[attachment=7225]
MAGNETIC LEVITATION SYSTEM
plant consists of an electromagnet, an optic position sensor, a
ferromagnetic sphere and a power interface.
Due to the spherical shape the measurement is nonlinear and needs
to be electronically or digitally linearised.

Velocity estimation
For fast nonlinear and unstable dynamical systems, such as magnetic
levitation, high quality of control is essential.
The ball velocity measurement is a dicult task.
Measurements of position and current is used for the velocity
estimation.
state observers which along with diererent controllers will create a
nonlinear dynamical feedback structure.
Determine system observability.

Experiments will performed in Simulink with RTWT
All observer based structures are considered for both observer types.
All these structures, are forms of a dynamical feedback all of which,
except classical PID, are nonlinear.

We can simulate the following control structures:
PID controller with a nonlinear feedforward
PID controller with a nonlinear feedforward and a nonlinear Observer
Cascade linearising feedback with an observer

Classical PID control
Used as a comparison for nonlinear controllers, to show what
improvements can be made.
To show how large improvements are introduced to the system
through the replacement of numerical dierentiation with the
nonlinear observer.

CONTENTS
Introduction
Magnetic levitation system
Observability
High-Gain observer
Reduced observer with linear error dynamics
considered cntrol structures
Experiment
conclutions

Reference
1 J. Baranowski, P. Piatek, A. Piat , Nonlinear observer design for the
magnetic levitation system, Recent advances in control and
automation
2 W. Barie, J. Chiasson. Linear and nonlinear state-space controllers
for mag-netic levitation International Journal of Systems Science,
1996, vol. 27, no.11, pp. 1153-1163.
3 E. H. el Yaagoubi, A. el Assoudi, H. Hammouri (2004) High gain
observer: Attenuation of the peak phenomena Proceedings of the
2004 American Control Conference ACC (June 30-July 2, 2004,
Boston Massachusetts).
4 K. Rbenack, F. Lynch Observer design using a partial nonlinear
observer canonical form Int. J. Appl. Math. Comput. Sci., 2006,
Vol. 16, No. 3, 333-343.