# Comparing the control performance of a given closed loop system

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 ?