Automatics A - L

Module SYSTEM THEORY

The course aims at reaching the following objectives, according to the Dublin descriptors:

CONTROLLI AUTOMATICI
1. Knowledge and understanding: at the end of the course the students will :

- analyse a linear time invatiant system, deriving a state space model and then solving the dynamic equations, also through the Laplace Transform; 

- determine the properties of stability,controllability,observability;

- write the transfer function and determine the frequency response;

2. Applying knowledge and understanding: at the end of the course the students will be able to apply the knowledge before to  design a linear regulator for an LTI dynamical system  and the related observer

3. Making judgements: students will be able to judge the potential and limits of the LTI syste  theory, in relation to modeling and stability issues.
4. Communication skills: students will be able to illustrate the basic aspects of LTI Systems, interact and collaborate as a team with other experts in the field of dynamical modeling.

Lessons will be mainly frontal; sometimes personal computer will be used to maximise learning objectives. It will also be used to make numerical exercises and simulations.

During exercitations some students will be asked to actively participate together wiith the professor, at the aim to stimulte attention and to perform a "sample check" of the real state of the learning status

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Students have not to attend the lessons mandatorily.  Regular attendance at lectures and exercises is however strongly recommended for
achievement of the expected training objectives on schedule.

Concept of dynamic system, MIMO, SISO, MISO, SIMO systems; state variables, block diagrams; state space models; Laplace transform; Dirac impulse; teorems of frequency translation, delay, derivative and integral; initial and final value; Iverse Laplace transform; poles and zeros; transfer function; periodic functions transform; transfer function invariance; Lagrange formula for continuous and discrete systems; transition matrix: definition,properties and calculation; monimal form; poles and eigenvalues; demonstration of lagrance formula; Cayley Hamilton theorem and its use for calculation of the transition matrix; movement, trajectory and equilibrium; Lyapunov theory of equillibrium; stability for nonlinear systems; application of the definition and calculation of equilibrium point; basin of attraction;  stability in linear continuous and discrete time systems through the eigenvalue analysis; BIBO stability; diagonal form realization and characteristics; minimal form and role of residues; Routh criterion; linearization; diagonalization and Jordan form; algebraic versus geometric multiplicity;linearization; movement geometry; phase portrait; focus; nodeand saddle point; Controllability and reachability: definition, controllability matrix; A- invariance, Kalman canonical form; controllability canonical form; state linear regulator: pole placement; Ackerman formula; stabilizzability; Observability; Kalman canonical form for observability; minimal formrevisited; Observability canonical form; Luenberger observer; compensator; Separation Theorem; Linear systems of I and II order; Frequency response; Bode diagrams; Seta transform; Zeta Inverse transform; Bilinear transformation; FIR -IIR systems; Dear Beat Control, Practical exercitation are focussed to appli  some theoretical issues both through exercises and examples during lettons and using  Matlab.  In details key case study refer to frequency response, and to the design of controller and observer.

Giua, Seatzu, Analisi dei sistemi dinamici, Springer; II edizione