linear operators, vector spaces.
Knowledge of Physics:
basic knowledge in the various fields of physics, sufficient to understand the application examples used.
Books
S. Monaco, C.Califano, P. Di Giamberardino, M. Mattioni, Teoria dei Sistemi. Lineari, stazionari a dimensione finita, Esculapio, 2021, 9788893852685
Frequency
Lessons in presence in classroom, mainly using a blackboard.
On line remote connections in case of COVID-19 related problems
Exam mode
Weighted average of the results of the two tests
Lesson mode
Lessons for the theoretical aspects, numerical exercitations for practical implementations.
Channel 2
CLAUDIA CALIFANO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to dynamical systems and their state space representations; linear, time invariant, finite dimensional, representations, implicit and explicit forms. Free and forced evolutions; from the transition matrix to the impulse response and their properties.
Analysis in the time domain: natural modes, temporal laws and trajectories, natural modes in the free and forced evolution. The cases of continuous time and discrete time systems.
Analysis in the transformed domain: the Laplace transform and its use in the analysis of continuous time systems; the Z transform and its use in the analysis of discrete time systems. Steady state and transient behaviours; steady state with respect to canonical inputs.
Frequency analysis: harmonic response, Bode diagrams, characteristic parameters of the harmonic response and the unit-step response.
Matrix transfert functions and their realisations; state space representations from input-output maps. Interconnected systems resulting from multiple elementary interconnections: cascade, parallel and feedback connections; their representations and properties.
Elements of stability theory: from definitions to conditions and criteria. Internal stability of linear systems; Routh and Jury criteria. Input-output stability: conditions and relation to internal stability.
Structural properties of the state space: reachability and observability; characterisation and decompositions with respect to them, Kalman scomposition and the system's internal structure. Properties.
Prerequisites
Knowledge of Mathematical Analysis:
functions of one and more variables in the real and complex domain and their graphic representations;
basic knowledge on calculus;
Knowledge of Geometry:
fundamentals of linear Algebra, linear operators, vector spaces.
Knowledge of Physics:
basic knowledge in the various fields of physics, sufficient to understand the application examples used.
Books
S. Monaco, C.Califano, P. Di Giamberardino, M. Mattioni, Teoria dei Sistemi. Lineari, stazionari a dimensione finita, Esculapio, 2021, 9788893852685
Frequency
Lessons in presence in classroom, mainly using a blackboard.
On line remote connections in case of COVID-19 related problems
Exam mode
Weighted average of the results of the two tests
Lesson mode
Lessons for the theoretical aspects, numerical exercitations for practical implementations.
CLAUDIA CALIFANO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to dynamical systems and their state space representations; linear, time invariant, finite dimensional, representations, implicit and explicit forms. Free and forced evolutions; from the transition matrix to the impulse response and their properties.
Analysis in the time domain: natural modes, temporal laws and trajectories, natural modes in the free and forced evolution. The cases of continuous time and discrete time systems.
Analysis in the transformed domain: the Laplace transform and its use in the analysis of continuous time systems; the Z transform and its use in the analysis of discrete time systems. Steady state and transient behaviours; steady state with respect to canonical inputs.
Frequency analysis: harmonic response, Bode diagrams, characteristic parameters of the harmonic response and the unit-step response.
Matrix transfert functions and their realisations; state space representations from input-output maps. Interconnected systems resulting from multiple elementary interconnections: cascade, parallel and feedback connections; their representations and properties.
Elements of stability theory: from definitions to conditions and criteria. Internal stability of linear systems; Routh and Jury criteria. Input-output stability: conditions and relation to internal stability.
Structural properties of the state space: reachability and observability; characterisation and decompositions with respect to them, Kalman scomposition and the system's internal structure. Properties.
Prerequisites
It is recommended to have already taken the courses of Analysis, Geometry and Physics.
Books
MONACO CALIFANO DI GIAMBERARDINO MATTIONI - Teoria dei Sistemi. Lineari stazionari a dimensione finita
CODICE: 3909 I Ed.2021
ISBN 13: 9788893852685
additional material will be posted on moodle
Teaching mode
The course will be held face to face (provisional schedule monday 1-4 pm tuesday 3-6 pm, wednesday 1-3 pm, starting date september 28, 2020) and it will be available online through zoom or google meet in streaming.
Link zoom a.a. 2021/2022
https://uniroma1.zoom.us/j/88019069162?pwd=aFhJZEFpbURMbENVR0IrQy9zS1VXQT09
Frequency
The course is held in person
Exam mode
Written and oral exam
Lesson mode
The course will be held face to face
- Lesson code10606930
- Academic year2024/2025
- CourseComputer and System Engineering
- CurriculumInformatica
- Year2nd year
- Semester1st semester
- SSDING-INF/04
- CFU9
- Subject areaIngegneria dell'automazione