ID: 0609
Course type: scientific and vocational
Course coordinator: Jovanović Ž. Radiša
Lecturers: Jovanović Ž. Radiša
Contact: Jovanović Ž. Radiša
Level of studies: M.Sc. (graduate) Academic Studies – Mechanical Engineering
ECTS: 6
Final exam type: oral
Department: Department of Control Engineering
• Building the foundations of nonlinear control design and analysis. • Introducing commonly used nonlinear control tools. • Analysis and control of nonlinear systems using Matlab/Simulink programming software.
On successful completion of the course the students should be able to: • Perform basis of dynamical analysis of certain classes of nonlinear systems. • Apply various methods for testing the system stability by Lyapunov techniques and input-output analysis. • Understand and use diferent control techniques of nonlinear systems. • Perform simulations, analysis and control of nonlinear systems using software package Matlab/Simulink.
Lurie's direct and indirect control systems. Linear and Aizerman Conjecture. Absolute stability. Popov's and Circle criteria. Tsypkin's trasnformation. Exact (feedback) linearization. Input-state linearization. input-output linearization. Zero dynamics and input-to-state stability. L2 gain and small gain theorem. Sliding mode control. Backstepping. Gain scheduling. Approximate methods. Describing function analysis. Modified Nyqiust criteria.
PA: Practical work includes computational exercises that follow the content of course: stability of Lurie direct and indirect systems; дerermination stability of nonlinear systems using linear and Aizerman conjecture; Popov's and circle criteria; exact (feedback) linearization: input-state linearization, input-output linearization; zero dynamics and input-to-state stability; sliding mode control: backstepping:gain scheduling; describing function analysis; modified Nyqiust criteria. PL: Application programming languages C and Matlab in the analysis, simulation and control of nonlinear systems. Practice and experiments: analysis, design and simulation of nonlinear systems; experimental application of nonlinear control algorithms using the PC and the software Matlab/Simulink on different control plants (DC servo motor, inverted pendulum, coupled tanks experiment, heat flow system).
Defined by curriculum of the study programme.
• Lj.Grujić, D. Lazić, Nonlinear systems, Lecture notes in electronic form. • Radiša Jovanović, Nonlinear systems 2, Lecture notes. • Modular educational real time control system with various control plants (DC servo motor, inverted pendulum, double inverted pendulum, heat flow experiment, coupled water tanks experiment), with acquisition hardware and software. • PC and PC Embedded controllers, Siemens Simatic PLC, National Instruments controllers. • Installation for control system testing and acquisition of electrical variables. • Intelligent Control Systems Laboratory, Control Systems Laboratory.
Total assigned hours: 75
New material: 20
Elaboration and examples (recapitulation): 10
Auditory exercises: 20
Laboratory exercises: 5
Calculation tasks: 5
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0
Review and grading of calculation tasks: 3
Review and grading of lab reports: 3
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 4
Test: 0
Final exam: 5
Activity during lectures: 5
Test/test: 50
Laboratory practice: 5
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 30
Hassan K. Khalil, Nonlinear Systems, 3rd Edition, Prentice-Hall, 2002.; Jean-Jacques E. Slotine, Weiping Li, Applied Nonlinear Control, Englewood Cliffs, NJ: Prentice-Hall, 1991.; Radiša Jovanović, Mаtlab and Simulink in Automatic Control, Faculty of Mechanical Engineering, Belgrade, ISBN 978-86-7083-896-3, 2021 (in Serbian).