Rewrite the compensator formula for a pd controller into the general formula.

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I'm currently working on a project where my team and I have to let a magnetic ball hover under/above a magnet and for doing so we would have to implement a pd controller in order to create the feedback in the system. However, the formula in my lecture notes states that the transfer function of a pd controller is H(s)=k*(1+(Td*N)/(N/s+Td)) with Td the time constant of the differentiator and k the gain. However in Matlab the compensator formula is given by H(s)=P(1+P/D*N/(1+N/s)). I think that D/P is proportional to Td and that P is proportional to K but I'm not sure about it. Any help would be welcome.

Accepted Answer

Sam Chak
Sam Chak on 3 Mar 2023
The PD compensator from your lecture note appears to have the same structure as the standard form of the PD controller, pidstd(Kp,Ti,Td,N), when :
The PD controller from the Ideal-type PID Controller Block has the form
Comparing both, then we can deduce that
You can also find the relationships between the gains for the Parallel-type PID Controller Block.

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