Notes on numerical control calculations
PID control applications - Temperature and position control

Control quality depends on the accuracy of the model identified. Continuous models (transfer function in p ) are generally more realistic, as their parameters have a physical "reality", such as an oscillation pulse or a time constant. The parameters of sampled models do not have this advantage, making it more difficult for the system designer to make a "realistic" identification. For this reason, only the control obtained by discretizing continuous models is presented here. However, the implementation of the control is, of course, digital. It is essential that the sampling period T is very small compared with the system's shortest time constants.

In this case, the calculation of the control from the error signal can be carried out based on the approximation...