Course objectives

The course aims to illustrate the fundamentals of systems and control theory and the main techniques of analysis and design of control systems. To this aim, after exemplifying some major problems that this framework proposes to solve, the basic methodological tools are presented. The ultimate goal is to enable students to analyze simple dynamic systems and to set up and solve simple design problems of automatic control systems.

Course plan

1. Introduction.
1.1. The control problem.
1.2. Open and closed loop control.
1.3. Instrumentation (notes).
2. Dynamic systems
2.1. Definition of dynamic system.
2.2. Examples of dynamic systems. Classification of dynamical systems. Distributed parameter systems (elements).
2.3. Motion. Free and forced motion. Principle of superposition. Motion calculations for continuous time linear systems. Motion calculations for discret time systems.
2.4. Linearization.
3. Signals and transforms.
3.1. Recalls of signal theory.
3.2. Laplace transform.
3.3. Heaviside method.
3.4. Z transform
4. Transfer function.
4.1. Transfer function for continuous-time systems. Equilibrium and gain.
4.2. Transfer function for discrete-time systems. Equilibrium and gain.
5. Stability.
5.1. Stability of equilibrium.
5.2. Linearization and stability.
6. Block diagrams.
7. Response to canonical signals.
7.1. Step response of first and second order systems.
8. Frequency response.
8.1. Bode plots. Asymptotic diagrams of magnitude and phase.
8.2. Dynamical systems as filters.
8.3. Polar plots.
9. Formulation of the control problem.
9.1. Nyquist criterion.
9.2. Gain and phase margin.
9.3. Bode criterion.
9.4. Dynamic analysis.
9.5. Static analysis.
9.6. Specifications assignment.
10. Sythesis of the regulator
10.1. Sythesis of the regulator.
10.2. PID controllers
11. Digital control
11.1. Sampling
11.2. Digital implementation of analog controllers.
12 Control of servomechanisms 
12.1 Current control.
12.2 P/PI control.
12.3 Model of compliant joints.
12.4 Position control of compliant joints.

Other informations

Teacher
Prof. FERRETTI Gianni
Tel. 02 2399 3682 or 0372 567745 - E-mail: gianni.ferretti@polimi.it
Course web site
https://beep.metid.polimi.it/

The evaluation will be written.