BASIC CONTROL ENGINEERING

The course is one of the mandatory educational activities of the Degree Program in Engineering Physics, and it allows the student to acquire the fundamentals of the analysis of dynamic systems (models) and their stability, as well as of automatic control systems. The first part of the course provides the theoretical foundations and introduces the mathematical tools for modeling linear dynamic systems in the time domain and in the Laplace domain. The second part of the course, on the other hand, is dedicated to stability analysis through control theory. Some of the topics covered are multidisciplinary in nature, so the knowledge acquired is also useful for other courses taken by the student.

The main objective of the course is to provide students with the basic elements for the design of control systems, with particular reference to dynamic engineering models.

Knowledge and understanding
- Knoweldge about the basic principles of the functioning of the main components of a linear dynamic model
- Knoweldge about the basic principles of the operation of a feedback control system

Ability to apply knowledge and understanding
- Ability to perform a static / dynamic analysis of control systems for linear systems
- Ability to design control systems based on specific stability performances

Autonomy of judgment
- Ability to evaluate, among various possibilities, how to configure and design the structure of an automatic controller, based on the operating requirements imposed

Communication skills
- Ability to describe the main functions of a control system with technical and formal language

Learning skills
- Ability to use and interpret reference texts on dynamic and control systems

Having achieved the educational objectives of the previous Mathematics courses. In particular, the student should be familiar with the concepts and methods related to the study of differential equations, functions of complex variables and elements of linear algebra.

Introduction to the course and problems of interest for automation.
Modeling problems of dynamical systems: objectives of automatic control (examples in the engineering field); Derivation of linear and nonlinear state space models; Balance points and linearization around them; Block diagrams; Open-loop and closed-loop control systems and the relative advantages and disadvantages of each.
Analysis of linear systems: Dynamics of linear systems (transient and steady state); Principle of superposition of effects; Laplace transforms; Canonical signals and their transforms; Transfer functions; Bode plots; Frequency response; Stability of equilibrium points; Step response for first and second order systems and time-frequency relationship; Interconnections.
Requirements and design of control systems: stability, precision (steady-state error, speed and overshoots), sensitivity to disturbances, robustness; Analysis of the stability of control systems and stability criteria; PID controller design.
Notes on digital control: Discrete-time systems and signals, and discretization of systems and controllers; Notes on the choice of sampling frequency.

Notes on the use of programming languages (Matlab or Python) for the analysis of dynamic systems and for the design of control systems.

Bechhoefer, John. Control theory for physicists. Cambridge University Press, 2021.

Ferrante: “Appunti di Automatica per Ingegneria Biomedica”, Edizioni Progetto Padova, 2023.

In addition, lecture notes and exercises will be provided.

The achievement of the course objectives is assessed through a final written exam.

The final written exam consists of two parts:

1) Three exercises similar to those completed in class and assigned as homework.
2) A theoretical question on the topics covered during the lectures.

written

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

A fully successful exam (27-30/30) requires demonstrating a solid and extensive mastery of the concepts discussed during the lectures. An average grade (22-26/30) will result from a fairly comprehensive understanding of individual topics, but with limited interconnections between the subjects. A passing grade (18-21/30) will correspond to a minimal knowledge of the individual concepts.

Lectures, tutorials, and coding sessions.