A 140V permanent magnet DC motor has the following parameters: - Armature resistance Ra = 0.26 - - - Armature inductance La = 1.7 mH Back EMF constant K = 0.425 V/(rad/s). K₁ = KE Moment of inertia J = 0.00252 Kg.m² Coefficient of viscous friction B = 0.0001 Kg.m²/sec Part 1: DC Machine Modeling a) b) c) d) Using block diagrams, show the complete model of the DC machine including the electric model, torque equation and the mechanical model using the machine parameters above. Find the transfer functions H₁(s) and Ha(s) if, w = H₁(s) V₁ + H₂(s) T₁. Derive and plot the speed response (in rpm) for a step input voltage of 70V and 140V if the load torque is zero. Find the poles of the system and calculate the damping ratio, the overshoot and the rise time.