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Informazioni aggiuntive

Course Curriculum CFU Length(h)


According to the scope of the undergraduate course in Electrical, Electronic and Computer Engineering, the aim of the course is to give the basic knowledge, capacity and competence on automatic control, as detailed in the following:

* Knowledge and Understanding:
students will know how dynamical systems can be represented and the tools to verify their properties while understanding the relevant physical meaning. They will know the components of a control systems and they will be able to evaluate the performance of each component and of the overall system. They will know the basics design approaches for single loop control systems while understanding their application contests.

* Applying knowledge and Understanding:
students will able to evaluate the performance of linear dynamical systems on the base of their mathematical and graphical representation and the overall performance of a feedback control system on the basis of its components characteritics. They wiil be able to design the controller's transfer function to satisfy prescribed closed loop performance by means of the most effective design approach.

* Making judgements:
students will be able to carry on a critical analysis of the system performance both for open-loop and closed loop systems in order to check the effectiveness of the control design to improve it, even by means of approximate methods.

* Communication skills:
students will be able to clearly present technical and scientifical statements in the field of automatic control systems and generally in the field of the electrical and information enginnering.

* Learning skills:
students will be able to get the information from different sources and to integrate them in order to achieve a comprehensive understanding of the aspects related to a control system analysis and design problem.


For an effective approach to the study of system and control system theory, students should have the following skills.

Basics of linear algebra. Trigonometirc, esponential and logarithmic functions and their properties. Ordinary linear differential equations. Integrals. Complex numbers. Polynomials. Fourier transforms. Phisic principia of the solid body and of electrical systems.

Algebraic, differential calculus. Analysis and representation of functions depending on one or more variables. Variable transformations.

To be able to apply the methods of algebra, differential calculus and function analysis to represent physical systems and evaluate their characteristics.

It is required to have achieved the credits related to the Calculus 1 and Physics 1 courses. It is strongly recommended to have achieved the credits related to the Math and Physics 2 courses and to carefully attend the lectures of the Applied math and Electrotecnics.



1. Introduction (lecture: 2 h)
Automatic control and systems.

2. Systems, models and their properties (lecture: 6 h, ex: 2 h)
Input-Output (IU) and State-Variable (SV)models. Exemples. Properties.

3. Analysis in the time domain of IU models (lecture: 7 h, ex: 2 h)
IU models and analysis problems. Homogeneous equation and modes. Free evolution. Signals and evolutions. Respons to an impulse. Foced evolution and Duhamel integral.

4. Analysis in the t domain of VS models (lecture: 6 h, ex: 2 h)
Prob. of analysis. State transition matrix and Sylvester approach. Lagrange formula. Equivalence transformations. Diagonalization. Jordan form.

5. Analysis in the s domain (lecture: 12 h, ex: 4 h)
Laplace's transform and its inverse. Fundamental properties. Analysis of IU and SV models. Trasfer function and matrix. Forced evolution.

6. Analysis in the frequency domain (lecture: 6 h, ex: 2 h)
Armonic response. Response to signals with Fourier series. Bode diagrams. Characteristic parameters of the armonic response and filtering actions.

7. Stability (lecture: 4 h, ex: 2 h)
BIBO stability. Lyapunov stability. Linear and time invariant systems. Routh criterion.

8. Laboratory (3 h)
MATLAB and control system toolbox.


9. Introduction (lecture: 1h, test: 1h)
Presentation of the course topic, characteristics and methods. Initial self-assessment and discussion.

10. Control system structure (lectures: 7h, exercise: 2h)
Components of a control system. Examples of feedback control systems from pratics. Approximations in the analitic model of a dynamical system: the coil and D.C motor examples. Dynamical systems with dominant modes. Blocks algebra. Load effects in connected systems. Tranfer function of connected systems.

11. Stability of feedback systems (lectures: 8h, exercise: 4h)
Nyquist diagram and criterion. Phase and gain margins. Roots locus. Modal analysis of feedback systems via roots locus.

12. Requirements in control systems (lectures: 10h, exercise: 4h)
Physical meaning of control system requirements. Sensitivity functions with respect to external disturbances and parameters variations. Tracking error. Asymptotic tracking error with respect to canonical inputs and disturbances. Tracking systems type. Transient behaviour and closed loop characteristics. Relationships between step and frequency response. Relationships between open-loop and closed-loop characteristics.

13. S-plane design (lectures: 4h, exercise: 2h)
Closed loop requirements representation in the s-plane. Control design by means of zero-pole compensation. Controller design for non-minimum phase systems. Influence of additionals poles and zeroes on the roots locus.

