Servo System Using Pole-Placement with State Observer for Magnetic Levitation System
The electromagnetic levitation system is a nonlinear system. The force applied by the electromagnet on the levitating magnet can be approximated a nonlinear model. The conventional controller with linearization of nonlinear systems design is presented wit
- PDF / 244,589 Bytes
- 6 Pages / 439.363 x 666.131 pts Page_size
- 99 Downloads / 191 Views
Abstract. The electromagnetic levitation system is a nonlinear system. The force applied by the electromagnet on the levitating magnet can be approximated a nonlinear model. The conventional controller with linearization of nonlinear systems design is presented without highly controlling performance enough. This paper is demonstrated the design of servo system using pole-placement with state observer for the magnetic levitation system from the equilibrium point. In addition, these closed-loop poles correspond to the desired closed-loop poles in the pole-placement approach and state observer estimate immeasurable state variables. Finally, the simulation and experimental results showed effective control objective. Keywords: Servo system, Observer, Magnetic levitation ball.
1
Introduction
Magnetic levitation technology has been widely used in various fields, such as high-speed trains, wind tunnel levitation for eliminating mechanical friction, magnetic bearings, decreasing maintainable cost and achieving high-precision positioning. However, it is difficult to build an accurate mathematical model for the magnetic levitation system because the magnetic levitation systems are unstable and nonlinear dynamical systems. In recent years, a lot of works have been reported in the literature for controlling magnetic levitation systems. The feedback linearization technology has been used to design controller for magnetic levitation system [3, 6]. The input-output, input state, and exact linearization techniques have been used to develop nonlinear controllers [12]. [7] Using Pole-Placement, Lead Compensator and PID Controller. The mathematical modeling and linearization, system design and control and observation using linear state feedback in the equilibrium point [4]. This paper is presented as follows. A mathematical model of the magnetic levitation system is shown in the part two. The third part demonstrates a design of servo system using pole-placement with state observer. The fourth part contains experimental and simulation results. The magnetic levitation system with the proposed control algorithm is implemented. James J. (Jong Hyuk) Park et al. (eds.), Future Information Technology, Lecture Notes in Electrical Engineering 309, DOI: 10.1007/978-3-642-55038-6_139, © Springer-Verlag Berlin Heidelberg 2014
921
922
2
T. Aunsiri et al.
Mathematical Description
The motion of the permanent magnet ball in the magnetic field is presents as m
d2y = − F (u , y ) + mg dt 2
(1)
Where y is the vertical position of the levitating magnetic measured from the bottom of electromagnet, m is mass of the permanent magnet ball, g is the acceleration due to gravity, and F (u , y ) = k i y 3 is the force on the levitating magnet generated by the electromagnetic, k is a constant that depends on the geometry of the electromagnetic strength. Moreover, if following from the Kirchhoff’s voltage law and the voltage across the hall-effect sensor induced by the levitating magnet and the electromagnet, which are a function of constants that dep
Data Loading...
