Mechanical engineering
Study-unit Code
In all curricula
Mario Luca Fravolini
  • Mario Luca Fravolini
  • 54 ore - Mario Luca Fravolini
Course Regulation
Coorte 2020
Learning activities
Attività formative affini o integrative
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
• Model of real systems
• Analysis of linear systems
• Controlled systems
• Analisi of feedback control systems
• Root Locus
• Specifications
Reference texts

P.Bolzern, R. Scattolini, N. Schiavoni.
Fondamenti di controlli automatici.
4a ed. McGraw-Hill Education, 2015.
Biblioteca ingegneria: ING 731-123.
Educational objectives
The aim of the course is to provide basic notions on system analysis and feedback control design for linear time-invariant continuos-time systems.
In particular, at the end of the course the student should have:
a) knowledge of control oriented modeling techniques of mechanical, thermal and electrical systems;
b) knowledge of the basic methods for system analysis;
c) knowlegde of the basic methods for feedback control system design;
d) ability of designing control system architectures.
e) ability of using software tools for analysis, design and simulation of dynamic systems.
Matematica I and II courses (derivatives, integrals, ordinary differential equations).
Fisica generale.
Elettrotecnica (electric circuits, dc motor).
Teaching methods
Standard lectures and exercises in classroom.
Other information
Learning verification modality

The examination consists of a written and an oral test.
The written test duration is 3 hours and consists of 2 exercises and an open question.
The exercises deal with continuous time control systems analysis and design.
The open question requires the schematic illustration of a topic discussed during the course.
The aim of the written test is to evaluate the ability of applying the different analysis and design methods and the ability of expose the results in a clear and concise manner.

The oral exam, typically, takes place some days following the written text.
The aim of the oral test is to evaluate the understanding of the different arguments and the ability of expose them in a clear and rigorous manner.
Extended program

1) Modeling.
Modeling of continuous time dynamical systems (mechanical, thermal and electrical)
Input-output models. Linearization.
2) Linear systems analysis.
Laplace transform for systems representation and analysis. Natural modes of linear systems.
Step response of first and second order systems.
Harmonic response, Bode diagrams, Nyquist diagram.
3) Control systems architectures.
Feedforward, feedback and disturbance compensation schemes.
Sensitivity, disturbance rejection, process and measurement noise.
4) Feedback control systems analysis.
Stability of feedback control systems: Routh method, Nyquist criterion. Stability margins.
5) Feedback control system design.
Steady state error for polynomial reference signals. Rejection of step disturbances.
Specifications: time domain and frequency domain.
Feedback control system using lead-lag networks.
PID control.
Multi input- multi output systems: decoupling.

6) Software tools (in parallel to the other topics).
Software tools for time and frequency domain analysis of linear systems.
Software tools for dynamical systems simulation.
Condividi su