Q3 Determine the closed-loop transfer function of the system shown in Figure Q3a. The plant transfer functions are: (a) 1 g1(s) = 52 + 1 4 92(s) = s+2 and the feedback transfer functions are: h1(s) = 0.25s h2(s) = s+1 R(s) C(s) g1(s) 82(s) h(s) h2(s) Figure Q3a Please see overleaf for part (b)... Continued overleaf Page 3 of 11 (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter 'a' for which the system shown in Figure Q3b is stable. Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) s+4 s2 +s+9 Figure Q3b
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Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
Probability of Error
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![Q3 (a)
Determine the closed-loop transfer function of the system shown in Figure
Q3a. The plant transfer functions are:
1
g1(s) =
g2 + 1
4
92(s) =
s+2
and the feedback transfer functions are:
h1(s) = 0.25s
1
h2(s) =
s+1
R(s)
C(s)
g1(s)
82(s)
h(s)
h2(s)
Figure Q3a
Please see overleaf for part (b)...
Continued overleaf
Page 3 of 11
(b)
Using the Routh-Hurwitz criterion, find the range of values of parameter
'a' for which the system shown in Figure Q3b is stable.
(i)
Is the system stable for a = 30? If not, how many positive (unstable)
poles does it have?
(ii)
R(s)
E(s)
C(s)
a
s2 +s+9
Figure Q3b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc012420-4d67-48a3-8e85-bac83b5d2ff3%2F75bd0705-6135-476f-979a-09adbf31617f%2Fv8nehll_processed.jpeg&w=3840&q=75)
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