DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 187 
If this remaining system is designed to be stable, the system will not fail 
completely, though its performance will deteriorate. 
Digital Data 
controller hold 


Fic. 7.22. System employing bypass digital controller. 
The relations which hold for a system like this one are more compli- 
cated because the continuous and reconstructed sampled signals are 
mixed. Referring to Fig. 7.22, it is seen that 
C(s) = G(s) E3(s) (7.68) 
Also, the command signal transform H;(s) is given by 
E3(s) = Bi(s) + Et(s) D*(s)H(s) (7.69) 
Substituting (7.69) into (7.68), 
C(s) = G(s)Ei(s) + G(s) H(s) D*(s) ET (s) (7.70) 
Now it is readily seen that 
He (S)e— hc (s) eat: (S) (eile) 
and Eas) a —acea(S) nas) (7.72) 
Substituting (7.71) and (7.72) into (7.70), there results 
C(s) = G(s) R(s) — G(s)C(s) + G(s) H(s) D*(s) R*(s) 
— G(s)H(s)D*(s)C*(s) (7.73) 
Collecting terms and solving for C(s), 
GG) G(s) Neal 
C(s) = 1 + Gs) R(s) + Tae aie) Oe (s) R*(s) 
ey Ta) H(s)D*(s)C*(s) (7.74) 
Defining A(s) as 
aC) us (7.75) 
where it is recognized that A(s) is the over-all transfer function of the 
continuous system with the digital controller omitted, (7.74) can be 