14. Frequency response design (lectures: 5h; exercise: 4h)
Harmonic respons diagram via test. Closed loop requirements in the frequency response. Lead, lag, lead-lag compensators. Normalized diagrams for the lead compensator. Nichols chart. Feedback requirements verification by Nichols chart. Controller design via passive and active electrical networks.

15. PID controllers (lectures: 4h; exercises:4h)
P, PI and PID controllers. parallel and serie configuration of a PID. PID tuning via open-loop and closed-loop Ziegler and Nichols methods. PID controllers as approximate realization of the lead-lag compensator.

Teaching Methods

The course is divided into two main modules (60 hours each one): System theory in the fall semester and Automatic control in the spring semester. The fall semester modul considers the analysis of dynamical systems as stand-alone units while the second deals with closed-loop systems analysis and design.

The fall semster modul includes 43 h devoted to theoretical explanations, 14 h of exercises, and 3 hours of laboratory to introduce MATLAB.

The spring semester modul includes:
* initial test for self-assessment of the base knowledge and expertise (1 hour);
* lectures with the support of a digital presenter for the real-time video projection of the mathematical developments and graphical representation which are useful for teaching and learning (39 hours);
* guided exercises with individual and/or groups activities with the support of the teacher and tutors. Part of these exercises are carried on by means of the Matlab Control System Toolbox in a LIDIA''''s laboratory or in the classroom.

In both modules during lectures students are actively involved by prompts from the teacher regarding the interpretation of the analytic results, the critical analysis of applicative aspects, and relationships with other topics.

Additional tutorial activities will be organised as follow up of the continuous checking of the exercise results and on students' request.

Lectures could be integrated by on-line strategies to improve their effectiveness and inclusivity.

Verification of learning

The final evaluation consists in an oral exam during which the students should show the knowledge of the basic techniques and methods of linear system theory, the ability of carrying on the critical analysis of a feedback control systems and its controller design with respect of required closed loop performance.
To pass the exam the student has to demonstrate an appropriate and correct knowledge of the methods for the analysis of closed-loop systems and of the methods for the design of the relevant control law. He has also to show and adequate expertise in applying the above knowledge on a specific case and the ability of identifying the general aspects of the problem as well.
Furthermore, the student has to show adequate skills in speaking and using a technical language as well as a sufficient synthesis and critical analysis ability.
The final marks is derived as a weighted sum of the evaluation on the single questions and on the presentation.

Students who are attending the lectures are admitted to mid-term evaluations which are scheduled for the System theory module. Such evaluations include written tests on the analysis of dynamical systems described by both a state-space representation and a transfer function. The tests verifies the student's knowledge of the basic methodologies and techniques used for the analysis of linear dynamical systems. The mark will be given as a weighted evaluation of the results in each question of the tests.

Students who pass the mid-term evaluation are not required to answer to specific quaesita on system theory topics; nevertheless, during the final oral examination, the student has to demonstrate an adequate knowledge of the methods for the system analysis achieved during the first module.

The mark achieved in the mid-term evaluation, if passed, contributes to the final mark with a decreasing weight depending on the time left between the last September exams session and the final oral examination.

Students can always ask to do the full final oral exam whatever the mid-term evaluation is.


Alessandro GIUA, Carla SEATZU, Analisi dei sistemi dinamici- 2a edizione, Springer-Verlag Italia, MIlano, 2009.

Norman S. Nise, Controlli automatici - a cura di Paolo Pugliese, Edizioni Città studi, De Agostini Scuola, Novara, 2013.

Altri testi utilizzabili / Other references

Paolo Bolzern, Riccardo Scattolini, Nicola Schiavoni, Fondamenti di controlli automatici- 4ª edizione, McGraw-Hill, Milano, 2015.

Giovanni Marro, Controlli automatici - 4ª ed., Zanichelli, Bologna, 1997.

J.J. D’Azzo, C.H. Houpis, Linear control systems analysis & design – Conventional and modern (3rd edition), McGraw-Hill, 1988.

More Information

Additional material in the teachers' web site includes:
* Detailed program of the Automatic control module with references to the suggested books;
* Class exercises with solutions for the Automatic control module;
* Control problems (without the solution);
* Semi-logarithmic grid for Bode diagrams;
* Nichols chart;
* Normalised Bode diagrams of the lead compensator;
* Diagrams of the approximate relationships between the phase margin and closed loop performance;
* Tutorials;
* Slides and notes about the lectures on Automatic control.

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