1. SylabUZ
2. Wydział Nauk Inżynieryjno-Technicznych
3. semestr zimowy 2021/2022
4. Automatyka i robotyka / Komputerowe Systemy Automatyki - Program Erasmus drugiego stopnia
5. Control theory

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Control theory - opis przedmiotu

Cel przedmiotu

1. To recognize the basic description methods of nonlinear control systems.

2. To familiarize students with analysis and synthesis methods for continuous-time control systems based on Lapunov's theory.

3. To familiarize students with the methods of formulating and solving optimal control problems.

Wymagania wstępne

Zapisz zmiany

Mathematical analysis, Linear algebra, Control Engineering

Zakres tematyczny

Introduction to nonlinear systems. The most common nonlinear systems. The state space representation. An equilibrium point. Typical behaviour of nonlinear systems. Limit cycles.

 Analysis of dynamic properties of nonlinear systems with the phase plane method. The second order nonlinear systems; graphical representation with phase portraits. Singular points. Graphical and numerical methods for generating of a phase portrait. Stability analysis of  nonlinear systems by using the phase plane method.

Stability analysis. Different definitions to a nonlinear system stability. Lyapunov’s linearization method. Lyapunov’s second (direct) method. Global asymptotic stability analysis. La Salle's theorem. Stability of time-varying nonlinear systems. Instability theorems. Absolute stability criterions. A sector nonlinearity. Popov and circle criterion. Controller synthesis based on  Lyapunov’s method.

 The describing function method. Definitions of a limit cycle and characteristics. The existence theorem. Definition of the describing function. Describing function for systems with input saturation, output deadzone and hysteresis respectively. Using the describing function method for limit cycle analysis. Stability analysis of a limit cycle.

 Feedback linearization. Mathematical basics of feedback linearization. Lie’s algebra. Input-output linearization. Linearization conditions. Controllability conditions. Algorithm for an input-state linearization. Normal forms. Diffeomorphism. Algorithm for an input-output linearization. Internal dynamics. Asymptotic properties of nonlinear minimum phase systems.

Metody kształcenia

Lecture, laboratory exercises.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture – obtaining a positive grade in written or oral exam.

Laboratory – the main condition to get a pass is scoring sufficient marks for all laboratory exercises.

Literatura podstawowa

1.       D. Atherton, An introduction to Nonlinearity in Control systems, Ventus Publishing, 2011.

2.       H. K. Khalil, Nonlinear Systems,  3^rd edition, Prentice Hall, 2002.

3.       S. Skogestad, I. Postlethwaite: Multivariable feedback control. Analysis and design. John Wiley and Sons, 2^nd edition, 2005.

4.       P. Albertos, A. Sala : Multivariable control systems: An engineering approach, Springer, London,  2004.

5.       K.J. Åström, R.M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, Princeton, 2009

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr hab. inż. Wojciech Paszke, prof. UZ (ostatnia modyfikacja: 30-08-2021 11:23)