2 z-1
T z+1 (8-4)
where s Laplace operator (sec1'),
z z-transform operator, and
T sample period (sec).
Thus, the discretized compensator was converted to
S(2KcTd+K)z + K- 2KeCTd
T T
H(z) =
2 i + 1 z 2 i + 1
ST ) T (8-5)
And, the difference equation for implementation of the digitized compensator was
22Ti 2Kcd K) (K 2Kcd)
T T T
un = Un-1 + -en + Ien-1
2,i +2i +2i
)T T T (8-6)
where un and Un1 output control signal at time t and t-1, respectively, and
en and en-1 error signal calculated for time t and t-1, respectively.
For implementation, equation 8-6 was simplified as
un = B1 un-1 + Al en + A2e (8-7)
where
---- + 1 n
T 1i / (8-8)
(2T I+K
Al = T_____
T and (8-0)
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