AUTOMATICA M - Z

Learning Objectives

• 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 course aims at making the students able to: - understand the basics of feedback control for a linear time-invariant continuous-time and discrete-time dynamical system; -analyse the closed loop stability even in front of disturbamces or parametric perturbations; - understand the performances of a control system, both in the time and in the frequency domani; - perform the design of a feedback controller for a linear time-invariant, time-continuous system, with the possibility to derive a digital implementation; - perform the controller design via standad PID controllers

Course Structure

• 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

Detailed Course Content

• 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

  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.

  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. 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.

Textbook Information

• 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