You are here: Home » Study Plan » Subject


Subject: AUTOMATIC CONTROLS (A.A. 2020/2021)


Course year 1
Teaching units Unit Automatic Controls
Related or Additional Studies (lesson)
  • TAF: Supplementary compulsory subjects SSD: ING-INF/04 CFU: 6
Teachers: Paolo FALCONE
Exam type written
Evaluation final vote
Teaching language inglese
Contents download pdf download




The course aims at providing the following fundamental system analysis and control design tools: 1) describe and analyze linear feedback dynamical systems both in time and in frequency domains; 2) design simple regulators starting from specifications which define the desired static and dynamical behavior of the controlled systems; 3) provide a few examples of controlled system in the automotive field.

Admission requirements

Compulsory prerequisites: Calculus 1
Recommended prerequisites: Calculus 2

In particular: Complex numbers. Differential equations (basic elements).

Course contents

1. Basic Concepts
Systems and mathematical models. Block schemes. Mason's formula. Feed-forward control and feedback control. Dynamic models of physical systems.
2. Analysis of linear dynamic systems
Differential equations. Laplace transform and its properties. Partial-fraction decomposition. Impulse response. Analysis of the first and second order systems. Systems with dominant poles.

3. Frequency-domain analysis
The frequency response. Bode plots. Frequency response of systems with dominant poles. Nyquist plots. Rules for the qualitative drawing of the Bode and di Nyquist plots.

4. Stability of the closed-loop systems
Stability of linear dynamical systems. Routh criterion. General properties of the closed-loop systems. Sensitivity to parameter variations and disturbances. Steady-state errors. Nyquist criterion. Gain and phase margins. Stability of linear systems with finite time delays. Resonant frequency, resonant peak and bandwidth.

5. Root-Locus technique
Definition and properties of the Root-Loci. Rules for the graphical drawing of the Root-Loci. Root-Loci contour.

6. Design of lead and lag compensators
Design specifications. Lead, Lag and Lead-Lag compensators. Inversion formulas. Design of a lead/lag compensator on the Nyquist and Nichols planes. PID standard regulators.

7. Feedback nonlinear systems (basic elements)
Stability of nonlinear systems. Operating points. Circle criterion. Describing function method (basic elements).

8. Digital control
Difference equations. Z-transform. Inverse Z-transform. Mapping between S-plane and Z-plane. Compensator design via discretization.

Teaching methods

Lectures with slides and exercises sessions.

Assessment methods

Written and oral (upon student's request) examination on theoretical topics of the course.

Learning outcomes

Knowledge and understanding: Through classroom lessons the students learn the main methods of time and frequency analysis of linear dynamic systems and the synthesis of simple lead and lag networks.

Applying knowledge and understanding: The student is able to analyze the time and frequency dynamics of physical systems described by linear transfer functions.

Autonomy of judgment: The methods of analysis and the control techniques studied provide students with the skill of analyzing and controlling linear physical systems.

Communication skills: The theoretical lessons provide students with the ability to express the learned concepts with an appropriate language and to properly discuss the topics of the course.

Learning skills: the activities described allow the student to acquire the methodological tools to continue their studies and to be able to arrange their own update.


Testi di riferimento:
- - P. Bolzern, R. Scattolini, N. Schiavoni, “Fondamenti di Controlli Automatici”, McGraw-Hill Libri Italia, Milano, 1998.
- G.F. Franklin, J.D. Powell, A. Emami-Naeini, “Feedback Control of Dynamic Systems”, Third Edition, Addison-Wesley, 1994.
- Slides delle lezioni in aula.
- Zanasi Roberto, "Esercizi di Controlli Automatici", Esculapio, Bologna, 2011.

Testi aggiuntivi
- R.C. Dorf, R.H. Bishop, “Modern Control Systems”, Eighth Edition, Addison-Wesley, 1998.
- B.C. Kuo, “Automatic Control Systems”, Seventh Edition, Prentice Hall, 1995.
- C.L. Phillips, R.D. Harbor, “Feed Control Systems”, Fourth Edition, Prentice Hall International, 2000.
- G.F. Franklin, J.D. Powell, M. Workman, “Digital Control of Dynamic Systems”, Third Edition, Addison-Wesley, 1998.