ID:
21018
Dettaglio:
SSD: Automatics
Duration: 72
CFU: 9
Located in:
DALMINE
Url:
COMPUTER SCIENCE AND ENGINEERING - 21-270/PERCORSO COMUNE Year: 2
Approval Status:
Draft
Year:
2025
Overview
Date/time interval
Primo Semestre (15/09/2025 - 20/12/2025)
Syllabus
Course Objectives
At the end of the course the student has a basic knowledge of systems theory for the mathematical modeling of phenomena, machines and processes through linear models, both in continuous time and in discrete time and both in state variables and input / output.
He/she knows the tools for the analysis of linear systems both in time and frequency domains.
He/she knows the design methods of simple feedback controllers, including PID controllers.
He/she knows the methods for digitizing continuous time control laws.
The student is able to analyze linear continuous-time dynamical systems in state variables.
He/she is able to calculate the movement of a system and understand it in light of the properties of the state matrix.
He/she is able to do an equilibrium analysis of linear systems.
He/she is able to calculate the equilibrium of a non-linear system and to calculate an approximate linear tangent system.
He/she can calculate the Laplace transform and the Z transform of continuous and discrete signals.
He/she is able to calculate the transfer function of continuous and discrete linear systems.
He/she is able to manipulate complex systems by decomposing them into subsystems and solving block diagrams.
He/she is able to draw Bode diagrams and interpret them in the light of the frequency response theorem.
He/she is able to analyze the filtering action of dynamic systems.
He/she is able to analyze feedback systems and predict their behavior based only on information in open loop.
He/she is able to design feedback controllers for minimum phase systems and to tune a PID controller.
He/she is able to design digital FIR controllers and digitize analog controllers.
He/she knows the tools for the analysis of linear systems both in time and frequency domains.
He/she knows the design methods of simple feedback controllers, including PID controllers.
He/she knows the methods for digitizing continuous time control laws.
The student is able to analyze linear continuous-time dynamical systems in state variables.
He/she is able to calculate the movement of a system and understand it in light of the properties of the state matrix.
He/she is able to do an equilibrium analysis of linear systems.
He/she is able to calculate the equilibrium of a non-linear system and to calculate an approximate linear tangent system.
He/she can calculate the Laplace transform and the Z transform of continuous and discrete signals.
He/she is able to calculate the transfer function of continuous and discrete linear systems.
He/she is able to manipulate complex systems by decomposing them into subsystems and solving block diagrams.
He/she is able to draw Bode diagrams and interpret them in the light of the frequency response theorem.
He/she is able to analyze the filtering action of dynamic systems.
He/she is able to analyze feedback systems and predict their behavior based only on information in open loop.
He/she is able to design feedback controllers for minimum phase systems and to tune a PID controller.
He/she is able to design digital FIR controllers and digitize analog controllers.
Course Prerequisites
Basic linear algebra and matrix computation.
Complex numbers calculus.
Solving ordinary linear differential equations with constant parameters.
Complex numbers calculus.
Solving ordinary linear differential equations with constant parameters.
Teaching Methods
The educational path proposed to the student is the following:
1) Follow the lecture 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 following it.
2) Study the topics of the lesson with the help of the textbook, slides and personal notes.
3) Answer the questions related to the lesson prepared on Teams. 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
4) Follow the frontal 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 following the lecture.
5) Carry out the proposed exercises, available on Teams in a limited number and carefully selected. The purpose of the proposed exercises is to verify the level of understanding of the concepts presented in the lectures and the student's ability to use them.
6) Towards the end of the lessons the student is able to carry out some exam examples, proposed with their solution and chosen from the most representative and paradigmatic ones.
7) In parallel to this path, 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.
Some application examples are carried out in the field of industrial systems control. Educational seminars by industrial and academic researchers are usually given during the course.
Great importance is given to students' active participation in lessons, which is stimulated through continuous dialogue. Students can find the teacher at any time (preferably by appointment) by going to the teacher's office (Office 303 Building C).
1) Follow the lecture 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 following it.
2) Study the topics of the lesson with the help of the textbook, slides and personal notes.
3) Answer the questions related to the lesson prepared on Teams. 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
4) Follow the frontal 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 following the lecture.
5) Carry out the proposed exercises, available on Teams in a limited number and carefully selected. The purpose of the proposed exercises is to verify the level of understanding of the concepts presented in the lectures and the student's ability to use them.
6) Towards the end of the lessons the student is able to carry out some exam examples, proposed with their solution and chosen from the most representative and paradigmatic ones.
