Teaching code

4S009000

Teacher

Paolo Fiorini

Coordinator

Paolo Fiorini

Credits

9

Language

English

Scientific Disciplinary Sector (SSD)

ING-INF/04 - SYSTEMS AND CONTROL ENGINEERING

Period

Semester 1 dal Oct 3, 2022 al Jan 27, 2023.

Lessons timetable Moodle Seminars 0

Learning objectives

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.

Prerequisites and basic notions

The course requires knowledge in Mathematical Analysis I and II, Physics I and II, Linear Algebra and Geometry, Fundamentals of Computer Science.

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:

Bibliography

Didactic methods

The course will consist of lectures in the classroom, along with shared slides, notes and possible additional material that could be useful to deepen the topics, and practical exercises in the classroom

Learning assessment procedures

The exam consists of two parts, a written test and an oral test. The written test consists of exercises on the topics covered in teaching aimed at assessing both the level of learning and understanding of the theoretical foundations studied during the course and the ability to put them into practice, critically, to solve engineering problems. The oral exam will deal with the theoretical insights of the course.

Evaluation criteria

At the end of the course, the student must demonstrate that:
1. have fully understood the main issues inherent to the course, both in a continuous and discrete context.
2. have a critical view of the issues addressed during the course and the results obtained from the application of specific methods;
3. knowing how to apply the knowledge acquired to solve in an appropriate way certain engineering problems of varying degrees of complexity;
Both parts (written and oral) will be carefully evaluated, thus giving equal importance to the correctness and effectiveness of the solutions adopted in solving concrete problems, as well as to the understanding of theoretical concepts.

Criteria for the composition of the final grade

The composition of the final grade will be given by the sum of the evaluations of the theory part (2/3) and of the oral exam (1/3). The exam is considered passed if in each of the two parts a score greater than or equal to 18 is achieved. Each evaluation remains valid for the entire current academic year.

Exam language

Inglese / English