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

Dear,

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.

Answer 1

[Sam Chak]

Hi @Joris Bogaerts

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 :

https://www.mathworks.com/help/control/ref/pidstd.html

The PD controller from the Ideal-type PID Controller Block has the form

https://www.mathworks.com/help/simulink/slref/pidcontroller.html#mw_8008046a-81c5-4ae0-9fd7-3834478483b3_sep_mw_88993414-f49e-4ddb-a92a-4bc5cd2fa840

Comparing both, then we can deduce that

You can also find the relationships between the gains for the Parallel-type PID Controller Block.

[Joris Bogaerts]

Thank you so much Sam

[Sam Chak]

You're welcome, @Joris Bogaerts. If you have a control issue with the Maglev system later, feel free to post a new question.