Question

Question 1: For the system shown in the above figure, assume that: G(s)=3+* +25-0.5, C6)=1+”,K20 1) Find the CLTE. 2) Using the Routh array criterion, find the range of K such that the system is stable. 3) In terms of K, obtain the Steady State Error of the above system given that the input is a unit ramp function.

I want a clear line solution

Answer 1

CLTE . [cc] [cc] 1+ [C6][66] (+5) enes-os) ++ft+Matt 25-os) _ stk 84 +3²+28² - 0.55 + stk Hence, CLTE 1 stk $4+53 +252 +0.55 +k of louth assay Characteristic criterion s + s +25² +0.5stk polynomial

si 2 k i 0.5 PP s² 112 - 1x0.5 lik lak o o o IS s' 105x0.5-k so k o o - Hence, fa stability, and k to 1.500.5 ak so 105 k-0.75 20 * and k so k<0.45 and ko Hence, ke (0, 0:+5) At k=0.75 ., the system is marginally stable.

_3 un Now, steady-state essor (e) it s. E(3) sto - - 4. s. [Ule) - You] at sto y (8) Slo() - Ul.GC ItGC.J fto att Sto 5.0(e) it Gres.CE) at sx ls² s to sis²+28-0.51 $40 S + stk). - ² + 3²4 25 -0.5. I