Nonlinear Systems

Prerequisite:

Theory of Dynamic Systems (XE35TDS)

The course is a substitute for:

Nonlinear Systems (E35NES)
Nonlinear Systems (X35NES)

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

State model of nonlinear dynamical systems and its analysis, Lyapunov's

stability, asymtotic stability and Lyapunov's methods. Control synthesis via

approximate linearization, „High-gain“ observers, gain scheduling.

Structural methods for the nonlinear control design. Basics of differential

geometry, Lie derivative, various types of exact feedback linearization.

Input-output linearization. Zero dynamics, minimum phase systems. MIMO

systems, decoupling.

Requirements:

Basic course of higher mathematic, basics of modern control theory (state-space description), basics in control (regulation, transfar functions, characteristics, Bode, Nyquist, Popov, etc.)

Syllabus of lectures:

1. State space model of nonlinear dynamical system, typical nonlinear phenomena, examples.

2. Further practical examples of nonlinear dynamical systems.

3. Mathematical basics. Existence and uniqueness of solutions, dependence on initial conditions and parameters..

4. Definitions and methods of stability analysis. Ljapunov's function method and approx. linearization method.

5. Analysis of stability of perturbed asymptotically and exponentially stable systems.

6. Control synthesis via approximate linearization and obust linear methods. High gain observers.

7. Control synthesis via approximate linearization and gain scheduling.

8. Structural methods in nonlinear control synthesis - basic notions, exact transformations of nonlinear systems.

9. Structural methods and various types of exact linearization. Zero dynamics and minimum phase.

10.Structural methods and some basics of differential geometry and advanced analysis.

11. SISO systems. Relative degree. Input-output linearization. Zero dynamics, minimum phase systems.

12. MIMO systems I. Vector relative degree. Input-output linearization.

13. MIMO systems. Zero dynamics, minimum phase systems.

14. MIMO systems. Decoupling.

Syllabus of tutorials:

1. Examples of nonlinear systems based on simulation, system analysis

2. Examples of nonlinear systems based on laboratory experiments, system

analysis

3. Definition of individual projects, laboratory models, for control systém

analysis and design

4. System modeling

5. Simulation model design

6. Simulation model testing

7. Stability analysis

8. Control task statement and control algorithm design

9. Control algorithm implementation

10. Controller validation in simulation

11. Feedback linearization

12. Bang-bang control design

13. Implementation of a bang-bang controller, testing in simulation

14. Defend of the report

Study Objective:

Study materials:

[1] H. K. Khalil, Nonlinear Systems. Third edition. Prentice Hall 2002. .

ISBN 0-13-067389-7.

[2] M. Vidyasagar, Nonlinear Systems Analysis, Second Edition. SIAM Classics

in Applied Mathematiacs 42. SIAM 2002. ISBN 0-89871-526-1.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Science and Engineering (elective course)