Question

? Load Shaft 2: inertia $I_2$ 21 2 ?? ? Shaft 3: inertia $I_3$ Shaft 1: inertia $I_1$ ?? Feedback pot $V_m$ Motor $\theta_2 = \frac{1}{2}\theta_1$ $\theta = \frac{1}{4}\theta_2$ parameters: $R_a = 0.3 \Omega$ /// $J_1 = 0.01 kg. m^2$ /// $J_2 = 5 \times 10^{-4} kg. m^2$ /// $J_3 = 0.2 kg. m^2$ /// $K_t = 0.6 N. m/A$ /// $K_{pot} = 2 Volt/rad.$ Assume that the armature inductance, $L_a$, is small compared to the armature resistance, i.e. $L_a = 0$ carry out the modelling of the system using differential equations and find the transfer function $T(s) = \frac{\theta}{\theta_r}$ of the open loop and then the closed loop system.

          ?
Load
Shaft 2:
inertia $I_2$
21
2
??
?
Shaft 3:
inertia $I_3$
Shaft 1:
inertia $I_1$
??
Feedback
pot
$V_m$
Motor
$\theta_2 = \frac{1}{2}\theta_1$
$\theta = \frac{1}{4}\theta_2$
parameters: $R_a = 0.3 \Omega$ /// $J_1 = 0.01 kg. m^2$ /// $J_2 = 5 \times 10^{-4} kg. m^2$ /// $J_3 = 0.2 kg. m^2$ /// $K_t = 0.6 N. m/A$ ///
$K_{pot} = 2 Volt/rad.$
Assume that the armature inductance, $L_a$, is small compared to the
armature resistance, i.e. $L_a = 0$ carry out the modelling of the system
using differential equations and find the transfer function $T(s) = \frac{\theta}{\theta_r}$ of
the open loop and then the closed loop system.

?
Load
Shaft 2:
inertia I2
21
2
??
?
Shaft 3:
inertia I3
Shaft 1:
inertia I1
??
Feedback
pot
Vm
Motor
θ2 = (1)/(2)θ1
θ = (1)/(4)θ2
parameters: Ra = 0.3 Ω /// J1 = 0.01 kg. m^2 /// J2 = 5 × 10^-4 kg. m^2 /// J3 = 0.2 kg. m^2 /// Kt = 0.6 N. m/A ///
Kpot = 2 Volt/rad.
Assume that the armature inductance, La, is small compared to the
armature resistance, i.e. La = 0 carry out the modelling of the system
using differential equations and find the transfer function T(s) = (θ)/() of
the open loop and then the closed loop system.

Added by Daniel W.

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