I am having a question about comparing the control performance of a given closed loop. In this link there are some characteristic values that need to be calculated, but there is no description of what they mean or their interpretation for example: the root-mean squared control error and root-mean squared change in the manipulated variable (manipulating effort).
This is the formula for the root-mean squared control error :
$$ S_e = \sqrt{\frac{1}{M} \sum e^2(k)} $$
Where the $e$ is the error
And root-mean squared change in the manipulated variable :
$$ S_u = \sqrt{\frac{1}{M} \sum \Delta u^2(k)} $$
where
$$ \Delta u = u(k)-u(\infty) $$
Could someone please explain their source or their interpretation ?