A unity feedback system has a forward path transfer function G(s) = $\frac{10 (1 + 4 s)}{s^{2} (1 + s)}$ . If the system is subjected to an input r(t) = 1 + t + $\frac{t^{2}}{2}$ , the steady state error of the system will be

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UPPSC AE Electrical 29 May 2022 Official Paper I

Answer 1

Concept:

The steady-state error for different inputs is given by:

Ka = position error constant = $lim_{s \to 0} G (s) H (s)$

Kv = velocity error constant = $lim_{s \to 0} s G (s) H (s)$

Ka = acceleration error constant = $lim_{s \to 0} s^{2} G (s) H (s)$

Steady-state error for different inputs is given by

Calculation:

Given, $G (s) = \frac{10 (1 + 4 s)}{s^{2} (1 + s)}$

$r (t) = 1 + t + \frac{t^{2}}{2}$

Type = 2

Error = $\frac{1}{K_{a}}$

$K_{a} = L t \overset{s = 0}{\to} s^{2} G (s)$

$K_{a} = L t \overset{s = 0}{\to} s^{2} \frac{10 (1 + 4 s)}{s^{2} (1 + s)}$

K_a = 10

Error = $\frac{1}{10}$

Error = 0.1