What is the relation between filter coefficient (N) of Simulink pid block and filter time constant of MATLAB pid command? According to my experience they are not same or equal, there is some other relation between them
According to my understanding based upon simulation experiences,they both are almost inversely related. Is my understanding correct?
I have attached snapshots of both simulink pid model and MATLAB pid command and highlighted the confusing terms
\$N\$ equals \$\frac{1}{T_f}\$, to see this start with the third term of the block equation:
$$ \frac{DN}{1 + \frac{N}{s}} $$
rewrite the denominator:
$$ \frac{DN}{\frac{s+N}{s}} $$
this equals
$$ \frac{DNs}{s+N} $$
divide numerator and denominator by N and finally you get:
$$ \frac{Ds}{\frac{s}{N}+1} $$
now compare that with the other formula
$$ \frac{K_d s}{T_fs+1} $$
and you can identify \$K_d = D\$ and \$N = \frac{1}{T_f}\$
The derivative term in practical situations often needs some low-pass filtering. If you look at the equation to the right bottom you'll see that the right-hand term is the derivative of a low-pass filtered input, where N = \$\omega_0\$ of the LPF.
You would want the time constant of the filter (1/\$\omega_0\$) to be longer than the derivative time, but not too much longer, to keep the effect of noise in the error signal in check, but in the end it's another controller parameter, and as such the optimal setting is related to your situation (the amount and nature of noise in relation to the required derivative time constant for tuned response).
