Saturday 14 September 2019

voltage - Mistake in published paper about magnetic levitation?


As I was reading through this paper: Nonlinear Model & Controller Design for Magnetic Levitation System, I stumbled cross section 3.3 which I could not follow.


Summarizing section 3.3 Non Linear Model.


The magnetic levitation system can be described in terms of the following equations.



enter image description here


Equation (2) indicates that L(x) is a nonlinear function of the ball position x. Therefore we need to approximate the inductance for the MLS. The authors chose the following approximation:


enter image description here


They then proceeded to substitute into equation 2.


enter image description here


Should it be 2*C or simply C in Eq.5?


How did they end up with equation 5, from equation 2? I am having trouble understanding the origins of the negative sign (which I am sure that there is an explanation to) in the second equation of the image above, but also where the 2 in front of C has gone.


Is there a mistake here, or am I missing something? Can someone help me with the math and show how this was worked out?




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