MAGLEV | Education

Model description:

The model of the MAGLEV system is unstable and nonlinear

$$ m\ddot{x}=mg-\dfrac{K_{c}V^{2}}{x^{2}}, $$

where $x$ is the metal ball position being the system output, $V$ is the system input as the voltage. Other parameters are $m$ as the mass of the metal ball, $K_c$ as constant for magnet circuit, and $g$ is the gravitational acceleration of 9.8 m/s$^2$. A free-body diagram is shown also in the attached image.

Type:

Academic, Mechanical

Form:

Input-output

Model order:

Time domain:

Continuous time

Linearity:

Nonlinear

Attachment:

MAGLEV.gif

Publication details:

Title	Identification of a class of unstable processes
Publication Type	Conference Paper
Year of Publication	2009
Authors	Shahab, M., and Doraiswami R.
Conference Name	5th IEEE GCC Conference & Exhibition, 2009.
Date Published	03/2009
Publisher	IEEE
Conference Location	Kuwait City
ISBN Number	978-1-4244-3885-3
Accession Number	11875656
Keywords	constraint theory, identification, least squares approximations, magnetic levitation, transfer functions
Abstract	Identification of a practical process, especially if unstable, is challenging as its model is generally stochastic and nonlinear. In this work we consider a class of unstable processes where the model is identified in a closed-loop operating regime. Important issues in identification are addressed, namely: identification scheme, the closed loop identification of unstable plants, choice of sampling period, and constraints on the estimated model parameters. Further the structure of the identified model may not be identical to that of the physical system due to noise artifacts, and inability to capture faster dynamics. Generally least-squares identification is employed to estimate the parameters of the system wherein all the coefficients of numerator and the denominator coefficients of system transfer function are estimated. In many practical system there are constraints on the model parameters. The identified coefficients using the conventional scheme may not obey the constraint. In this work a novel constrained least-squares identification scheme is proposed where in a priori known structural constraint is factored in parameter estimation. This scheme is evaluated on a physical magnetic lévitation system.
DOI	10.1109/IEEEGCC.2009.5734284