3. The main difference
The main difference between those structures is the effects of setting coefficients on the controller’s behavior. The parallel form allows for a complete decoupling of proportional, integral and derivative actions whereas with a standard structure a modification of the Kp coefficient will affect proportional, integral and derivative actions. It is the reason why people who manually set the controller rather use the parallel form.
The serial form is sometimes implemented in control automaton available on the market. There is a second way to formulate it:
Cserie(s) = (1+τ1)(1+τ2)⁄τi(1+τNs)
This formulation eases the link between time constants of the process and setting parameters of the controller, particularly with the two real zeros in the numerator.
In the industry sector, standard and parallel form are the most common. Then, with Simulink software, the “PID controller” block can be set to standard (“Ideal”) or parallel form.
Another important aspect of parallel and standard PID: they are not able to cancel the integral action. This results in the inability to turn this kind of PID into a PD controller.