Optimal Control of a Nonlinear Magnetic Bearing System Using the Trigonometric Collocation Method

2008 ◽  
Author(s):  
C. Nataraj ◽  
Steven Marx
Keyword(s):  
Optimal Control ◽  
Collocation Method ◽  
Degrees Of Freedom ◽  
Magnetic Bearing ◽  
Degree Of Freedom ◽  
Lookup Table ◽  
Base Excitation ◽  
Strongly Nonlinear ◽  
Trigonometric Collocation ◽  
Bearing System

Magnetic bearings are non-contacting, with the rotor being suspended between electromagnets, and therefore they can eliminate the need for lube oil and reduce machinery wear. The magnetic bearing is naturally unstable, and very nonlinear. This paper proposes a method designed to suppress the motion of a nonlinear magnetic bearing system rotor due to base excitation. The method combines PD feedback with feedforward optimal control, where a measured base motion is used to select a control signal designed to suppress the rotor response. The signal is generated from a combination of subharmonic frequencies and optimized coefficients stored in a lookup table. The trigonometric collocation method (TCM) is used to generate solutions for the four degree-of-freedom system made up of a shaft suspended at each end by a magnetic bearing. The TCM method uses a trigonometric series to simulate the multiharmonic behavior of each degree-of-freedom of strongly nonlinear systems. The method is easy to use and its advantage over numerical methods is that it demands less computation, particularly with higher numbers of degrees-of-freedom.

scholarly journals Using the Modal Method in Rotor Dynamic Systems

2003 ◽  
Vol 9 (3) ◽  
pp. 181-196
Author(s):  
Eduard Malenovský
Keyword(s):  
Finite Element Method ◽  
Collocation Method ◽  
Dynamic Systems ◽  
Theoretical Basis ◽  
The Finite Element Method ◽  
Transient Responses ◽  
Technical Application ◽  
Trigonometric Collocation ◽  
Rotor Dynamic ◽  
Modal Method

This article deals with computational modeling of nonlinear rotor dynamic systems. The theoretical basis of the method of dynamic compliances and the modal method, supplemented by the method of trigonometric collocation, are presented. The main analysis is focused on the solutions of the eigenvalue problem and steady-state and transient responses. The algorithms for solving this range of problems are presented. The finite element method, the method of dynamic compliances, and the modal method are supplemented by the trigonometric collocation method. The theoretical analysis is supplemented by the solution of a model task, which is focused on the application of the trigonometric collocation method. The solution of a technical application, which is a pump, is presented in this article.

scholarly journals A Fully-Discrete Trigonometric Collocation Method

1993 ◽  
Vol 5 (1) ◽  
pp. 103-129 ◽  
Author(s):  
W. McLean ◽  
S. Prössdorf ◽  
W.L. Wendland
Keyword(s):  
Collocation Method ◽  
Fully Discrete ◽  
Trigonometric Collocation
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