[ G(s) = \fracK\tau s + 1 ]

Is discretized (Tustin method, sampling time ( T_s = 0.05 ) s):

[ u[n] = u[n-1] + K_p(e[n]-e[n-1]) + K_i T_s e[n] + \fracK_dT_s(e[n] - 2e[n-1] + e[n-2]) ]