2. Modeling of a DC motor 2.1 [2pts] Write down the system equations for the following armature-controlled DC motor and draw its block diagram representation AIL A vb Armature circuit The system parameters are: Symbols Description Units Volts Armature voltage Amps Armature current LR Armature resistance Ohms Armature inductance Henry vb Motor back emf Volts LT N-m Motor torque kg-m Rotor inertia IT Load torque rad s Angular speed of motor C Damping coefficient IN-m-srad Note that in your system equations, vb needs to be expressed in terms of Kb, the back emf constant, and co And the torque T needs to be expressed in terms of ia and KT, the torque constant. 2.2 12pts] Determine the values of Ra, La, Kb, KT using the Maxon A-max26 datasheet. Use motor number 110947. Be sure to check the units. Assume c 1.26x10 N-m-s/rad 2.3 [2pts] Assume a constant input armature voltage of 5V, calculate the steady state no-load motor current (in) and speed (c). 2.4 [7pts] Using MATLAB, develop a Simulink model to solve the system. Assume a constant input armature voltage of 5V. Submit the plots of the no-load co and ia, for 0 Sts0.5s. 2.5 [2pts) Calculate the input armature voltage needed to spin the motor at 2500rpm with no load. 2.6 [2pts Assume the input armature voltage is a pulse width modulated (PWM) waveform as shown below with a maximum amplitude of 5V. Determine the duty cycle such that the average voltage value is the same as the voltage calculated in part 1.5 above