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forward transfer function of a unity feedback system is given by, G(S)=1(S2+2S+3)

Using first principle

i. Determine the position error & steady state error for a unit step input.

ii. Obtain the equation for close loop response in time domain C(t) due to step input.

iii. What is steady state error of close loop response for ramp and parabolic inputs?

1 Answer
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G(S)=1(S2+2S+3)

Position error kp= lim(S0) G(S) H(S), H(S)=1

=lim(S0) 1(S2+2S+3) x 1

kp=13

For unit step input, magnitude A=1

ess=A(1+kp)=1(1+1/3)

ess=0.75

Comparing the given equation with second order standard equation

(w2n)(S2+2ξwnS+w2n)

w2n=3

Therefore,wn=1.732

2ξwn=2

Therefore, ξ=0.577 underdamped system

Θ=〖tan^(-1)(1ξ2)ξ]

Θ=tan^(-1)(10.577)0.577]

=54.76

Θ=0.9557 radians wd=wn (1ξ2)

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