DALMINE
Overview
Date/time interval
Syllabus
Course Objectives
At the end of the course, the student knows:
- The fundamental notions of the theory of discrete time systems theory for the mathematical modeling of phenomena, machines and processes through linear discrete time models.
- The tools for the analysis of linear systems in the time domain and the evaluation of the main structural properties
- The design methods of simple feedback controllers
- The main tools used to model and analyze stationary stochastic process
The student is able to:
- Compute the Z transform of discrete signals
- Compute the transfer function of discrete linear systems
- Manipulate complex systems by decomposing into subsystems and solving block diagrams
- Assign the eigenvalues in closed loop and designing model reference feedback controllers
- Compute the main properties of a stochastic system and to use them in simple prediction problems
Course Prerequisites
Elements of linear algebra and matrix computation.
Complex numbers.
Derivatives.
Basic notions on differential equations.
Teaching Methods
The educational path proposed to the student is the following:
- Attend the lectures presented using slides. These are all available before the course starts, and it is useful for the student to view the slides of a lesson before attending it.
- Study the topics of the lesson with the help of the textbook, slides and personal notes.
- Answer the questions related to the lesson prepared on Moodle. The purpose of these questions is to test the knowledge of the concepts exposed and not their understanding or the student's ability to use them.
- Attend the exercise lectures carried out on the blackboard (electronic or traditional). The text and the development of the exercises are all available before the start of the course and it is useful for the student to view the development of the exercises before attending the lecture.
- At the end of the lectures, the student is able to carry out some exam examples, proposed with their solution and chosen from the most representative and paradigmatic ones.
- In parallel to this track, lessons are proposed on the Matlab implementation of the concepts presented in the lessons. The goal is to make the student independent in the use of Matlab for solving Control Systems problems.
Great importance is given to students' active participation in lessons, which is stimulated through continuous dialogue.
Students can find the teacher by email or with an appointment.
Assessment Methods
The exam is done through a final written exam of 2 hours. It usually consists of 5 or 6 questions: 3 or 4 exercises and 2 or 3 theoretical questions. Each question assigns from 5 to 8 points.
IMPORTANT NOTE
For the “Ingegneria Gestionale” students, this course is integrated with “Elettrotecnica”. The overall grade of the integrated course will be calculated as the average (approximated to the upper integer) of the marks obtained in the two modules.
Contents
INTRODUCTION
- Introduction to Control Theory.
- Formulation of a control problem.
- Controlled variables, control variables and disturbances
- Open loop control and closed loop control
- Sensors and sampling of signals
- Continuous and discrete time signals
- Dynamic systems
- Modeling of dynamic systems using discrete-time models
LTI SISO DISCRETE TIME SYSTEMS
- State representation of discrete-time LTI SISO dynamic systems models
- Movement of the state and of the output
- Equilibrium
- Static gain
- Stability
- Equivalent representations
- Z-transformation
- Anti-transformation by recursion
- Transfer function and its properties
- Block diagrams
- Connections in series, parallel and feedback
- Stability of interconnected systems
- FIR systems, discrete integrators
CONTROL OF LTI SISO DISCRETE TIME SYSTEMS
- General scheme of the feedback control
- Control system requirements
- Reachability, controllability and observability
- Canonical form
- Assignment of the eigenvalues in closed loop
- Ragazzini method for the reference model project
STOCHASTIC PROCESSES
- Notions of estimation theory
- Stochastic processes
- AR, ARMA and ARMAX processes
- Prediction
- Identification of ARX processes
Online Resources
More information
The course is in Italian. Foreign students can ask the professor for material, books etc... in English. Materials to attend lectures and for personal study are available on the Moodle page.