Nonlinear Systems

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

Models of nonlinear dynamic systems, state space analysis of nonlinear systems and typical phase portraits, comparison of linear and nonlinear systems, simulation. Software for analysis of nonlinear systems. Stability by Lyapunov, the first and the second method. Equilibrium states, periodic solutions, describing functions. Triangular systems. Control algorithm design, exact linearization, Lie algebra. Differential geometry, feedback linearization. Multi Input-Multi Output discontinuous and discrete-time systems. Adaptive control. Bifurcations, chaos and fractals. Theory of Catastrophes.

Requirements:

Syllabus of lectures:

1. Models of nonlinear dynamic systems. Examples

2. Analysis of nonlinear system dynamics in state-space

3. Stability of nonlinear systems. Ljapunov stability

4. Equilibrium states and periodic solutions

5. Absolute stability. Stability analysis based on describing functions

6. Numerical algorithms for analysis of nonlinear systems

7. Design of nonlinear control systems

8. Exact linearization methods. Lie algebra

9. Differential geometry. Feedback linearization

10. Nonlinear systems with multiple inputs and outputs

11. Discontinuous and discrete nonlinear systems

12. Adaptive control of nonlinear systems

13. Chaos in nonlinear systems. Fractals

14. Catastrophe theory. Synergetics. Examples

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. Razím, M.: Nonlinear Control Systems (In Czech). Lecture Notes ČVUT, Praha 1997

2. Khalil, H.K.: Nonlinear Systems. Prentice Hall Inc. London, 1996

3. Sastry S.: Nonlinear Systems. Springer Verlag Inc. New York, 1999

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory elective course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory elective course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory elective course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory elective course)