Hàm truyền của bộ điều khiển PID rời rạc là:

\({G}_{PID}\left. z \right.={K}_{P}+\frac{{K}_{1}T}{2}\frac{z+1}{z-1}+\frac{{K}_{D}}{T}\frac{z-1}{z}\)

\({G}_{PID}\left. z \right.={K}_{P}+\frac{{K}_{1}T}{2}\frac{z+1}{z-1}-\frac{{K}_{D}}{T}\frac{z-1}{z}\)

\({G}_{PID}\left. z \right.={K}_{P}-\frac{{K}_{1}T}{2}\frac{z+1}{z-1}-\frac{{K}_{D}}{T}\frac{z-1}{z}\)

\({G}_{PID}\left. z \right.=-{K}_{P}-\frac{{K}_{1}T}{2}\frac{z+1}{z-1}-\frac{{K}_{D}}{T}\frac{z-1}{z}\)