# Systems and Signals (2007/2008)

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Course code
4S00045
Credits
7
Coordinator
Paolo Fiorini
Other available courses
Teaching is organised as follows:
Laboratorio 2 ING-INF/04-SYSTEMS AND CONTROL ENGINEERING 3° Q Debora Botturi
Teoria 5 ING-INF/04-SYSTEMS AND CONTROL ENGINEERING 3° Q Paolo Fiorini

#### Learning outcomes

Module: Teoria
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The objective of the course is to give students the mathmatical foundation to model, analyse and simulate, simple dynamical systems. The first part of the course deals with the introduction of transforms, which are then used to represent the model of a dynamic system in a domain different from the original time domain. The second part of the course aims at presenting the main methods for the analysis of the mathematical models of dynamic systems, and to study their main properties. The main concept that will be studied is stability. Stability analysis will allow student to make useful connections between the mathematical formalism and the physical behaviour of the dynamical systems, which will be the subject of the following courses.

Module: Laboratorio
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The objective of the course is to give to the students the possibility to translate in simulation and practice the theory concepts. Moreover the students will apply the knowledge from the mathematics and physics courses to dynamic system modeling.

#### Syllabus

Module: Teoria
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* Introduction: general structure of a dynamical system
* General properties of input/output maps and their representaiton with the convolution integral, and differential equations
* The Laplace Transform and its applications
* The Fourier Transofrm and its applications
* The Zeta Transform and its applications
* Bode diagrams
* Input/output stability of linear systems
* Introduction to the characterization and analysis of stability
* Discrete time systems
* Stability analysis in the discrete time domain

Module: Laboratorio
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* Introduction to basic concepts (mass, spring, dumper, Newton laws)
* Mechanical Systems (translational and rotational)
* Mathematical Models: Input-Output models
* Analytical solution of system equations
* Numerical solution
* Dynamic system simulation with Matlab and Simulink
* Electrical System
* Case Study

#### Assessment methods and criteria

Module: Teoria
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The exam consists of two theory tests and a laboratory test. The theory tests are a midterm and a final, whreas the laboratory test is only done at the end of the period. The theory part consists of a closed book test with exercises and theory questions. The laboratory test requires the writing of differential equations of a simple system and their solution using MatLab. the average of the two test, weighted by the credits of each Module is the final grade of the course. The student is entitled to receive an oral examination which is decided on a case by case basis.

Module: Laboratorio
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The laboratory exam is an exercise that summarize all the points of the course program.