Academic Year 2021/2022 - 3° Year

12 CFU - 1° and 2° Semester

**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.**Automatic Control**The course aims at reaching the following objectives, according to the Dublin descriptors:

1.

**Knowledge and understanding:**at the end of the course the sthudents will :

- understand the basics of retroactive control of a linear dynamic system, continuous time and discrete time;

- analyze the stability of closed-loop systems produced by external disturbances or parametric variations;

- know the specifications of a control system, both in the time and frequency domain;

**2. Applying knowledge and understanding**: at the end of the course the students will be able to:

- perform the design of a feedback control systems for a linear time-invariant continuous-time system and

performing its discrete-time realization;

- carry out the project using standard PID type controllers

**3. Making judgements:**students will be able to judge the potential and limits of the control of Linear and Time-

Invariant Systems (LTI).

**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 control.

**5. Learning skills:**students will be able to autonomously extend their knowledge on the Theory of Control of LTI

Systems, drawing on the vast literature available in the field.

**System Theory**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.

**Automatic Control**Lessons will be mainlyfrontal; 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.

**System Theory**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.

**Automatic Control****1.**Introduction to control systems; Characteristics of the response for linear systems of the first and the second order in the time domain: time constant, response time, rising time, settling time. relation between the response characteristics and the pole-zero position in the s plane. Characteristics of the frequency response for first and second order systems, cut-off frequency, band, resonance modulus. Non minimum phase systems. Polar plots.**2.**Open and closed loop control. feedback influence on the sensitivity to parameter variations, disturbance both in the direct chain and in the feedback path, and to the band width for a linear system. Steady state accuracy for a feedback system for input signals like step, ramp, parabolic ramp; classification of control systems in "types". Stability analysis via the Nyquist criterion. Gain and Phase margins. Root locus: drawing rules and examples.**3.**Performances of a control system: static and dynamic performances. Transformation of time domain to frequency domain performances. Frequency response design using lead and lag elementary controller network using Bode diagrams. Root locus design. realization of controller networks via operational amplifiers. Standard PID controllers: empirical and analytical tuning strategies.4. realization of controller networks via operational amplifiers. Standard PID controllers: empirical and analytical tuning strategies.

**5.**Relation between the s plane and the z plane. Bilinear transformation. Discretization and reconstruction of a signal. Sampling theorem. Performances of a discrete control system. Design of a discrete control system via translation of a continuous controller.**6.**Exercitations. The practical lessons are focussed ad deepening of theoretical aspects using key exercises, using the Matlab tool. particular examples are related to the frequency response design and root locus design.

**System Theory**Giua, Seatzu, Analisi dei sistemi dinamici, Springer; II edizione

**Automatic Control**1. Norman Nise, Controlli Automatici,,CittàStudi;

2. Dorf, Bishop, Controlli Automatici, Pearson