Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Differential equations, Linear algebra, Complex numbers

The course aims to provide the theory fundamentals of the dynamic systems and some interesting problems about the automatic control theory. This is achieved through a mathematical model based approach. This model is used both to evaluate the behavior of continuous-time and discrete-time systems, and to define and evaluate important aspects of the behavior of the considered dynamical system, starting from the definition and the study of certain model properties, such as stability, controllability, observability, its permanent and transient regime. The mathematical model is also studied to design state- or output-feedback laws in order to improve the stability of the overall system. Course provides an essential understanding of linear system characteristics, the fundamental aspects of the automatic control theory, and the techniques that are the bases for more advanced design methods. At the end of the course, the student knows the modeling and analysis concepts and methods for studying dynamic systems, with an emphasis on the linear time-invariant single-input, single-output, continuous-time and discrete-time systems. The student is able to apply the main analysis techniques to linear or linearizable dynamic systems.

The course allows students to understand how to properly model and analyze different dynamic systems (such as electrical, mechanical, electronic, economic, environmental, management systems, etc.), with an emphasis to linear or linearizable dynamic systems. In detail, students are capable to derive the mathematical model of a real dynamic system and to describe it with a state-space or an input-output representation. Using the system model, the student is able to derive the system block diagram, identifying its input and output variables; the student is also able to study the main properties of the system such as internal and external stability, controllability, observability, transfer-function matrix, and to develop state or output feedback laws, and state observers.

The student should be capable to autonomously analyze and (critique) verify the system properties and, consequently, to assess the required actions to achieve the desired goals. Evaluation skills are also developed through the critical study of the proposed course-self-study books. The student can also evaluate her/his learning and written and oral communication skills, during the written and oral exam sessions which she/he has to attend. In addition, the course aims to stimulate interest and to develop her/his passion for using the systematic approach adopted during the course. The student who acquires this methodological approach, is definitely able to continue her/his course studies with a greater autonomy and successfully achievements

The course aims to provide the theory fundamentals of the dynamic systems and some interesting problems about the automatic control theory. In detail, analysis methods of linear time-invariant systems will be studied, in continuous-time and discrete-time, stability analysis and state- feedback and output-feedback techniques are addressed together with some methodologies to solve simple control problems. The various topics covered are as follows: - Introduction to dynamical systems - Linear Time Invariant Systems - Systems, Models and their classification - Inpunt-Output Models - State Variable Models - Non-Linear Systems Linearization - Block Diagram Algebra - Modelling of Real Physical Systems - Continuous-time and Discrete-time Systems - Time Domain Analysis of Input-Output Models - Time Domain Analysis of State Variable Models - Time-Domain Responses of Continuous and Discrete Time Model - Transient and Permanent Regime of Linear Systems - Modal Analysis - Laplace and Zeta Transforms - s-Domain Analysis - z-Domain Analysis - Internal and External Stability of Linear Systems - Lyapunov Stabilty: definitions and functions of Lyapunov stability - Structural properties: Reachability, Observability, Controllability, Detectability - State-feedback, output-feedback techniques and observers - Eigenvalue assignment - Introduction to controller design

The student skills evaluation is based on a term-end written exam and on an oral exam. The written exam consists on the resolution of different exercises relative to the course topics. The oral assessment consists on two questions regarding the topics covered during the course. Note that, for organizational reasons, both the written and oral exam may be held on the same day. In any case, the written and oral tests must be held in the same exam session. If the overall evaluation is not sufficient, the student must repeat both the written and oral test. During the course, additional and not mandatory tests may be held, which could be taken into account for the overall skills evaluation of the student.

In order to successfully pass the skills evaluation, the student must demonstrate, through the written test and the oral one, to understand the concepts covered in the course regarding the analysis of dynamical systems. Moreover, the student must demonstrate to know criteria and techniques for evaluating the performance of linear systems, in both discrete and continuous time. The student knowledge is required both from a theoretical point of view, showing that the student understands all topics of the course, and from a practical point of view, showing that the student is able to solve examples and exercises on analysis of dynamical systems.

During the written and oral tests, it is evaluated the student's independent ability to set and to solve problems regarding the course topics. It is also evaluated the ability to properly and corectly apply concepts, methods and tools, developed during the course.

The course adopts a 30-point system for final marking. To the written test and to each of the two oral questions, it is assigned a score between zero and ten. The overall grade, thirty, is the sum of these three scores. In order to obtain a positive evaluation, the student must achieve an overall score of at least eighteen. The maximum score, 30 points with distinction, is reserved to those students who have achieved the highest rating on both written test and oral test, and additionally who have shown a particular mastery of the topics covered during the course.

Paolo Bolzern, Riccardo Scattolini, Nicola Schiavoni, Fondamenti di controlli automatici 4/ed, McGraw-Hill Richard C. Dorf, Robert H. Bishop, Modern Control Systems, 12th edition, Prentice Hall

- Ingegneria Gestionale (Corso di Laurea Triennale Fuori Sede (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

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