An accelerometer with natural angular frequency on- 50 rad/s, damping ratio 0.6

Question

An accelerometer with natural angular frequency on- 50 rad/s, damping ratio 0.6 and static sensitivity K-5V/g is subject to a step acceleration of 2g. Witlh reference to the normalised step response curves shown in Figure Q3.1, determine approximate estimates of The maximum output voltage of the accelerometer during the transient. i ii) The time required for the output voltage to reach the maximum value 3 calculated in (i) above Damping coefficient 0.1 0.2 0.3 1.5 0.4 0.5 0.6 0.9 0.8 0.8 0.7 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 6 10 0 co.t Figure Q31

Explanation / Answer

i)Given figure shows output for A unit step input.For zeta =0.6 we see that peak ouput is 1.1.Since we are dealing with linear Time invariant system(This is a given because we are applying Classical Control theory and it is applicable for LTI systems)

Therefore if input is 2u(t) then output will be also multiplied by 2.So therefore for zeta =0.6 the peak output will be 2×1.1=2.2

ii)tp=peak time =?/wd

wd= wn×[(1-(zeta)^2)]^0.5

Now zeta =0.6 ,therfore wd=50×{1-0.36}^0.5=50×0.8=40rad/sec

therefore tp=?/40=0.078539 sec

We can verify this result by multiply tp with wn and checking the graph.So 0.078539×50=3.92

Which is very near to x coordinate of the graph.

Hope this helps...

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