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3. Question 3 [25 marks] Consider a DC motor with armature control configuration described by the standard electro- mechanical equations of the DC motor with parameters: Ra = 1422 (resistance), La = 0.9-10-3H (inductance), km = 0.02 NmA-? (torque constant), Km = 0.02 Vradº's (emf constant). Assume Jm = 2.5-10-4kg m² for the inertia of the load. Note that km = km. The maximum voltage that can be applied to the motor is Vmax = 20 V. Friction terms should be ignored. (a) Draw a graph of the motor's steady-state characteristics corresponding to armature voltage values va = 10V and va = 20V. [5 marks) (b) The steady-state operation of the motor corresponds to a rotating frequency Om 5001/s under a load torque TL=0.01 Nm. What is the corresponding voltage input? [5 marks) (c) Following a mechanical fault, the load torque becomes Tu = 0.02 Nm. Is the above steady-state operation still achievable? [5 marks) (d) Under the approximation that the armature circuit inductance is null, obtain the ex- pression of the continuous-time transfer function from va to om [4 marks] (e) Following an electrical fault, the resistance becomes Ra = 1012. How does this fault affect the characteristic of the motor? [6 marks)