Teacher

prof. Paolo GARDONIO

Credits

12 CFU

Language

Italian

Objectives

The module is organised in two parts. The first part introduces the student to the input-output formulation of dynamic systems and provides the concepts and mathematical formulations necessary to evaluate the response of a given dynamic system. The second part provides the student with the concepts and mathematical tools for the stability analysis and for the synthesis of feedback control systems. The module introduces practical examples of mechanical systems control.

Acquired skills

- Use of mathematical tools for the analysis of dynamic systems.
- Modelling of mechanical systems with Newton and energy (i.e. variational) approaches.
- Modelling of electro-mechanical systems.
- Modelling with transfer functions and state-space formulations.
- Time-domain systems analysis.
- Frequency-domain systems analysis.
- Stability analysis of feedback control systems.
- Analysis and design of feedback control systems.
- Simulation of dynamic systems with MatLab.

Lectures and exercises (topics and specific content)

Mathematical tools for the analysis of dynamic systems: matrix algebra; complex numbers, complex variables, complex functions; Laplace transform; Solution of linear, time-invariant, differential equations (10 hours).
Modelling of mechanical systems with Newton’s approach: mechanical elements; equations of motion of systems with one, two and multiple degrees of freedom, equation of motion of distributed systems,  equations of motion in matrix form, free and forced response, transfer functions, block diagrams (10 hours).
Modelling of mechanical systems with energy approach: Variational formulation of the equations of motion: review of d’Alembert, virtual work and Hamilton principles; variational approach, equations of motion of systems with one, two and multiple degrees of freedom; equations of motion in matrix form: Lagrange equations, free-response: eigenvalues-eigenvectors, natural modes and natural frequencies, equations of motion diagonalisation (10 hours).
Forced response of dynamic system: singularity functions, convolution integral, numerical integration (6 hours).
State-space modelling of mechanical systems: equations of motion in the state-space, block diagram representation, transfer function from state-space formulation (10 hours).
Modelling of electro-mechanical systems: electrical elements and electrical circuits; electro-mechanical transducers; modelling of electro-mechanical systems (10 hours).
Frequency analysis: frequency response function; Bode diagram, polar diagram, Nyquist diagram (14 hours).
Feedback control systems: introducction and definitions for feedback control systems, stability analysis (10 hours).
Control performance of feedback control systems: block diagrams typical of regulation, disturbance rejection and noise rejection problems, steady state error, transient performance (6 hours).
Synthesis of control systems: PID compensators, integrative effect, derivative effect, phase lag/lead compensators (10 hours).
Labs (24 ore).

References

- P. Gardonio “Controlli Automatici” note disponibili sul portale materiale didattico
- Katsuhiko Ogata "System Dynamics" 4a Edizione, Pearson Prentice Hall, London (2004)
- B. C. Kuo, F. Golnaraghi "Automatic Control Systems" 8a Edizione, John Wiley & Sons, Inc. (2003)
- G. Marro "Controlli Automatici" Zanichelli, Bologna (2004)
- R. C. Dorf, R. H. Bishop "Controlli Automatici" 11a Edizione, Pearson, Prentice Hall, Milano (2010)
- Katsuhiko Ogata "Modern Control Engineering" 4a Edizione, Pearson Prentice Hall, London (2004)
- P. Bolzern, R. Scattolini, N. Schiavoni "Fondamenti di Controlli Automatici" 3a Edizione, McGraw-Hill, Milano (2008)
- G. F. Franklin, J. D. Powell, A. Emami-Naeini "Feedback Control of Dynamic Systems" 4a Edizione, Prentice Hall, London (2004)

Type of exam

Written and oral