**Magnetic Levitation SYSTEM IDENTIFICATION**

A fundamental concept in science and technology is that of mathematical

modeling. System identification is conducted to obtain the plant transfer function

needed for the control design. Once a good model is obtained and verified, a

suitable control law can be implemented to compensate the plant instability and

improve performance.

**Analytical Model**

Analytical and experimental plant models were obtained for comparison

and verification. According to T. H. Wong, laboratory-scale maglev systems are

represented with electrical and mechanical equations [1]. Figure 3 shows the RLC

coil circuit that displaces the steel ball using electromagnetism.

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**Determination of the Levitation System Model**

The force/current/displacement relationship in the considered equipment given in Fig. 5

is extremely difficult to determine using an analytic method. Moreover, the obtained approximate

analytical expression f(x, i) is very complex for the further experimental purpose

[3]. However, the magnetic force characteristics may be experimentally calibrated as

a function of the applied current I and the ball position X. Namely, the experiment could

be consisted of resting the levitation metallic sphere on a non-magnetic stand directly

under the electromagnet. This special kind of xyz-stage (some solutions are shown in

Fig.8(a)-(c)) should be capable, for example, of 1mm incremental positioning and determining

the minimum current required to pick up the ball at various heights. Then the

model of the force/distance relationship can be determined by means of least squares fitting.

Note, that the validity of such obtained curve is limited to some range

Xmin ≤ X ≤ Xmax. At the moment, in the Laboratory of Automatic Control at the Faculty of

Electronic Engineering in Niš, the problem of the remote placement of the steel sphere

among the vertical axis of the electromagnet is still not realized adequately. Hence, this is

one of the basic problems in remote control of MagLev system in the underdeveloped

web-based laboratory at the Faculty, which was established in order to support learning in

automatic control. For now, as shown in Fig. 8, it is expected that the ball be placed along

the electromagnet vertical axis by the laboratory technician.

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Magnetic Levitation System

General Description

The process consists of a disk whose position can be controlled by a top and a bottom coil. Depending on which coil is used, this system can be either open loop stable (using the bottom coil) or unstable (using the top coil). Disk position is measured by laser sensors. The coil voltage is limited to [0, 3] V .

Initial tests perform system identification to quantify

the plant parameters and measure the strong

nonlinearities. Early experiments demonstrate application

of simple linear closed loop control to stabilize

and regulate the closed loop system about some

setpoint. It is shown that for the open loop stable

plant, (see front page) the system is stabilizable for all

positive gains but that for the unstable plant a minimum

gain (bandwidth) is necessary for closed loop

stability. Further tests vividly show the effect of the

nonlinear dynamics on closed loop tracking control

(see upper plots). By inverting these dynamics, rapid

and precise tracking control is demonstrated.

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**Design and Implementation of a Controller for a**

**Magnetic Levitation System**

**System Analysis and Design**

1. Dynamic Model Analysis

The magnetic levitation system in this paper is

illustrated in Figure 1a; it keeps a steel ball suspended

in the air by counteracting the ball’s weight with

electromagnetic force. x(t) is the distance between the

steel ball and the electromagnet. X0, the reference

position, is the proper levitation distance. The electromagnetic

force, f(x,t), acts on the ball, which can

be expressed as the following dynamic formula in an

upward direction according to Newton’s law.

Control system block diagram of the magnetic levitation

system.

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**Design of Magnetic Levitation Controllers Using Jacobi Linearization, Feedback Linearization and Sliding Mode Control**

THE goal of this project was to design three (one linear;two nonlinear) magnetic levitation controllers for the system shown in Fig. 1. Despite the fact that magnetic levitation systems are described by nonlinear differential equations [2], a simple approach would be to design a controller based on the linearized model (Jacobi linearization about a nominal operating point [6]). But this means the tracking performance deteriorates rapidly with increasing deviations from the nominal operating point. Nevertheless, a controller based on Jacobi linearization is a good ”litmus test” for our system identification, hence this controller is designed first.

**II. SYSTEM IDENTIFICATION (BART AND KEVIN)**

A. Physical Description of the System Components (KEVIN)

In Fig. 1, the different components are:

_ HV oltage to Current Inverter: This subsystem converts the output voltage from our controller into input current for the electromagnet .The reason for using this system is to separate the power amplifier (for a high current sink like the electromagnet) from the controller.

_ HSensor Electronics: For our Jacobi Linearization based controller, we use a simple red LED and a photoresistor. The reason for this is we emperically found that we need large gain values for the Hall Effect sensor solution. But for our nonlinear controllers, in order to sense a wider range of motion for the ball, we obtained data from two Melexis [4] Hall Effect sensors s1 and s2. We need two sensors instead of one because we emperically determined that the reading from a single sensor is

saturated by the magnetic field of the electromagnet. We are able to subtract the readings of the two sensors to get a nonlinear voltage function for the position of the ball.

_ Electromagnet: This is our plant, the model is derived below.

_ Controller: Designing this subsystem was the goal of this project. Again, as stated earlier, we were only able to design and implement the Jacobi linearization version.

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**Buy Cheap Magnetic Levitation Toy**