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STUDIJNÍ PLÁNY
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Linear Systems

Přihlášení do KOSu pro zápis předmětu Zobrazit rozvrh
Kód Zakončení Kredity Rozsah Jazyk výuky
BE3M35LSY1 Z,ZK 6 3P+2S anglicky
Garant předmětu:
Petr Hušek
Přednášející:
Petr Hušek
Cvičící:
Petr Hušek
Předmět zajišťuje:
katedra řídicí techniky
Anotace:

The purpose of this course is to introduce mathematical tools for the description, analysis, and partly also synthesis, of dynamical systems. The focus will be on linear time-invariant multi-input multi-output systems and their properties such as stability, controllability, observability and state realization. State feedback, state estimation, and the design of stabilizing controllers will be explained in detail. Partially covered will be also time-varying and nonlinear systems.

Some of the tools introduced in this course are readily applicable to engineering problems such as the analysis of controllability and observability in the design of flexible space structures, the design of state feedback in aircraft control, and the estimation of state variables. The main motivation, however, is to pave the way for the advanced courses of the study program.

The prerequsites for this course include undergraduate level linear algebra, differential equations, and Laplace and z transforms.

Požadavky:
Osnova přednášek:

Systems and signals. Linear and time-invariant systems. Differential and difference systems. The concept of state, state equations.

Solving the state equations, modes of the system. Equivalence of systems. Continuous-time, discrete-time, and sampled-data systems.

Lyapunov stability, exponential stability, internal and external stability properties of linear systems.

Reachability and controllability of systems.

Observability and constructibility of systems. Dual systems.

Standard forms for systems, Hautus' tests, Kalman's decomposition.

Internal and external descriptions of systems, impulse response and transfer function. Poles and zeros of systems.

State realizations of external descriptions. Minimal realizations, balanced realizations.

State feedback, state regulation, pole assignment, LQ regulator.

Output injection, state estimation, LQ estimator.

Interconnection of systems, feedback controllers, stabilizing controllers.

State representation of stabilizing controllers. Separation property of state regulation and estimation.

Osnova cvičení:

For each exercise session, a list of exercises from the previous lecture is made available that the student is requested to solve and deliver the solutions prior to the session. Each session begins by a short test, then the exercise solutions will be checked and discussed, and difficult points will be explained.

Cíle studia:
Studijní materiály:

There are no formal prerequisites to register the course. However, an undergraduate course on systems and control.

The knowledge required for the course includes undergraduate level differential equations, linear algebra, Laplace and z transforms as presented in the recommended textbook (P. J. Antsaklis, A. N. Michel: A Linear Systems Primer, Birkhäuser, 2007 - Sections 1.2, 1.3, 1.5; Tables 3.1, 3.2, 3.3, 3.4; Appendix A).

Poznámka:

Stránky předmětu: http://moodle.dce.fel.cvut.cz/course/view.php?id=18 .

Rozvrh na zimní semestr 2023/2024:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Po
Út
místnost T2:C3-132
Hušek P.
16:15–17:45
(přednášková par. 1)
Dejvice
T2:C3-132
St
místnost KN:E-26
Hušek P.
16:15–17:45
(přednášková par. 1
paralelka 1)

Karlovo nám.
Laboratoř TŘ2
Čt

Rozvrh na letní semestr 2023/2024:
Rozvrh není připraven
Předmět je součástí následujících studijních plánů:
Platnost dat k 27. 3. 2024
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/cs/predmet6693706.html