Teaching code

4S02785

Academic staff

Diego Dall'Alba, Riccardo Muradore

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

ING-INF/05 - INFORMATION PROCESSING SYSTEMS

Period

I semestre dal Oct 1, 2018 al Jan 31, 2019.

Lessons timetable Moodle Seminars 0

To show the organization of the course that includes this module, follow this link:  Course organization

Learning outcomes

The course aims to provide the theoretical foundations of the theory of dynamical systems, using the state-space representation, with particular attention to the properties of linear time-invariant systems and to the methods for designing controllers for such class of systems.

At the end of the course the student should demonstrate that s/he able to analyze the structural properties of a linear dynamic system (e.g., reachability and observability) and its stability.

This knowledge will allow the student to: i) calculate the observability and reachability matrices; ii) design a state feedback controller; iii) design an asymptotic state observer; iv) apply the main results of the stability theory.

At the end of the course the student will have acquired the ability to define the technical specifications to design a modern control system and to choose the most appropriate design technique.

Furthermore, at the end of the course the student will be able to: i) work together with other engineers (e.g., electronic, automatic, mechanical engineers) to design advanced controllers for complex electromechanical systems; ii) continue the study autonomously in robust and optimal control for linear and non-linear systems.

Program

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.

State models:
- 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.

Reachability:
- main concepts and the reachability Gramian,
- state space control,
- standard form of reachability, canonical control form,
- PBH criterion of reachability,
- state feedback.

Observability:
- main concepts and observability Gramian,
- State estimation (open and closed loop),
- standard form of observability, canonical observation form,
- PBH criterion of observability.

Duality:
- overview of discrete time Kalman filter,
- overview of optimal linear, quadratic controller in discrete time domain.

Examination Methods

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.