Answer Happy

Question 3 [25 marks] Figure 3 shows a motor and motor driver that has been created using an operational amplifier. A load is connected through a gear set. The motor armature has a mass moment of inertia of Ja and the load has an inertia J₁. Note that there is no damping on either the load or the armature, i.e. Da = D₁ = 0 Nm.s/rad. The parameters of the motor are given in the following table. Motor Parameters Kt Ra La Armature resistance Armature inductance v; (t) 1 [0] 0 [H] Other parameters relevant to the model (and their values) are given in Figure 3. a) Why does the torque constant, K₁, have the same numerical value as the back emf constant, K,,? [3 marks.] R₁ = 10[kn] b) Find the transfer function between the input voltage v, (t) and the motor armature current i(t). [15 marks.] R₁ = 1 [kn] c) If v; (t) = 100 u(t) is applied to the input of the system, calculate the final value ia (00). [7 marks.] Kb R₁ = 10[kn] iu (t) + ea(t) R₂ = 10 [2] Torque constant Back emf constant Figure 3 Ja DC Motor C 3 [Nm/A] 3 [V.s/rad] = 0.05 [kgm²] Da = 0 N₁ = 200 Nm = 20 Load J₁ = 95 [kgm²] D₁ = 0