Course detail
Control Theory 2
FEKT-BPC-RR2Acad. year: 2023/2024
Analysis and synthesis of advanced control systems, especially nonlinear, is discussed in this course. Basic methods for nonlinear systems stability analysis, state trajectory behaviour evaluation and nonlinear control design are presented. Methods for robust control design and system parameters estimation are also described.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Entry knowledge
Rules for evaluation and completion of the course
30 points projects and tests done on seminars
Conditions for awarding the course-unit credit:
1. Active participation in exercises
2. Minimum of 10 points awarded for tests at exercises
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.
Aims
Student can:
- analyse nonlinear systems behaviour
- design nonlinear control systems
- analyse stability of nonlinear dynamical systems
- design control algorithms based on linearisation techniques
- design control structures based on relay control and sliding mode control
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
Kotek, Kubík,:Teorie automatického řízení II. (CS)
Razím, M., Štecha, J.: Nelineární systémy, ČVUT 1997 (CS)
Slotine, J., Weiping, L.: Applied Nonlinear Control. Pearson Education, 1990. (EN)
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2 Nonlinear systems state trajectories, equilibrium points.
3 State trajectory of the first and second order systems.
4 Phase trajectory, time computing using phase trajectory, limit cycle existence determination using index theorems.
5 Describing function method, harmonic balance method.
6 Nonlinear systems stability.
7 Nonlinear systems stability analysis using Lyapunov method.
8 Popovov's stability criterion, instability theorems. Nonlinear systems control using linear controllers, wind-up.
9 Nonlinear systems control - gain scheduling, exact feedback linearization.
10 Relay control systems, switched structure systems, time optimal relay control. Nonlinear systems solution existence.
11 Sliding mode control.
12 Identification of controlled plants parameters.
13 Summary.
Fundamentals seminar
Teacher / Lecturer
Syllabus
2 Describing functions, harmonic balance method.
3 Lyapunov stability.
4 Popov stability criteria. Non-linear systems control – gain scheduling, feedback linearization.
5 Relay controllers.
6 Sliding mode control
7 Summary
Exercise in computer lab
Teacher / Lecturer
Syllabus
2 Non-linear systems state trajectories, limit cycles, equilibrium states
3 Harmonic balance method, measurement of parameters for Ziegler-Nichols method using relay feedback experiment
4 Wind-up, exercise on BLDC motor
5 Linear control of non-linear systems, gain scheduling, feedback linearization
6 Sliding mode control, relay approximation
Elearning