Provide to the students methodologies and techniques for the analysis and modeling of linear time-invariant systems by focusing on the state-space representation. Provide the knowledge for the design of feedback control systems. Derive the state-space model of Multi-Input Multi-Output systems. Provide the knowledge of the structural properties of MIMO dynamical models and the asymptotic observer for the eigenvalue assignment problem and the regulation problem. Provide the students with basic concepts for the analysis of nonlinear system.
Curriculum
teacher profile teaching materials
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. NONLINEAR SYSTEMS AND LINEARIZATION
2.1. Motivations and Definitions
2.2. Linearization Method
3. DIFFERENTIAL EQUATIONS
3.1. Linear Differential Equations with Constant Coefficients
3.2. Exponential Matrix
3.3. Free Evolution
3.4. Forced Evolution
4. RELATIONSHIP BETWEEN REPRESENTATIONS
4.1. From State-Spate to Transfer Function
4.2. From Transfer Function to State-Spate
5. MODAL DECOMPOSITION
5.1. Eigenvalues and Eigenvectors
5.2. Coordinate Transformation
5.3. Diagonalization and Jordanization
6. STRUCTURAL PROPERTIES
6.1. Controllability and Observability
6.2. Controllability and Observability Kalman Forms
6.3. Kalman Canonical Decomposition
7. REALIZATION AND CANONICAL FORMS
7.1. Realization
7.2. Canonical Forms for Realization
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
Programme
Linear Systems1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. NONLINEAR SYSTEMS AND LINEARIZATION
2.1. Motivations and Definitions
2.2. Linearization Method
3. DIFFERENTIAL EQUATIONS
3.1. Linear Differential Equations with Constant Coefficients
3.2. Exponential Matrix
3.3. Free Evolution
3.4. Forced Evolution
4. RELATIONSHIP BETWEEN REPRESENTATIONS
4.1. From State-Spate to Transfer Function
4.2. From Transfer Function to State-Spate
5. MODAL DECOMPOSITION
5.1. Eigenvalues and Eigenvectors
5.2. Coordinate Transformation
5.3. Diagonalization and Jordanization
6. STRUCTURAL PROPERTIES
6.1. Controllability and Observability
6.2. Controllability and Observability Kalman Forms
6.3. Kalman Canonical Decomposition
7. REALIZATION AND CANONICAL FORMS
7.1. Realization
7.2. Canonical Forms for Realization
Core Documentation
1. An Introduction to Linear Control Systems, Thomas E. Fortmann, Konrad L. Hitz2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
Type of delivery of the course
Lectures and classroom exercises are planned.Type of evaluation
Learning verification tests are based on two examinations: a written exam of a duration of two hours and an oral exam. The written exam is composed of several exercises aiming at assessing the students capability to apply the fundamental concepts. The oral exam aims at assessing the level of understanding of the fundamental concepts. In order to take the oral exam it is mandatory to have successfully pass the written exam during the current academic year. ----- During the COVID-19 emergency learning verification tests will be conducted according to the art.1 of the Rectoral decree n°. 703 of 5 May 2020 teacher profile teaching materials
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. NONLINEAR SYSTEMS AND LINEARIZATION
2.1. Motivations and Definitions
2.2. Linearization Method
3. DIFFERENTIAL EQUATIONS
3.1. Linear Differential Equations with Constant Coefficients
3.2. Exponential Matrix
3.3. Free Evolution
3.4. Forced Evolution
4. RELATIONSHIP BETWEEN REPRESENTATIONS
4.1. From State-Spate to Transfer Function
4.2. From Transfer Function to State-Spate
5. MODAL DECOMPOSITION
5.1. Eigenvalues and Eigenvectors
5.2. Coordinate Transformation
5.3. Diagonalization and Jordanization
6. STRUCTURAL PROPERTIES
6.1. Controllability and Observability
6.2. Controllability and Observability Kalman Forms
6.3. Kalman Canonical Decomposition
7. REALIZATION AND CANONICAL FORMS
7.1. Realization
7.2. Canonical Forms for Realization
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
Programme
Linear Systems1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. NONLINEAR SYSTEMS AND LINEARIZATION
2.1. Motivations and Definitions
2.2. Linearization Method
3. DIFFERENTIAL EQUATIONS
3.1. Linear Differential Equations with Constant Coefficients
3.2. Exponential Matrix
3.3. Free Evolution
3.4. Forced Evolution
4. RELATIONSHIP BETWEEN REPRESENTATIONS
4.1. From State-Spate to Transfer Function
4.2. From Transfer Function to State-Spate
5. MODAL DECOMPOSITION
5.1. Eigenvalues and Eigenvectors
5.2. Coordinate Transformation
5.3. Diagonalization and Jordanization
6. STRUCTURAL PROPERTIES
6.1. Controllability and Observability
6.2. Controllability and Observability Kalman Forms
6.3. Kalman Canonical Decomposition
7. REALIZATION AND CANONICAL FORMS
7.1. Realization
7.2. Canonical Forms for Realization
Core Documentation
1. An Introduction to Linear Control Systems, Thomas E. Fortmann, Konrad L. Hitz2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
Type of delivery of the course
Lectures and classroom exercises are planned.Type of evaluation
Learning verification tests are based on two examinations: a written exam of a duration of two hours and an oral exam. The written exam is composed of several exercises aiming at assessing the students capability to apply the fundamental concepts. The oral exam aims at assessing the level of understanding of the fundamental concepts. In order to take the oral exam it is mandatory to have successfully pass the written exam during the current academic year. ----- During the COVID-19 emergency learning verification tests will be conducted according to the art.1 of the Rectoral decree n°. 703 of 5 May 2020