# 28630 - Control Systems T-A

### Course Unit Page

• Teacher Elena Zattoni

• Credits 6

• SSD ING-INF/04

• Teaching Mode Traditional lectures

• Language Italian

• Teaching Material

• Course Timetable from Feb 20, 2019 to Jun 06, 2019

## Learning outcomes

Acquisition of the methodological tools (in the time domain and in the frequency domain) required for the analysis of the properties of linear dynamic systems, both in open loop and in close-loop. Development of the skills needed for the synthesis, by means of consolidated techniques, of feedback control systems. Achievement of the sensitivity needed for the tuning of the most common regulators in the industrial field.

## Course contents

Fundamentals: systems; oriented systems; systems with zero initial conditions; dynamic and algebraic mathematical models; linearization of steady-state models; linearity; time-invariance; block diagrams; block-diagram reduction techniques; open-loop control systems and closed-loop control systems; effect of feedback on robustness; dynamic models; models of electrical systems, mechanical systems, heat- and fluid-flow models; models of electromechanical systems: model of a DC motor with gear train (rotational transformer).

Analysis of linear dynamic systems: linear time-invariant ordinary differential equations; differential equations of physical systems; solution of homogeneous differential equations with nonzero-initial conditions; solution of forced differential equations with zero initial conditions; solution of forced differential equations with nonzero initial conditions; the Laplace transform; conditions for a function of time to be L-transformable; the theorem of convergence; linearity of the Laplace transform; theorems on the Laplace transform; application of Laplace transform to the solution of linear differential equations; the transfer function of linear systems; the Ward-Leonard electromechanical system; inverse Laplace transform by partial-fraction expansion: simple poles and multiple-order poles; modes; canonical responses; Dirac impulse; convolution integral; convolution integral for systems with distributed parameters and for time-varying systems; first order system step response; second order system step response; damping ratio and undamped natural frequency; response versus pole locations;  evaluation of overshoot and settling time.

Frequency-domain analysis: the frequency response and its relationship with the transfer function; deriving the impulse response from the frequency response; Bode plots; drawing the Bode plots by adding the Bode plots of the elementary terms; asymptotic Bode plots; resonant peak and resonant frequency of the prototype second-order system; Bode's phase-gain relationship; application of Bode's phase-gain relationship to straight-line approximations of the Bode gain plot; examples of systems not satisfying the conditions for application of Bode's phase-gain relationship; polar plots (Nyquist plots);  magnitude-phase plot (Nichols plots).

Stability of feedback control systems: zero-input stability; bounded-input bounded-output stability; necessary and sufficient condition for bounded-input bounded-output stability; equivalence between bounded-input bounded-output stability and zero-input stability in linear time-invariant systems; Routh-Hurwitz criterion; special cases when Routh's tabulation terminates prematurely; evaluation of the marginal value of a system parameter for system stability by means of the Routh-Hurwitz criterion; feedback control systems: effect of feedback on sensitivity (parameter variations and disturbances in feedback control systems); bandwidth; the steady-state error of feedback control systems; steady-state error of nonunity feedback systems; the Nyquist criterion: systems with a number of poles in the right-half complex plane equal to zero and systems with a number of poles in the right-half complex plane other than zero; conditionally stable systems; relative stability: gain margin and phase margin; relative stability with Nyquist plots, Bode plots and Nichols plots; time-delay systems: Nyquist plot for system with time delay; stability analysis for time-delay systems by using the Nyquist criterion; stability analysis for systems with time-delay dominant on time constants; constant-M loci and constant-N loci in the polar coordinates; constant-M loci and constant-N loci in the magnitude-phase plane: the Nichols chart; determination of reasonant peak, reasonant frequency and bandwidth by means of the Nichols chart (type 1 and type 0 systems).

The root-locus design method: a perspective on the root-locus design method; guidelines for sketching a root locus; selected illustrative root loci; selecting the parameter value; extension of the root-locus method.

Design of control systems: design specifications, controller configurations, fundamental principles of design; cascade compensation networks (integration network, derivation network, phase-lead network, phase-lag network, lead-lag network) and their diagrams (Bode and Nyquist plots); design with phase-lag controller: effects and limitation of phase-lag control, frequency-domain interpretation and design of phase-lag control (inversion formulas); design with phase-lead controller: effects and limitation of phase-lead control, frequency-domain interpretation and design of phase-lead control (inversion formulas); pole-zero cancellation design; design with lead-lag controller; design with the PI controller; design with the PID controller; Ziegler-Nichols' and related methods for determining the parameters of PID controllers.

G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

E. Zattoni, "Controlli automatici: raccolta di prove scritte con soluzione" in G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

http://online.universita.zanichelli.it/marro/files/2015/05/prove_risolte.pdf

E. Zattoni, "Controlli automatici: raccolta di  Esercitazioni risolte con TFI" in  G. Marro, "Controlli automatici", 5a ed. con cd-rom, Zanichelli, Bologna, 2006.

http://online.universita.zanichelli.it/marro/files/2015/05/esercitazioni.pdf

G. F. Franklin, J. D. Powell, A. Emami-Naeini, "Feedback Control of Dynamic Systems: 5th Edition", Pearson-Prentice Hall, Upper Saddle River, NJ, 2006.

R. C. Dorf, R. H. Bishop, "Modern Control Systems: 10th Edition", Pearson-Prentice Hall, Upper Saddle River, NJ, 2005.

F. Golnaraghi and B. C. Kuo, "Automatic Control Systems: 9th Edition", John Wiley & Sons, Hoboken, NJ, 2010.

K. Ogata, "Modern Control Engineering", Pearson Education, Upper Saddle River, NJ, 2010.

L. Qiu and K. Zhou, "Introduction to Feedback Control", Pearson Education, Upper Saddle River, NJ, 2010.

MATLAB & Simulink Student Version Release 2011a. ISBN: 978-0-9825838-3-8.

## Teaching methods

Lectures and written exercises. Demos concerning the use of Matlab and TFI for computer aided control system design.

## Assessment methods

Questions on practical and theoretical topics.

## Teaching tools

Lab activities in Computer Aided Control System Design for single-input single-output systems. The main CACSD tool used in the course is TFI (Transfer Function Interpreter): a collection of Matlab routines directly processing transfer functions and implementing of the synthesis procedures discussed in the theoretical part of the course.

## Office hours

See the website of Elena Zattoni