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.
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:
They then proceeded to substitute into equation 2.
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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