SylabUZ
| Course name | Control theory |
| Course ID | 06.0-WE-AutD-ConTheory-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | WIEiA - oferta ERASMUS / Automatic Control and Robotics |
| Education profile | - |
| Level of studies | Second-cycle Erasmus programme |
| Beginning semester | winter term 2018/2019 |
| Semester | 1 |
| ECTS credits to win | 7 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Laboratory | 30 | 2 | - | - | Credit with grade |
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.
Mathematical analysis, Linear algebra, Control Engineering
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.
Lecture, laboratory exercises.
| Outcome description | Outcome symbols | Methods of verification | The class form |
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.
1. D. Atherton, An introduction to Nonlinearity in Control systems, Ventus Publishing, 2011.
2. H. K. Khalil, Nonlinear Systems, 3rd edition, Prentice Hall, 2002.
3. S. Skogestad, I. Postlethwaite: Multivariable feedback control. Analysis and design. John Wiley and Sons, 2nd 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
Modified by dr hab. inż. Wojciech Paszke, prof. UZ (last modification: 29-04-2020 11:42)
