28015 - Automatic Controls T

Learning outcomes

At the end of the course the student owns the basic skills regarding feedback control systems and has notions on the Laplace transform, the harmonic analysis and the stability criteria. Moreover, the student owns skills regarding the most important methods for the synthesis of regulators in continuous time, both for linear systems and nonlinear systems with algebraic non-linearity.

Course contents

Introduction to automatic control. Control problems. Open-loop and Closed-loop (feedback) control.

Systems. State-space modeling of dynamical systems. System classification.

Stability theory. Trajectories, equilibria, and equilibrium pairs. Internal and external stability.

Linear time-invariant (LTI) systems. Closed-form solution. Superposition principle. Free and forced response. Natural modes. Stability for LTI systems. Linear approximation of nonlinear systems.

Stabilization and regulation. Stabilization via state feedback. Introduction to regulation.

Transfer functions. Laplace transform. Transfer functions. Heaviside expansion.

Response of elementary systems. Step response of first- and second-order systems. Settling time and overshoot. Mapping time-domain specifications into the complex plane.

Frequency domain analysis of LTI systems. Fourier series and Fourier transform. Frequency response of an LTI system. Bode plots.

Stability and performance of feedback systems. Output-feedback regulation. Sensitivity functions. Phase margin. Bode criterion.

Design of feedback systems. Mapping static and dynamic specifications to the loop function. Internal model principle. Loop shaping. Cascade control.

PID controllers. Structure and frequency analysis. Realization in the time domain. Elements of digital implementation.

 

Laboratory activities. Introduction to Matlab/Simulink. Numerical methods for the modeling and simulation of dynamic systems. Implementation methods for control system design and validation. Focus on electric motor/generator applications.

Prerequisites: Before taking this course, it is suggested to review the basic concepts of calculus (functions, limits, integrals, differential equations, complex numbers, etc.), linear algebra (matrices, vector spaces, eigenvalues and eigenvectors, etc.), and physics (Newtonian mechanics, electrical circuits, etc.).

 

Readings/Bibliography

Although the lecture slides provide a structured outline of the topics covered, they are not designed to be a standalone study tool; therefore, it is recommended to supplement your preparation with a foundational textbook on automatic control. The suggested books are:

• Bolzern, Scattolini, Schiavoni, Fondamenti di Controlli Automatici, McGraw-Hill, 2015 (4° ed)
• Marro, Teoria dei sistemi e del controllo, Zanichelli

Teaching methods

Traditional frontal lectures.

Assessment methods

Oral examination (open-ended questions covering the entire syllabus, graded on a 30-point scale).

Students with SLD (Specific Learning Disabilities) or temporary/permanent disabilities: please contact the relevant University office (https://site.unibo.it/studenti-con-disabilita-e-dsa/it ) and the professor in advance to arrange any necessary accommodations. Generally, concept maps, extra time, and step-wise questions are permitted.

Student with the student-athlete or working students status: please contact the professor to arrange, if possible, an alternative date close to the scheduled exam day.

Teaching tools

Slides, scripts, and additional material on Virtuale.

Office hours

See the website of Michelangelo Bin

See the website of Alessandro Bosso