9.4 Realizing a PID Controller: Causality and PIDF Controllers

Proportional-integral-derivative (PID) control!PIDF variant of

We are almost ready to use MATLAB to define and tune the controller, discretize it, and export it to a C header file for use on the target system. There is just one final consideration. To improve the robustness of the controller, we will implement a variation of a PID controller called a proportional–integral–derivative-filter (PIDF) controller. The only difference is that a low-pass filter is applied to the derivative term of the PID controller. However, properly designed, the PIDF performance will be similar to that of the PID.

A limitation of the ideal continuous PID controller, as described in Equation 9.4, is that it is noncausal: its transfer function has more zeros than poles. A noncausal system depends on future inputs, as well as current and past inputs. We cannot, of course, …