# AUTOMATIC CONTROL M - Z

ING-INF/04 - 9 CFU - 2° Semester

GIUSEPPE NUNNARI

## Learning Objectives

The aim of the course is to introduce the student with the basics of representation and control of dynamical systems. According with the introductive aim of the course, the focus will be with methodologies for dealing with Linear Time-Invariant (LTI) systems.

## Course Structure

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.

## Detailed Course Content

1. Basic concepts

Assiomatic definition of dynamical systems . Representation of linear and non-linear systems using state equations. Classification of dynamic systems: linear and non-linear, continuous time and discrete time, finite and infinite dimension, finite and infinite states. Equilibrium of the state. Analysis of equilibrium using the Lyapunov criterion. Linearization of non-linear systems. Linear Time-invariant (LTI) systems. Transfer function, characterization of SISO systems by means of poles and zeros, impulse response, Lagrange formula. Calculation of the a LTI system response by using the inverse Laplace transform. Reachability and Observability of LTI systems, Canonical forms. Systems in minimal form. Linear state feedback. Theory of the poles allocation. Asymptotic state observer. Separation theorem. Stability analysis using the Routh-Hurwitz criterion. Representation of linear dynamic systems using block diagrams. Block diagram algebra rules. Characteristics of the response of linear systems in the time domain: time constants, response time, rise time, settling time, overshoot. Dependency of the characteristics of the response from the position of the system poles in the s-plane. Harmonic analysis of a linear system, frequency response and its representation through Bode diagrams. Characteristics of the frequency response of first and second order systems, crossing pulsation, bandwidth, resonance module. Non-minimum phase systems. Polar diagrams. Discrete time LTI systems: representation in the form of difference equation and by transfer function by using the Z-transform. Main properties of the Z-transform. Stability analysis of discrete time systems.

2. Properties of feedback systems.

Open and closed loop control systems, transfer function of a feedback system, characteristic equation. Effects of feedback on sensitivity to parametric variations, external disturbances and bandwidth of a linear system. Steadt-state error of a feedback system for step, ramp and parabola inputs; classification of counter-reaction control systems in types. Stability analysis of back-fed linear systems using the Nyquist criterion. Phase and profit margin. Representation of the module and phase frequency response in the form of a polar diagram.

3. Controller design

Constrais of a control system: static and dynamic constrains. Transformation of time domain constrains into constrains for the frequency response. Synthesis of a controller in the frequency domain by using the trial-and error approach.. Elementary compensation networks. Synthesis by using the direct approach. Standard PID controllers. Design of PID controllers by using the analytic approach. Design of PID controllers by using heuristic appraches both in open and closed-loop frameworks. The Ziegler and Nichols approaches.

4. Digital control systems.

Basics for the study of digital systems: analog to digital conversion, sampling theorem, signal reconstruction, zero-order hold (zoh). Representation of linear digital systems in the time domain using finite difference equations. Analysis of the stability of a linear time-invariant and time-discrete system. Synthesis of a digital controller based on the translation of an analog controller.

## Textbook Information

S. Bittanti, Introduzione all’Automatica, Ed. Zanichelli

P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di Controlli Automatici, Ed. McGraw-Hill

Open in PDF format Versione in italiano