Academic Year 2019/2020 - 3° Year

12 CFU - 1° and 2° Semester

**System Theory**The course aims at making the students able to:

- 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;

- design a linear regulator and an observer.

**CONTROLLI AUTOMATICI**The module aims to make the student capable of:

- 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;

- 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

**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

**CONTROLLI AUTOMATICI**Teaching will be done through lectures and using, when necessary, the video-projector and software programs for the simulation of dynamic and control systems. This will serve to reinforce the concepts presented during the lectures.

**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.

**CONTROLLI AUTOMATICI****Module 1**Introduction to control systems; response performance of linear systems of the first and second order in the time domain: time constants, response time, time of

climb, settling time. Dependence of the characteristics of the response on the position of the system poles in the plane s. Characteristics of the frequency response of systems of the first and of the

second order, crossing pulsation, pass band, resonance module. Non-minimum phase systems. Polar diagrams. (Teaching hours: 9)

**Module 2**Open and closed chain control. Effect of feedback on sensitivity to parametric variations, on chain and feedback chain disturbances and on the band

pass of a linear system. Accuracy at steady state of a feedback system for step, ramp, parabolic entrances, classification of feedback control systems in types. Analysis

of the stability of linear systems fed back by the Nyquist criterion. Phase and earning margin. Root site method - Tracking rules and examples. (Teaching hours: 12)

**Module 3**Specifications of a control system: static and dynamic specifications. Transformation of time-specific specifications into harmonic response specifications. Nichols Charter. Synthesis for

attempts. Elementary compensating networks: anticipatory networks and attenuating networks. Synthesis by trial and error for compensation of frequency response. Synthesis with the help of the place of the roots. (Hours of

teaching: 12)

**Module 4**Realization of compensating networks through both passive electrical networks and operational amplifiers. Standard PID type controllers: empirical calibration methods, analytical methods of calibration. (Teaching hours: 6)

**Module 5**Relationship between the Z plane and the S plane. Discretization and reconstruction. Shannon theorem. Specifications of a discrete control system. Design of a control system

discreet. Synthesis of the discrete controller for translation. (Teaching hours: 5)**Module 6**. Exercises with the help of the Matlab code (Teaching hours: 6)

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

**CONTROLLI AUTOMATICI**1. Norman Nise, Controlli Automatici, CittàStudi;

2. Dorf, Bishop, Controlli Automatici, Pearson