Nonlinear Systems

The course is a substitute for:

Nonlinear Systems (XE35NES)

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. Triangular systems.

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.Introduction and basic notions. State space model of continuous time and discrete time nonlinear dynamical system, typical nonlinear phenomena, examples.

2.Further practical examples of nonlinear dynamical systems.

3.Nonlinear systems analysis I. Basics of advanced analysis. Basic properties of nonlinear ordinary differential equations: existence and uniqueness of solutions and their dependence on initial conditions and parameters. Definition of Lyapunov's and asymptotic stability.

4.Nonlinear systems analysis II. Methods for stability analysis: Ljapunov's function method and approximate linearization method.

5.Nonlinear systems analysis III. Perturbations of asymptotically and exponentially stable systems.

6.Control synthesis via approximate linearization I. Robust linear methods and their use to handle nonlinearities in observers and stabilizers design. High gain observers.

7.Control synthesis via approximate linearization II. Gain scheduling.

8.Structural methods in nonlinear control synthesis I - basic notions.

9.Structural methods in nonlinear control synthesis II. Exact transformations of nonlinear systems, various types of exact linearization.

10.Structural methods in nonlinear control synthesis III. Some basics of differential geometry.

11.Structure and control of SISO systems. Relative degree. Input-output linearization. Zero dynamics, minimum phase systems.

12.Structure and control of MIMO systems I. Vector relative degree. Input-output linearization. Zero dynamics, minimum phase systems.

13.Structure and control of MIMO systems II. Decoupling.

14.Structure and control of MIMO systems III

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: