AUTOMATIC CONTROL
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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- MARCELLO BONFE'
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ING-INF/04
Training objectives
- The aim of the course is to present the features of the mathematical models used to describe the behaviour of dynamical systems and to provide the basic tools for the design of feedback control devices.
Knowledge and understandings:
- basic methods for the analysis of linear time-invariant dynamic systems, with multiple-inputs/multiple-outputs (MIMO)
- basic tools for frequency-domain analysis of linear time-invariant systems (single-input/single-output, SISO)
- stability properties of feedback systems (Nyquist theorems, Routh-Hurwitz criterion)
- graphic tools (Bode diagrams, root loci) for the analysis of loop transfer functions
Such a knowledge can be applied by students to:
- analysis the response of engineering systems (mechanical systems, electrical networks, etc.), as a function of initial conditions or input signals
- design controllers for the stabilization of feedback systems
- solve simple control design problems according to given requirements on static (e.g. steady-state error) and dynamic (e.g settling time) performances of the closed-loop system Prerequisites
- Matrix algebra, differential equations,complex variables.
Course programme
- Mathematical models of dynamic systems.Continous-time and discrete-time models. Linear and nonlinear models.
Time-invariant and time-varying models. Equivalents models and minimal forms.General properties of dynamic systems.
Reachability and controllability. State observation and reconstruction. Stability with respect to initial state and input function perturbations.
Linear time-invariant systems.State evaluation of dynamic systems. The response function. State transition matrix and its properties.
Eigenvalues and modes of oscillation. Impulse response. reduction of a system to a minimal form. Change of basis in the state-space.
Bounded input - bounded state (bibs) stability. Bounded input - bounded output (bibo) stability. State and output feedback. Asymptotic state observers.
Linear time-invariant systems with single input and single output.Transfer functions and block diagrams.
Relation between input-output and input-state-output representation. Typical test signals for the time response of control systems.
Steady-state errors. Frequency response. Frequency domain analysis: Nyquist and Bode plots, gain margin and phase margin.
General properties of feedback systems. Stability of linear control systems: Routh Hurwitz criterion.
The root-locus technique. Didactic methods
- The teaching activity is organized so that the required knowledge is acquired during lectures.
Some of these lectures will be dedicated to the solution of numerical exercises, similar to those that students are required to solve during the final exam.
A single lesson will be given in the Computer Science laboratory, to present an introduction to the use of Matlab for control systems design. Learning assessment procedures
- The exam requires to complete in written form a set of 10 numerical exercises (3 marks per exercise) related to: analysis of structural properties of MIMO linear dynamic systems (controllability and observability); analysis of frequency response of SISO linear systems; design feedback control systems with specified dynamic and static performances.
Reference texts
- Lecture slides (in Italian).
Books suggested for optional in-depth analysis:
G.Marro: "Controlli automatici", Zanichelli, Bologna, 1992 (In Italian).
P.Bolzern, R.Scattolini, N.Schiavoni: "Fondamenti di controlli automatici", McGraw-Hill, 1998 (In Italian).
R. Dorf, R. Bishop: "Modern Control Systems", Prentice-Hall, 2010 (English vesion)
K.J.Astrom,R.Murray "Feedback Systems: An Introduction for Scientists and Engineers", online
http://www.cds.caltech.edu/~murray/amwiki/
