NMR Quadrupolar Splitting Control Theory

Governing Equation

$$ f_{split} = \lvert 3\cos^2 \theta – 1 \rvert $$

where:
\( f_{split} \) = the normalised split frequency (between 0-2)
\( \theta \) = the spin angle (between 0-90 degrees)

This equation shows that a split frequency can potentially have two possible spin angles (when the split frequency is between 0 and 1). It also shows that the split frequency is 0 when the spin angle is approximately 54.7degrees (this is called the magic angle).

Perturb And Observe

Would a perturb and observe technique work, similar to MPPT (maximum power-point tracking) of solar panels? For one, it would have to be slightly different in operation, as one split frequency can correspond to multiple shear angles.

Solid-State NMR

This website has some good info.