00196 - Automatic Controls

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Decent work and economic growth Industry, innovation and infrastructure Responsible consumption and production

Academic Year 2021/2022

Learning outcomes

The course of Automatic Control provide the student with the fundamental tools for the analysis and synthesis of feedback control systems. In particular the concept of transfer function, bode diagrams, stability definition and criterion, robustness to disturbances and parameter uncertainty and design of regulators on the basis of root locus and bode diagram are illustrated.

Course contents

  1. Historical notes, basic nomenclature and examples on automatic control system; notes on modeling and identification; notion of feedforward and feedback control; building up a control system: the component subsystems (regulator, actuator, power amplifier, sensors, AD/DA converter, micro controller, etc.)
  2. Modeling elements: electrical, mechanical (translational and rotational) and electro-mechanical (servomotor) systems; notes on hydraulic and thermic systems; continuous and discrete time systems
  3. Structural properties of dynamic systems: controllability and observability, stability with respect to perturbations of the initial state and of the input signals, equilibrium states.
  4. Linear time invariant state space systems: state and output time domain response, transition matrix, impulse response, modes, state space coordinate change, b.i.b.s. and b.i.b.o. stability, transfer matrix,
  5. Mathematic complements: definition of Laplace (Anti)transform (LT) and fundamental theorems, LT of elementary signals (Dirac impulse, step, ramp, etc.), transfer function. inverse transformation of rational functions. Complex variable domain analysis: zero state and zero input responses and connection with transfer function. State space to input/output transformation. Poles and zeros and their connection with time response (up to second order systems) to elementary signals. Time response of high order sysmens and dominamt pole concept. Time domain specification used to evaluate the response of a system. Block diagram reduction and computations.
  6. Frequency domain analysis: harmonic response function (HRF) and its connection with the impulse response and the transfer function. Identification of the HRF. Bode plot: definition, related theorems and drawing rules. Resonance in second order systems. Non minimum phase systems. Systems with time delay. Nyquist diagrams and drawing rules.
  7. Feedback systems analysis: transfer function, steady state errors, disturbances rejection, sensitivity function, parameter uncertainties sensitivities. Stability: Routh criterion, Nyquist criterion, root locus, root contour and their utilization in the analysis and synthesis of the control systems. Phase and gain margins. Bode stability criterion.
  8. Control Systems Design: project specifications in the time domain time and frequency domain. Phase lead and lag networks. PID controllers. Design with phase lead, lag, P, PD, PI, PID regulators by means of root locus techniques, bode diagrams or Nyquist diagrams with M and N constant locus


  • Notes of the teacher: theory, exercices and tests solutions. (downloadable in pdf o zip formats c7o AMS Campus
  • G. Marro. Controlli Automatici. Zanichelli Ed. Bologna
  • R.C. Dorf, R.H. Bishop. Modern Control Systems. Ninth Edition. Addison-Wesley Publ. 2001.
  • P.Bolzern, R.Scattolini, N.Schiavoni. "Fondamenti di Controlli Automatici", McGraw Hill 2004.
  • M.E. Penati, G. Bertoni. Automazione e Sistemi di Controllo. Volume I e II. Progetto Leonardo. Bologna

Teaching methods

The course is also supported by exercise in classroom by tutor. The exercices are part of the course and concern modelling, application to real cases of the control methodologies. In this way the student is able to deal with the fundamental control problems characterizing the professional activity of a control engineer.

Assessment methods

COMPLETE Written test: exercises and theoretical questions.

Oral test is optional depending on the request of the student.

Teaching tools

  • Design and analysis Software: Matlab/Simulink
  • iol.unibo.it
  • eol.unibo.it

Office hours

See the website of Paolo Castaldi