Academic Year 2023/2024 - Teacher: SALVINA GAGLIANO

Expected Learning Outcomes

Knowledge and ability to understand

Know the main methods of analysis and control of a linear time-invariant system

Applied knowledge and understanding

Being able to represent a dynamic system through a mathematical model. Being able to design an automatic regulation system

Autonomy of judgment

Knowing how to choose the type of control system to use in the control

Communication skills

Know how to use the technical terms related to linear and automatic control systems. To be able to present the main problems concerning these systems in research and professional fields

Learning ability

Apply basic knowledge on regulation systems to address the in-depth study of related topics not explicitly discussed in the course

Course Structure

Lectures and exercises

Required Prerequisites

Knowledge of Linear Algebra, Mathematical Analysis I, Physics I, Physics II

Attendance of Lessons


Detailed Course Content

Classification of systems. Representation of finite order linear systems, discrete time and continuous time by means of differential equations with constant coefficients. Concept of state. Choice of state variables. Mathematical model of a system. Relationship between models. Linearization. Controllability, Observability. Simulation. The Laplace transform properties and applications. Concept of the transfer function. Poles and zero. Block diagrams. Systems aggregates. First and second-order systems. Frequency response. Polar and Cartesian diagrams. Feedback systems: speed of response, accuracy, effect of disturbances, stability. Bode’s theorem. Stability indices.

Bode Criterion. Nyquist Criterion. Routh Criterion. Summary: Controller Design Definition. Trial Summary. Corrective nets: anticipating and attenuating. Universal diagrams. Standard controllers: PID controllers. Basic knowledge of the MATLAB program.

Textbook Information

1. Franklin, Powel, Emani-Naeini. “Controllo a retroazione di sistemi dinamici”, vol. I, EdiSES, NA


2. Di Stefano et al.: “Regolazione Automatica”, Collana Shaum, McGraw-Hill

Course Planning

 SubjectsText References
1Basic definitions and general concepts. Classification of systems. Representation of systems linear discrete-time and continuous-time finished orders by means of differential equations with constant coefficients.1
2Input-output representation and behavior. Free response and forced response. Laplace transform. Main properties and applications. Convolution integral. Impulsive response. Antitransformed. Concept of transfer function. Poles and zeros1-2
3First and second order systems. Time constants. Theoretical and experimental examples. Answer canonical at the step. Rise time, overstretch time, settling time. Dominant poles.1
4Block diagram algebra. Rules and elaborations1-2
5Mathematical model of a system. Choice of state variables. Parametric models. Equation of state. State and solution transition matrix. Controllability and observability. Relationship between parametric and non-parametric models (equation of state - transfer function)1
6Stability of linear systems. Routh stability criterion1-2
7Feedback systems. Specifications. Stability of feedback systems. Response speed. Accuracy. Effect of noise feedback.1-2
8Frequency response. Analysis of feedback systems. Harmonic function. Bode diagrams. Bode theorem. Minimum phase systems. Bode stability criterion. Stability margins. Bandwidth1
9Nyquist polar diagrams. Pure phase shifter. Nyquist path. Conjunction of singularity points. Nyquist stability criterion. Indices of relative stability1-2
10Definition of the controller design. Trial and error synthesis. Correction nets: anticipating and attenuating. Saddle net. Standard controllers: PID controllers1-2

Learning Assessment

Learning Assessment Procedures

Written test followed by oral test

Examples of frequently asked questions and / or exercises

State equations; transfer function; closed-loop systems; stability; controllability; observability; linear state regulator.

Exercises: to determine the impulse response of a system; to calculate compensators for linear time-invariant systems; to calculate the frequency response of linear time-invariant systems; to calculate eigenvalues.