Control Theory 2
BPC-RR2 FEKT BPC-RR2 Acad. year 2022/2023 Summer semester 6 credits
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
- 26 hrs lectures
- 13 hrs exercises
- 13 hrs pc labs
Kozubík Michal, Ing. (RG-3-02)
Richter Miloslav, Ing., Ph.D. (UAMT)
Subject specific learning outcomes and competences
- 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
Linear system control knowledge improvement. Learning of basic methods of nonlinear systems analysis and synthesis. Nonlinear systems control design, linearization, exact linearization, robust control.
Prerequisite knowledge and skills
The subject knowledge on the secondary school level is required. Knowledge of linear systems control (BRR1) and systems modeling (BMOD) is assumed.
- Slotine, J., Weiping, L.: Applied Nonlinear Control. Pearson Education, 1990.
- Khalil, H.K.: Nonlinear Systems. Prentice Hall, 2001.
- Gelb, A., Velde, W.: Multiple-input Describing Functions and Nonlinear System Design. McGraw-Hill, 1968.
Syllabus of lectures
1 Nonlinear systems description, basic nonlinearities, linearization.
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.
Syllabus of numerical exercises
1 State trajectories, isoclines method, linearization.
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
Syllabus of computer exercises
1 State equations, discrete controllers
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
70 points written exam
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
Teaching methods and criteria
Teaching methods include lectures, exercises and computer laboratories. Knowledge is verified using tests at exercises. Students have to write three assignments during the course.
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.
|Mon||comp.lab||even week||T12/SD 2.105||09:00||10:50||25||Richter|
|Mon||comp.lab||odd week||T12/SD 2.105||09:00||10:50||25||Richter|
|Mon||comp.lab||even week||T12/SD 2.105||14:00||15:50||25||3BIT||xx||Richter|
|Mon||comp.lab||odd week||T12/SD 2.105||14:00||15:50||25||Richter|
|Wed||exercise||even week||T12/SD 2.99||09:00||10:50||25||Friml, Kozubík|
|Wed||exercise||even week||T12/SD 2.99||11:00||12:50||25||3BIT||xx||Friml, Kozubík|
|Wed||exercise||even week||T12/SD 2.99||13:00||14:50||25||Friml, Kozubík|
|Wed||exercise||even week||T12/SD 2.99||15:00||16:50||25||Friml, Kozubík|
Course inclusion in study plans