All the books I have read say that when a proportional derivative controller is used the natural frequency remains the same. However, this is true only when the proportional part of the PD is unity. Otherwise the natural frequency is multiplied by Kp i.e. if the original Characteristeric equation is s2 + 2Zwns + w2n (I am using Z instead of Zeta for damping ratio & w for frequency instead of omega - it's difficult to type those out) With a PD controller (P & D connected additively) the new charac eqn becomes s2 + 2Zwns + Kdw2n + Kpw2n So now natural frequency here is Kp multiplied by the original frequency. So why do all textbooks say that natural frequency remains unchanged by PD controller? Also, above, I have TF of the Controller to be Gc = Kp + Kds However, in one textbook, I noticed that they have the TF of the Controller to be Gc = Kp(1 + Kds) I tried to figure out why they have it this way I feel the above will be true only if they have the connection in the following way. After the proportional gain, the line is split (with a takeoff point). The Takeoff point does a positive feed forward before it's connected to the plant/process. There is the derivative controller in one path of the split & a unity gain on the other path. Is this a standard way of connecting a PD controller?