7) In parallel to this path, 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.
Some application examples are carried out in the field of industrial systems control. Educational seminars by industrial and academic researchers are usually given during the course.
Great importance is given to students' active participation in lessons, which is stimulated through continuous dialogue. Students can find the teacher at any time (preferably by appointment) by going to the teacher's office (Office 303 Building C).
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 1 or 2 theoretical questions. Among them there is always the design of a feedback controller and an exercise on digital control systems.
Each question assign from 5 to 8 points.
It usually consists of 5 or 6 questions: 3 or 4 exercises and 1 or 2 theoretical questions. Among them there is always the design of a feedback controller and an exercise on digital control systems.
Each question assign from 5 to 8 points.
Contents
(In brackets the references to the main textbook).
1. PART ONE
Introduction to Control Systems. Formulation of a control problem. Controlled variables, control variables and disturbances. Open loop control and closed loop control. Uncertainty. (Chapter 1: up to 1.4).
1.1 Continuous Systems Analysis in Time Domain (State Space - SS)
Definition of dynamical system. Input, output and state. Representation of a dynamical system using differential equations. Movement, trajectories, equilibrium. Lagrange formula. Unforced Movement and forced movement. Superposition Principle. Structural properties (examples). Eigenvalues. Routh Criterion. Linearization and stability of equilibrium for nonlinear systems. (Chapter 2: all except 2.4. Chapter 3: up to 3.5 included except 3.4.5).
1.2 Continuous Systems Analysis in Time Domain (Input / Output - IO)
Laplace transform. Transfer function: definition, calculation, properties. Poles, zeros and gain. Method of Heaviside for the Inverse Laplace transform. Block diagrams. Connections in series, parallel and feedback. Step Response of first and second order systems in time domain. Time constant. Natural frequency and damping coefficient. "Dominant" time constant. "Dominant" Pole approximation. (Appendix B: up to B.3 included. Chapter 4: Up to 4.4 except 4.2.5, 4.2.6. Chapter 5: up to 5.4. Chapter 6: 6.9).
Frequency response. (Chapter 6: 6.1, 6.2). Bode diagrams. Polar diagrams. (Chapter 6: 6.6, 6.7). Filtering. (Chapter 6: 6.8).
Time delay. (Sections 2.4, 4.2.6, 6.2.2, 6.6.3)
2. PART TWO
Introduction to control systems in closed loop. General scheme of a feedback control system. Requirements of the control system. (Chapter 1: 1.5. Chapter 9: up to 9.4 included).
2.1 Analysis of feedback systems
Stability. Nyquist criterion. Bode criterion. Robust stability. Phase margin and gain margin. (Chapter 9: 9.5, 9.6).
Frequency response of feedback systems. Speed ¿¿of response. Bandwidth. Static accuracy. Steady state error. (Chapter 10: all except 10.4.4, 10.6).
2.2 Controller Design
Design specifications. Design outline. Examples of design for minimum phase systems. (Chapter 11: up to 11.5 included except non-minimum phase systems).
Linear controllers proportional-integral-derivative (PID). Implementation of the PID controllers. Tuning parameters using rules of Ziegler and Nichols. (Chapter 14: 14.1, 14.2, 14.3.1, 14.3.2, 14.4.1 except assignment of gain and phase margins, 14.4.2 only method of tangent and rule of Ziegler and Nichols).
2.3 Discrete-time Systems
Introduction to discrete-time systems. Stability (criterion of eigenvalues). Linearization and stability of equilibrium for nonlinear systems. Z transform. Transfer function. Poles, zeros and gain. Inverse Z transform by long division or recursion. Impulse and step response. (Chapter 7: up to 7.6 included except 7.5.4, 7.5.5, 7.5.6 and 7.4.5 only diagonalizable matrix. Chapter 8: 8.1, 8.2, 8.3.5, 8.5. Appendix C: C.1, C .2, C.3).
Digital control schemes. Sampling and holding. Design criteria for digital controllers using discretization of analog controllers. (Chapter 17: 17.1, 17.2, Theorem 17.2, 17.6, 17.7).
1. PART ONE
Introduction to Control Systems. Formulation of a control problem. Controlled variables, control variables and disturbances. Open loop control and closed loop control. Uncertainty. (Chapter 1: up to 1.4).
