Goals of this course are to provide basic tools for modelling and analyzing dynamic systems and to address fundamentals of feedback control design.

The student shall acquire the following knowledge and develop the following abilities:
- Knowledge of the concept of dynamic system and of its main mathematical representations (input-state-output equations, transfer function)
- Skill in building mathematical models of linear and nonlinear dynamic systems
- Skill in analytically computing the time evolution of the states and the output of linear dynamic systems
- Skill in evaluating the behaviour of dynamic systems through numeric simulation
- Knowledge of (internal, external) stability properties and structural properties (reachability, observability) of dynamic systems
- Skill in analyzing the stability properties and the structural properties of dynamic systems
- Skill in designing a dynamic regulator
- Knowledge of the concept of feedback control of a dynamic system
- Knowledge of the main performance requirements of feedback control systems
- Knowledge of the main feedback system analysis techniques based on sinusoidal tools to study stability and performances of feedback control systems
- Skill in analyzing stability and performances of feedback control systems
- Knowledge of the design techniques of feedback controllers based on lead and lag functions
- Skill in designing feedback controllers for single input single output systems through lead and lag functions
- Knowledge of industrial controllers (PID) and their design techniques
- Knowledge of sampled data control systems and realization through digital filters
- Skill in designing sampled data control systems
- Skill in evaluating the behaviour and the performances of controlled systems through numerical simulation

The following knowledge is essential: differential and integral calculus of vector valued real functions, basic concepts of physics (mechanics, electric circuits and thermodynamics), complex numbers, complex functions, Laplace transform, real rational functions, linear algebra and basic skill of MATLAB.

Course topics and relative devoted time:
- Introduction to dynamic systems. Modelling of linear and nonlinear dynamic systems in different fields (electrical, mechanical, electromechanical and thermal) and their mathematical representations through input-state-output equations or transfer function (15 hours)
- Solution of state and output equations, modal analysis and (internal, external) stability analysis of linear dynamic systems, in continuous or discrete time domain (15 hours)
- Linearization of nonlinear dynamic systems and local stability analysis in a neighbourhood of an operational point (4 hours)
- Analysis of structural properties (reachability, observability) of linear dynamic systems. Design of a static state feedback; design of an asymptotic state observer; design of a dynamic regulator through estimated state feedback (11 hours)
- Step response analysis of first and second order linear dynamic systems. Steady-state response of linear dynamic systems (5 hours)
- Introduction to output feedback control. Block diagrams and block algebra rules (3 hours)
- Use of MATLAB and Simulink to simulate feedback control systems (3 hours)
- Bode, polar, Nyquist and Nichols diagrams. Nyquist stability criterion. Stability margins (12 hours)
- Feedback system response to a polynomial reference; steady-state tracking error, disturbance attenuation and rejection (8 hours)
- Feedback system performance analysis: transient and steady state performances (4 hours)
- Control design for continuous-time linear dynamic systems by means of sinusoidal tools, using lead and lag functions (12 hours)
- Analysis and design of sampled data control systems and digital filter synthesis. Industrial controllers: PID (8 hours)

Exercise sessions are focused on the development of both academic and applicative examples. Students are not split in groups.
Some other sessions (15 hours) are carried out in computer laboratories and are focused on analysis, simulation and control of real-world dynamic systems (magnetic levitator, electric motor), on control system design using estimated state feedback, on stability analysis of feedback dynamic systems, and on controller design to meet given performances, using MATLAB tools (Control system toolbox, Simulink). Students are split in groups in the laboratories.

The following textbooks have been mainly addressed in the organization of the course:
- P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di Controlli Automatici, 3a edizione, McGraw-Hill, Milano, 2008 (in Italian)
- G. Calafiore, Elementi di Automatica, CLUT, Torino, 2004 (in Italian)
- G. Calafiore, Appunti di controlli automatici, CLUT, Torino, 2006 (in Italian)
- R. C. Dorf, R. H. Bishop, Modern Control Systems, XII edizione, Pearson Education, Upper Saddle River (U.S.A.), 2011
On the course web page, teaching material is available about the use of MATLAB and about single specific issues dealt during the course, mainly taken from the following DVDs:
- "Fondamenti di Automatica" (in Italian, edited by proff. M. Canale and M. Taragna), available on-line at the address http://corsiadistanza.polito.it/on-line/FdA/index.htm
- "Controlli Automatici" (in Italian, edited by proff. C. Greco and M. Indri), available on-line at the address http://corsiadistanza.polito.it/on-line/Controlli_automatici/index.htm

The final assessment consists of a written examination in the computer laboratory, composed of two parts whose duration is one hour and half each.
In the first part, the candidate has to answer ten questions proposed with "multiple choice" answers, without any computer help; in the overall grade computation, any wrong answer is worth a negative score as penalty. In order to participate in the second part of the final, the candidate has to correctly answer to a minimum number of questions specified at the beginning of the test.
The second part is made of a controller design practice (with the help of MATLAB/Simulink) and a brief exercise on polar and Nyquist plots, on closed-loop stability analysis or on PID controller design.