Unit CONTROL SYSTEMS

Course
Engineering management
Study-unit Code
A002922
Curriculum
In all curricula
Teacher
Francesco Ferrante
Teachers
  • Francesco Ferrante
Hours
  • 72 ore - Francesco Ferrante
CFU
8
Course Regulation
Coorte 2024
Offered
2025/26
Learning activities
Caratterizzante
Area
Ingegneria dell'automazione
Academic discipline
ING-INF/04
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
English
Contents
Modeling and simulation of dynamical systems; stability analysis; feedback control synthesis; PID regulators; performance specifications; application to engineering management problems.
Reference texts
-Karl Johan Aström and Richard M. Murray, “Feedback Systems: An Introduction for Scientists and Engineer”, PRINCETON UNIVERSITY PRESS, 2009. -Panos J. Antsaklis and Anthony N. Michel, "A Linear Systems Primer", Birkhauser, 2007.
Educational objectives
The purpose of the course is to introduce the main issues and engineering tools related to the design of management and control systems for manufacturing processes, in the broader context of dynamical systems. Specifically, the following topics will be discussed: modeling and simulation of dynamical systems; methodological tools for stability analysis; input-output behavior and performance; feedback control synthesis. Teaching activities include class exercises on simulated models of interests for management engineering.
Prerequisites
Basic courses in mathematics and physics; knowledge in the areas of matrix calculus and complex analysis.
Teaching methods
Lessons, exercises, and laboratory.
Other information
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Learning verification modality
Written and oral test.
Extended program
Definition of a control system. The control problem. Closed-loop vs open-loop control. The notion of feedback. Example of feedback systems in nature and engineering. Model-based approach. The notion of mathematical model. Dynamical systems. Differential equations as a modeling tool for dynamical systems. State space models and input-output models. LTI models. Definition of linearity and time-invariance. Hints about numerical integration of nonlinear ODEs. From linear high order ODEs to state-space models. Examples of physcial models that can be rewritten as LTI systems. The problem of response computation for a general LTI system. Computation of the zero-input response: Matrix exponential, transition map and its properties. Uniqueness and general expression of the zero-input response. Computation of the complete response: Uniqueness and general expression of the complete response. Dirac delta and the notion of impulse response. Use of the Dirac delta to define the impulsive response. Significance of the impulsive response from an input-output standpoint. Natural modes, zero-input response in terms of projections onto the eigenspaces, examples. Mass-spring-damper system: characteristic polynomial, analysis of the case on real eigenvalues. Zero-input response of a planar system with complex eigenvalues: general form of the solution, pseudoperiodic natural modes, analysis of the modes, damping and natural frequency. Analysis of the mass-spring-damper system in the case of complex eigenvelues. Zero-input response in the presence of both real and complex eigenvalues. Laplace transform: definition, example of computation and properties. Computation of the full response in the Laplace domain. Definition of the transfer function. Transfer function of SISO systems, definition of poles and zeros. Relationships between poles and zero, fractional partial expansion in the case of simple roots, controllability and observability of natural modes, definition of hidden dynamics. PBH test for controllability and observability. Minimal realizations. Definition of equilibrium point for an LTI system. Definition of asymptotic stability, marginal stability, and instability. Necessary and sufficient conditions for asymptotic and marginal stability. Routh criterion. Step response of asymptotically stable LTI systems. Definition of DC gain. Analysis of the step response. Transient and steady-state response. Initial and final value theorems. Harmonic response. Bode diagrams: motivation and generalities. Gain and phase plots, use of decibels for the representation of the gain plot. Bode canonical form. Approximate Bode diagrams of the elementary terms: constant, monomial, binomial, and trinomial. Controllability and reachability: Definitions, necessary and sufficient conditions, examples. Controllable canonical form. Eigenvalues assignment problem: problem statement and necessary and sufficient conditions for solvability. Ackermann formula. Stabilizability: definition and necessary and sufficient conditions for solvability. Observability: Definitions, necessary and sufficient conditions, examples. Observable canonical form. The state estimation problem. Design of asymptotic observers.
Obiettivi Agenda 2030 per lo sviluppo sostenibile

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