1.1 Continuous Systems Analysis in Time Domain (State Space - SS)
Definition of dynamical system. Input, output and state. Representation of a dynamical system using differential equations. Movement, trajectories, equilibrium. Lagrange formula. Unforced Movement and forced movement. Superposition Principle. Structural properties (examples). Eigenvalues. Routh Criterion. Linearization and stability of equilibrium for nonlinear systems. (Chapter 2: all except 2.4. Chapter 3: up to 3.5 included except 3.4.5).
1.2 Continuous Systems Analysis in Time Domain (Input / Output - IO)
Laplace transform. Transfer function: definition, calculation, properties. Poles, zeros and gain. Method of Heaviside for the Inverse Laplace transform. Block diagrams. Connections in series, parallel and feedback. Step Response of first and second order systems in time domain. Time constant. Natural frequency and damping coefficient. "Dominant" time constant. "Dominant" Pole approximation. (Appendix B: up to B.3 included. Chapter 4: Up to 4.4 except 4.2.5, 4.2.6. Chapter 5: up to 5.4. Chapter 6: 6.9).
Frequency response. (Chapter 6: 6.1, 6.2). Bode diagrams. Polar diagrams. (Chapter 6: 6.6, 6.7). Filtering. (Chapter 6: 6.8).
Time delay. (Sections 2.4, 4.2.6, 6.2.2, 6.6.3)
2. PART TWO
Introduction to control systems in closed loop. General scheme of a feedback control system. Requirements of the control system. (Chapter 1: 1.5. Chapter 9: up to 9.4 included).
2.1 Analysis of feedback systems
Stability. Nyquist criterion. Bode criterion. Robust stability. Phase margin and gain margin. (Chapter 9: 9.5, 9.6).
Frequency response of feedback systems. Speed ¿¿of response. Bandwidth. Static accuracy. Steady state error. (Chapter 10: all except 10.4.4, 10.6).
2.2 Controller Design
Design specifications. Design outline. Examples of design for minimum phase systems. (Chapter 11: up to 11.5 included except non-minimum phase systems).
Linear controllers proportional-integral-derivative (PID). Implementation of the PID controllers. Tuning parameters using rules of Ziegler and Nichols. (Chapter 14: 14.1, 14.2, 14.3.1, 14.3.2, 14.4.1 except assignment of gain and phase margins, 14.4.2 only method of tangent and rule of Ziegler and Nichols).
2.3 Discrete-time Systems
Introduction to discrete-time systems. Stability (criterion of eigenvalues). Linearization and stability of equilibrium for nonlinear systems. Z transform. Transfer function. Poles, zeros and gain. Inverse Z transform by long division or recursion. Impulse and step response. (Chapter 7: up to 7.6 included except 7.5.4, 7.5.5, 7.5.6 and 7.4.5 only diagonalizable matrix. Chapter 8: 8.1, 8.2, 8.3.5, 8.5. Appendix C: C.1, C .2, C.3).
Digital control schemes. Sampling and holding. Design criteria for digital controllers using discretization of analog controllers. (Chapter 17: 17.1, 17.2, Theorem 17.2, 17.6, 17.7).
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 Teams group.
Microsoft Teams group Fondamenti di Automatica
https://teams.microsoft.com/l/team/19%3atY3RoV7Efj55EmTge6Y5Hgf6goU6mnvX_C407-Bkc4g1%40thread.tacv2/conversations?groupId=c1d59365-c68e-4e70-8606-067709b8ee1e&tenantId=4f0132f7-dd79-424c-9089-b22764c40ebd
In case of public authority actions for the containment of epidemiological emergencies, teaching modality could undergo changes compared to what is stated in the syllabus to make the course and exams in
in line with the sanitary limitations.
Foreign students can ask the professor for material, books etc... in English.
Materials to attend lectures and for personal study are available on the Teams group.
Microsoft Teams group Fondamenti di Automatica
https://teams.microsoft.com/l/team/19%3atY3RoV7Efj55EmTge6Y5Hgf6goU6mnvX_C407-Bkc4g1%40thread.tacv2/conversations?groupId=c1d59365-c68e-4e70-8606-067709b8ee1e&tenantId=4f0132f7-dd79-424c-9089-b22764c40ebd
In case of public authority actions for the containment of epidemiological emergencies, teaching modality could undergo changes compared to what is stated in the syllabus to make the course and exams in
in line with the sanitary limitations.
Degrees
Degrees
COMPUTER SCIENCE AND ENGINEERING - 21-270
Bachelor's Degree
3 years
No Results Found
People
People (2)
No Results Found
Other
Main module
CONTROL SYSTEMS