I just need help with units. I know how to convert Hz to rad/s, but I don\'t kno

Question

I just need help with units. I know how to convert Hz to rad/s, but I don't know how to convert the units in the transfer function.

The transfer function for a DC motor is: where w = angular rate of the motor shaft (red/s) Vin = inpur voltage across the motor (volts) J = 3 ibm ft2 /Shaft Inertia R = 5000Omega Resistance L = 300 H Inductance Kt = 300 Motor Constant Assuming a feedback system with block diagram Design H(s) to meet the following reguirements The closed loop natural frequency shall be greater than or equal to 3 Hz.

Explanation / Answer

better u convert all the unit to MKS or CGS and then use it.

as you know that general form of a second order system is S^2 + 2*gi*wn*S + wn^2. for the close loop system in the forward path we have H(S)*W/Vin and in the feedback path 1.

so from the new denominator, the transfer function becomes

S^2 + (R/L)S + (Kt^2/(LJ)) + (Kt/(LJ))*H = 0

here wn = sqrt((Kt^2/(LJ)) + (Kt/(LJ))*H)

so we can use the formula now

sqrt((Kt^2/(LJ)) + (Kt/(LJ))*H) > = 3 (in CGS or MKS)

here we will get a constant transfer funtion. the motive is that we generally take second order system not beyond that because of stability problem. even for higher order system we approximate that to scond order system.

thats why as it was alredsy a second oreder system we chose to have H(s) a gain factor only.

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