What is a Pseudo Derivative controller
Because ideal derivative operation is not causal. For example if you want to calculate the derivative of a function at point a, you actually need to use the value of that function at a very small time after a. Depicted here (taken from https://calcworkshop.com/derivatives/limit-definition-of-derivative/):

For example, this is the s-domain representation of a sample PD Controller:
G(s) = K * (s + 3)
One of the first things we learn while stuyding s domain representations is, the fact that in order for a system to be causal; the degree of the numerator must not be greater than the denominator's degree. As you can see, the system above is non-causal; since the numerator degree is 1, whereas the denominator 0.
What you can do in that kind of situation is to, add a low-pass filter by simply adding a pole which is located at the far left-side plane. Such as:
G(s) = (K * (s + 3)) / (s + 40)
If you try to implement a derivative operation in a controller, you are probably going to experience some oscillations which are caused by the derivative action. When designing real-control systems I use, Backward Difference to make sure to be causal.