Teaching code

4S02785

Credits

6

Coordinator

Francesco Visentin

Language

Italian

Scientific Disciplinary Sector (SSD)

ING-INF/04 - SYSTEMS AND CONTROL ENGINEERING

Courses Single

Authorized

Moodle Seminars 0

The teaching is organized as follows:

Learning objectives

The course objective is to give students the mathematical tools required for the analysis and modeling of linear, time-invariant (LTI) systems, and of the input/output signals to an LTI system. The model will allow students to study the main system properties and to address the general concepts of controller and filters to perform simple control actions on the dynamic system and filter operations on the input/output signals. The mathematical tools will be based on analysis methods in the time domain, as well as of the complex variables s, z and the frequency of the input/output signals. Analysis and synthesis will be carried out both for continuous and discrete time systems and signals. The theoretical concepts acquired during the course will be consolidated with exercise sessions addressing the solution of basic problems with analytical approach and with numerical simulations.

Prerequisites and basic notions

The course requires knowledge in Mathematical Analysis I and II, Physics I and II, Linear Algebra and Geometry, Fundamentals of Computer Science. Notions of MATLAB programming are also required.

Program

1. Review: complex numbers, functions of complex variables, series of complex powers, convergence, Euler's formula
2. Distributions: impulse, step, ramp. Sampling and reproducibility. Sinusoidal exponential functions, time translation. Discrete signals
3. Continuous time systems. Causal LTI systems. Stability.
4. Characteristic equation of a system, elementary modes, convergence.
5. Convolution, impulsive response, forced response, BIBO stability, asymptotic stability
6. Frequency response
7. The Laplace transform. Convergence region. Properties
8. Free response and forced response in the complex plane, transfer function, zeros and poles, stability.
9. The Laplace's antitrasform, poles, residues.
10. The Fourier series for periodic signals. Frequency, pulsation, linear combination of periodic signals, synthesis equation, analysis equation. The energy and power of a signal, the discrete spectrum.
11. The Fourier transform. Conditions of existence, discontinuities.
12. Convolution and modulation. Spectrum.
13. Fourier trasform of the ideal sampling train, replication and sampling, reconstruction filters, Nyquist frequency, Shannon forumula.
14. Bode diagrams
15. Block diagrams
16. Discrete-time LTI systems. ARMA model. Impulsive response, forced response.
16. z trasform. Properties
17. The antitransformed z. Frequency response. Discrete Fourier transform

Didactic methods

The course will consist of lectures in the classroom, along with shared slides, notes and possible additional material that could be useful to deepen the topics, and practical exercises at the computer and in the classroom

Learning assessment procedures

The exam consists of two parts, a written test and an oral test. The written test consists of exercises on the topics covered in teaching aimed at assessing both the level of learning and understanding of the theoretical foundations studied during the course and the ability to put them into practice, critically, to solve engineering problems. The oral exam will deal with the theoretical insights of the course.

Evaluation criteria

At the end of the course, the student must demonstrate that:
1. have fully understood the main issues inherent to systems and signals, both in a continuous and discrete context, e
the related terminology;
2. have a critical view of the issues addressed during the course and the results obtained from the application of specific methods;
3. knowing how to apply the knowledge acquired to solve in an appropriate way certain engineering problems of varying degrees of complexity;
Both parts (written and oral) will be carefully evaluated, thus giving equal importance to the correctness and effectiveness of the solutions adopted in the phase of solving concrete problems, as well as to the understanding of the theoretical concepts relating to systems and signals.
As regards the composition of the final grade, this will be given by the sum of the evaluations of the theory part (2/3) and the oral exam (1/3). The exam is considered passed if in each of the two parts a score greater than or equal to 18 is achieved. Each evaluation remains valid for the entire current academic year.

Criteria for the composition of the final grade

The composition of the final grade, this will be given by the sum of the evaluations of the theory part (2/3) and the oral exam (1/3). The exam is considered passed if in each of the two parts a score greater than or equal to 18 is achieved. Each evaluation remains valid for the entire current academic year.

Exam language

italiano