A closed-loop sampled system with the reference input r(t) and the actual output c(t), as shown in block diagram fig. 6.1, consists of a system with the transfer function G, (s) in the feedforward path, a zero-order-hold in the feedforward path, two samplers which are synchronized with the sampling time T, and a system with the transfer function H(s) in the feedback path. The following transfer functions are given: 10 G,(s) = and H(s) s+10 r(t) c(t) z.o. h G,(s) H(s) Figure 6.1: Block diagram of closed-loop system a) Find the sampled-data transfer function G(z) = e of the closed-loop system C(2) R(z) as a function of the sampling time T. Hint: Check the sampler arrangement! b) Is the sampled closed-loop system stable for T = 10 [ms]? Please explain. %3D
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![A closed-loop sampled system with the reference input r(t) and the actual output
c(t), as shown in block diagram fig. 6.1, consists of a system with the transfer
function G, (s) in the feedforward path, a zero-order-hold in the feedforward path, two
samplers which are synchronized with the sampling time T, and a system with the
transfer function H(s) in the feedback path.
The following transfer functions are given:
10
G:(s) = and H(s) =;
s+10
r(t)
T
c(t)
z.o.h
G1(s)
H(s)
Figure 6.1: Block diagram of closed-loop system
a) Find the sampled-data transfer function G(z) =:
C(z)
of the closed-loop system
R(z)
%3D
as a function of the sampling time T. Hint: Check the sampler arrangement!
b) Is the sampled closed-loop system stable for T = 10 [ms]? Please explain.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1127a6ae-f493-475e-b31a-e239e843ebbc%2F4a3104a8-42b3-46cc-9959-c1dcf311b5de%2Fl1w6m8d_processed.jpeg&w=3840&q=75)
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