Digital PID Controller:

Digital control system offers many advantages over their analog counterparts. The PID controller in the continuous-data domain is described by

The proportional constant KP is implemented digitally by a constant gain KP. Since a digital

computer or processor has finite word length, the constant KP cannot be realized with infinite resolution.

The numerical integration rule that can be used to digitally approximate the integral controller KI/s

is Trapezoidal rule of integration

The time derivative of a function f(t) at t = kT can be approximated by the Backward difference

rule, using the values of f(t) measured at t = kT and (k -1)T.

A difference Equation model of PID Controller is

where

For programming convenience let here Y(z) and E(z) are the output and input of the PID controller

in the z domain

Where Y(z) and E(z) are the output and input of the PID controller.

Then Y(Z)=(a0+ a1Z-1+ a2Z-2)

and E(Z)=(1 - Z -1) M (Z)

using the inverse Z-transformation,

Y(K)=a0m(K)+a1m(K-1)+a2m(K-2)

m(K)=e(K) + m(K-1)

the above two equations are implanted in the programming.

Advantages :

1. The advantage of Digital controller over a analog control are higher immunity to environmental

changes such as temperature and ageing components.

2. More Advanced control algorithms such as adaptive control and non-linear control can be

implemented.

3. The ability to redesign the controller by changing the software(rather than hardware).

4. Digital control can be used to achieve power efficiency optimization.