308 SAMPLED-DATA CONTROL SYSTEMS 
assumed that the voltage across the condenser is zero and the current 
through the inductor is unity. Thus, e.(0) = 0,7(0) = 1. The block 
diagram for the system is obtained as shown in Fig. 11.184. This dia- 
gram can be obtained step by step 
from the relationships between the 
transforms of the variables. Re- 
placing the integration operations by 
the numerical equivalent as expressed 
Fie. 11.17. Resistance-capacitance-in- by the sampled elements using the 
ductance network used in example. polygonal approximation of Fig. 
11.14, a sampled model shown in 
Fig. 11.186 is obtained. From the original assumptions and the differ- 
ential equations for the system are obtained the following series of 
relationships: 

é-O)s— 0 
CAD) See 
a0) al 
(0) = —2 
These constitute the inputs to the sampled model in Fig. 11.185. The 
z transform of the output H,(z) is obtained directly from this model and 
is found to be 
p= Ur eS Se 
~ OE) C2 = 2) Te 
If T is chosen to be 0.314, then E,(z) is found to be 
1 — 0.96421 
SOO) Sera pies oer 
Inversion of this expression by the method of long division generates a 
sequence of sample values which differ from the exact solution by no 
more than | per cent. 
11.6 Evaluation of Infinite Series 
One of the relationships developed in connection with the Laplace 
transform of an impulse-modulated sequence is useful in the evaluation of 
infinite series. It has been shown in Chap. 2 that the Laplace transform 
F*(s) of an impulse-modulated signal whose continuous Laplace trans- 
form is F'(s) can be expressed in the form of two different infinite series. 
This relation expressed in (2.27) was stated to be equivalent to the Poisson 
summation rule and was used as the basis of alternate forms of expression 
