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DC motor controller with feedback

Solenoid

Jun 4, 2012
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Jun 4, 2012
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Hello,

I have a semester project where I made a circuit where I control a DC motor with PWM. It has a feedback loop to compensate for the load. Now I made the circuit, it works, but I'm not sure about the theory behind it.

This is what the system looks like:
UEbyb.png


I have to prove that the speed (omega_m) is independent of the load M_m for a certain K value. G has an inner resistance of R_out. I have to find this theoretical K value.

U_m = U_i + R_m . I_m // only in stationary mode
U_i = K_e . omega_m // induced voltage
M_m = K_e . I_m // moment

This is how far I got with the math:

V_in = V_c + K . U_R = V_c + K . R . I_m
V_in = R . I_m + U_m + R_out . I_m + G . V_in // this is bizarre...

=> V_in = 1/(1-G) . (U_m + (R + R_out)I_m)

1/(1-G) . (U_m + (R + R_out)I_m) = V_c + K . R . I_m
1/(1-G) . (U_i + R_m . I_m + (R + R_out)I_m) = V_c + K . R . I_m
1/(1-G) . (K_e . omega_m + (R_m + R + R_out)I_m) = V_c + K . R . I_m

=> K_e . omega_m/(1-G) + (R_m + R + R_out)I_m . (1/(1-G) - K . R) = V_c

We want omega in function of V_c:

We find (1/(1-G) - K . R) = 0 => K = 1/((1-G)R)

Is this correct?
 
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