A model for designing digital PID (proportional plus integral plus derivative) controllers, in the time domain and the frequency domain, according to given specifications is proposed. The model makes it possible to establish a parallel between the analog PID controller and the digital PID controller so that the design can be performed using the already known behavior of each part of the controller (PD and PI). Other models have been examined to find the best representation of the digital PID controller from an analog PID controller previously designed. Design and simulation have been done for a second- and third-order system plant. The proposed model allows the easy identification of the PD and PI terms with respect to the analog PID controller, does not introduce any undesired overshoot to the system, and allows the cancellation of the phase distortion introduced by the zero-order hold (ZOH) of the digital representation of the plant.
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