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:
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?
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:
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?