Scientific Disciplinary Sector (SSD)
ING-INF/04 - SYSTEMS AND CONTROL ENGINEERING
Primo semestre dal Oct 4, 2021 al Jan 28, 2022.
The course aims to provide knowledge on the theoretical basis of the theory of dynamic systems, in the representation of state, with particular reference to the properties of time invariant linear systems and the methods for the synthesis of controllers for these systems. At the end of the course the student will have to demonstrate ability to apply the acquired knowledge: to provide the knowledge to analyze the structural properties of a linear dynamic system (e.g. reachability and observability) and its stability. Calculate the observability and reachability matrices; design a state feedback controller; design an asymptotic state observer; apply Lyapunov's theory of stability. Must have the ability to define the technical specifications to design a controller for linear dynamic systems described by differential or difference equations. S/He will have to be able to deal with other engineers (e.g. electronic, automatic, mechanical) to design advanced controllers for complex electromechanical systems. It will have to show ability to continue studies independently in the field of designing robust and optimal controllers for linear and non-linear systems.
Review of the basic concepts of system analysis:
- Definitions and properties of linear, time invariant (LTI) systems,
- models in time, frequency and "s" and "z" domains,
- the transfer function
- main properties of LTI systems in "t", "f", "s" and "z",
- discrete time systems and Z transform
- main properties of feedback systems.
- AR, MA, ARMA models,
- input-state-output representation,
- definitions of state, causality, algebraic equivalence,
- state and output update map,
- exponential matrix and its properties,
- Jordan canonical form, characteristic polynomial, algebraic and geometric multiplicity,
- modes, their characteristics, simple/asymptotic/BIBO stability,
- Relation between state representation and Laplace and Z transforms,
- Transfer functions, eigenvalues and poles.
Stability in state models:
- equilibrium state,
- stability of an equilibrium state,
- Lyapunov stability criterion,
- Lyapunov equation,
- linearization and reduced Lyapunov criterion.
- main concepts and the reachability Gramian,
- state space control,
- standard form of reachability, canonical control form,
- PBH criterion of reachability,
- state feedback.
- main concepts and observability Gramian,
- State estimation (open and closed loop),
- standard form of observability, canonical observation form,
- PBH criterion of observability.
- overview of discrete time Kalman filter,
- overview of optimal linear, quadratic controller in discrete time domain.
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The exam will consist of a written test on the course topics. The exam will contain questions in the form of theoretical questions and exercises where it will be required to apply specific theoretical knowledge. Each question will contribute to the total score according to an additive metric that will be specified before the exam.
If the written test is evaluated positively, an optional oral test is foreseen, which will cover the theoretical part of the course. The overall score will be the mean of the oral and written tests scores.
Both tests (written and oral optional) will be aimed at understanding the theoretical arguments and the ability to apply logic schemes to specific problems.