Question

(s + 1) X X H(s) Figure 2 a) Find H(s) so that the closed loop (effective) transfer function of the system is (s + 9999) (s + 10000)(8 + 1) b) For typical step inputs, approximate the closed-loop system by a good first order system transfer function. Justify your approximation. c) What is the time constant of this first-order system. How long will it take for the system output to reach a value within 2% of the final steady-state value for a step-input? Note: H(s) is the ratio of 2 polynomials in s.

Answer 1

Solution → According to collect from the data → let us assume that the equations are → Now we have to consides that the data 3+1 closed loop into EL 46 @ To findout the Hes) should be a transfer function of the system are now we have to data will be write = 969) - Huis uknown then the positive feed back as followed - GES) (1+9999) —>0 T(s) = T-GM) HCS) Ts+10,000) (+) - (5+) (5410,000) > (5+1-10) = → +1) 8+9959) i šti #(s) [$410,000X1+1) = 4 (+9999) 3) HCS) = (+0)65795992_-- (stus+10,000) 100) => HOD=Lates) (5+9999)

good first order o - 6 They are closed-loop system should be system of the transfer function as tome will be take the equation TLs) = €79999). (st 10,000 + then satq999 and its of pole SE-1 $10,000 let us seal has the using dominat poles os s=-9999 and SF - 10,000 ið hny sloux st poles are then appronimation of Tcs) are 0.9995 sil © the time constant of the first-side system should be long suptem output should be reach values are 2% - T() = ie 10,000 > 9999>>S 9999 10,000 CS+ then A = 0.9999 then I=1. are man LAST st let us Tis) for the 27. band as followed Ts = 4T → (uxi) = 4 Tso use