Question

Concert the following pid controller into discrete form using difference equation x(k) ot x(Tk)

(1 0.091s (0.19s)A2) 1.9706

Answer 1

C(s) = 1.9706 * (1 + 0.091 s+ (.019s)2/s-0.1793 + 1.9706/s + 0.071 14.s

KThis is of the form $C(s)=K_p+K_i/s+K_ds$

where

K, 0, 1 793

K, 1.9706

Kd 0.07114

By forward Euler transform:

Given a sampling period $T_s$, the integral term $K_i/s$ can be represented in discrete-form by

K,T, 1-1

Similarly, the derivative term can be represented in discrete-form as

Kds

$K_dN(z-1)/((1+NT_s)z-1)$

discrete form is shown as:

$C(z)=K_p+K_iT_sz/(z-1)+K_dN(z-1)/((1+NT_s)z-1)$