An Accurate Model by Using the Legendre Polynomial Functions of a Dual Stator Induction Machine Dedicated to the Static Eccentricity Diagnosis

2007 ◽  
Author(s):  
R. N. Andriamalala ◽  
H. Razik ◽  
G. Didier ◽  
M. B. R. Correa ◽  
F. M. Sargos
Keyword(s):  
Legendre Polynomial ◽  
Induction Machine ◽  
Polynomial Functions ◽  
Accurate Model ◽  
Static Eccentricity

Optimal Control of Linear Distributed Parameter Systems by Shifted Legendre Polynomial Functions

1983 ◽  
Vol 105 (4) ◽  
pp. 222-226 ◽  
Author(s):  
Maw-Ling Wang ◽  
Rong-Yeu Chang
Keyword(s):  
Optimal Control ◽  
Boundary Value Problem ◽  
Legendre Polynomial ◽  
Boundary Value ◽  
Distributed Parameter ◽  
Polynomial Functions ◽  
Distributed Parameter System ◽  
Point Boundary ◽  
Parameter System ◽  
The Maximum Principle

The optimal control problem of a linear distributed parameter system is studied by employing the technique of shifted Legendre polynomial functions. A partial differential equation, which represents the linear distributed parameter system, is expanded into a set of ordinary differential equations for coefficients in the shifted Legendre polynomial expansion of the input and output signals. Expressing the performance index in terms of the expansion coefficients, we transformed an optimal control gain problem into a two point boundary value problem by applying the maximum principle. The two-point boundary value problem is reduced into an initial value problem, the solution of which can be easily obtained by the proposed computational algorithm. An illustrative example will be used to prove this point.

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