Learning objectives
The aims of the course in relation to understanding and knowledge are:
- Understanding of the two principles of active control, feedforward and feedback, and of the broad applications to automation.
- Understanding of the methods, based on Laplace and Zeta transforms, to
determine the time-evolution of linear scalar dynamic systems.
- Knowledge of harmonic analysis and of the stability theory for linear systems.
- Knowledge of the main methods of analysis and synthesis for feedback control systems.
In relation to the ability to apply knowledge and understanding, the aims are:
- Skill to analyze feedback control systems.
- Skill to set up and solve simple problems of regulation and control with a single controlled variable.
Prerequisites
Mathematical analysis (first course), in particular good knowledge of complex numbers; principles of Newtonian dynamics; basic knowledge of electrical circuits.
Course unit content
1) Fundamental concepts: systems and mathematical models. Block diagrams.
Feedforward and feedback. Robustness of feedback with respect to feedforward. Mathematical modeling of physical systems: examples from electric networks, mechanical systems, and thermal systems. [7 hours]
2) Analysis methods of LTI (linear time-invariant) SISO (single-input single-output) systems. Ordinary differential equations and Laplace transform. Inverse Laplace transform of rational functions. Generalized derivatives and elements of impulse function theory. The transfer function. Relations between the initial conditions of a differential equation. First and second-order linear systems. The concept of dominant poles. [14 hours]
3) Stability of dynamical systems: stability to perturbations, BIBO (bounded-input bounded-output) stability and related theorems. Routh’s Criterion. [5 hours]
4) Frequency-domain analysis: the frequency response function. Relation between the impulse response and the frequency response. Bode’s diagrams. Nyquist’s or polar diagrams. Asymptote of the polar diagrams. Bode’s formula and minimumphase systems. [7 hours]
5) Properties of feedback systems. The Nyquist criterion. Phase and magnitude margins: traditional definitions and their extensions. The Padé approximants of the time delay. [6 hours]
6) The root locus of feedback systems: properties for the plotting. Generalization of the root locus: the “root contour”. Examples. Stability degree on the complex plane of a stable system. [5 hours]
7) Control system design: the approach with fixed-structure controllers. Specification requirements and their compatibility. Phase-lead and phase-lag Compensation. The pole-zero cancellation technique and the internal stability of a feedback connection. Frequency synthesis with the inversion formulas. The Diophantine equation for the direct synthesis. Regulation of dynamic systems. The PID regulators: frequency design, tuning and implementation. Control of systems with time delay. Control systems with feedforward and feedback controllers. [13 hours]
8) Digital control systems: The z-transform. Conversion from continuous-time to discrete-time. Sampling frequency and anti-aliasing filtering. SISO discrete-time linear systems: free and forced response, stability and Jury’s Criterion. Glimpse on the synthesis of discrete-time controllers. [13 hours]
9) A design example: position regulation of a DC servo electric motor. Modeling and design of a PD controller by means of the root locus and simulations. Digital implementation with the Arduino board. Experimental results and final considerations. [2 hous]
Full programme
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Bibliography
Pdf slides of the lessons on the web site of the course.
FURTHER READINGS
1) G. Marro, ``Controlli Automatici'', quinta edizione, Zanichelli, Bologna, 2004.
2) P. Bolzern, R. Scattolini, N. Schiavoni, “Fondamenti di Controlli Automatici”, quarta edizione, McGraw-Hill Education, 2015.
3) M.P. Fanti, M. Dotoli, “MATLAB: Guida al laboratorio di automatica”, CittàStudi, 2008.
Teaching methods
Lessons with theory illustrated by examples. Exercitations with problem-solving on all teaching topics. A glimpse on the use of MATLAB and the Control Systems Toolbox.
The slides used to support the lessons and exercitations are available on the online teaching site (Elly) and constitute the main teaching material of the course.
Assessment methods and criteria
Learning assessment is carried out with a written test and an optional oral test.
The written test includes theory questions and analysis and synthesis exercises. The result of the written test, when sufficient, is divided into four grade bands: 18-21, 21-24, 24-27, and 27-30 (all expressed in thirtieths). Participation in the written test alone determines the attribution of the minimum grade of the band (for example, if the band is 27-30, the minimum grade of the band is 27/30).
The oral test is optional, chosen by the student, and intended to improve the band's minimum grade up to a maximum of 5/30. An unsatisfactory outcome could lead to a worsening of the band's minimum grade. Withdrawing from the oral test implies that the student will take a future written test.
Registering on the University's ESSE3 online site is mandatory to participate in the written tests. During these tests, it is not permitted to consult notes, handouts, books, etc. The use of a basic scientific calculator is recommended and permitted.
Further information and clarifications on learning assessment are provided in the first lesson of the course.
Other information
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2030 agenda goals for sustainable development
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