Goal of the course is to provide students with basic knowledge on dynamic systems analysis and on simple control system design for linear time invariant continuous time systems described in terms of state variables and transfer function. Attention is mainly focused on general methodologies that allow to deal with dynamic systems whose dynamic equations are provided. In the first part of the course systems described in state variables are considered. For such systems stability controllability and observability properties are defined and analyzed. State feedback and state observer are introduced as well.
In the second part of the course feedback control design for SISO systems with no poles in the right hand plane is considered.

Ability to study linear dynamical systems described in state variable form analyzing stability, controllability, and observability.
Ability to design simple feedback control systems for SISO systems.

Basic knowledge of analysis, physics and electrical engineering.

- Introduction
- Laplace transform
- Dynamic system description in state variable form and in transfer function form.
- Time response of dynamic systems. The transition matrix.
- Stability for linear dynamic systems
- Controllability and observability of dynamic systems and relevant canonic forms.
- State feedback.
- State observer.
- Open loop and closed loop control.
- Bode and Nyquist plots. Stability of closed loop systems: the Routh-Hurwitz criterion and the Nyquist criterion.
- Transient response and steady state response of dynamic systems. Time and frequency domain specifications. Attenuation of additive and parametric disturbances.
- Feedback control design based on the Bode plot of the open loop transfer function.

Lectures and tutorials are not rigidly separated. Tutorial cover exercises on the developed theory as well as the development of more practical parts of the program. There is no division in groups for activities in class.
Part of the study will be conducted in the LAIB to have access to multimedia material available through the web and to conduct lab sessions. Lab tutorials should enable to get basic knowledge of a modern program (MATLAB) for analysis and design of control systems. With the aid of such program students can carry on exercises similar to those developed in class lectures and tutorials, but they can also work out more complex problems that could hardly be developed without the aid of a computer.
Lab tutorials will cover:
Study of the time response of dynamic systems,
Analysis of controllability and observability as well as state feedback.
Drawing of Bode and Nyquist plots for different transfer functions.
Comparison of open loop and closed loop transfer functions.
Design of feedback compensators

Copies of the transparences used for conducting lectures and tutorials are available on the web site of Politecnico (Portale della didattica) at the page of the course. This material can be integrated with notes of the student.
To prepare the course the instructor mainly referred to the following texts:
1. D. Luenberger, Linear dynamic systems J. Willey & Sons, New York.
2. E. Rohrs, J. L. Melsa, D. G. Shultz Linear control systems, Mc Graw Hill, New York.
Those students who are interested in using a text can refer to:
1. P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici, McGraw-Hill
2. K. Ogata, Modern control engineering, Prentice-Hall, London.
3. R. C. Dorf, R. H. Bishop, Modern control systems, Addison-Wesley Reading, Ma.
For further study students can refer to:
1. N. S. Nise, Control systems engineering, The Benjamin/Cummings Publishing Co., Redwood City, CA.
2. G. F. Franklin, J. D. Powel, A. Emami-Naeini, Feedback control of dynamic systems, Addison-Wesley Reading, Ma.
3. B. C. Kuo, Automatic control systems, Prentice-Hall, London.
4. J. J. D'azzo, C. H. Houpis, Feedback control system analysis & synthesis, Mc Graw Hill, New York.
A simple popular introductory text on the problems covered by the course is:
R. Calimani, A. Lepschy, Feedback. Guida ai cicli di retroazione: dal controllo automatico al controllo biologico, Garzanti (Strumenti di studio).

- The exam consists in a 3 hour test conducted in the Lab with Matlab available.
- The exam consists of two exercises, one on the design of feedback compensators and the other on the analysis of dynamic systems described in state variable form.
- According to the law the exam grade is recorded even if a student withdraws. It is therefore not allowed to reject the grade. However the student can declare, at the time in which she/he hands over her/his exam book, which is the minimum grade she/he would like to have, so that, in case she/he does not reach that grade she/he will be considered as withdrawn.
During the exam it is not allowed do go out from the lab beside in the case in which one withdraws or has completed the test. Students that cannot stand with this regulation for medical reasons should contact the instructor in advance. Last minute requirements will not be considered.
- During the exam students can have on the desk only pencils, pens and drawing tools and white sheets. Any other material is banned (telephones, books, bags, cloths etc.) and should be deposited according to the instructions that will be given.
- During the exams it is not allowed to use any text book (or other book) notes etc., beside one A4 sheet on which the student can report any note she/he considers useful with the exception of exercises partly or totally solved and coded answers to specific exercises. The sheet should be hand written and not photocopied; it is strictly personal and should report name, surname and Identification number of the student. It is also allowed a second A4 sheet with the Laplace transforms and transformation rules as well as a third sheet with the universal plots and the Nichols charts.
- During the exam in the LAIB students are not allowed to bring in any calculator since they can use the PC in the lab.
- No material on electronic support (diskettes, USB keys etc.) is allowed in or out from the class/lab.