Problem $4.$ Steady$-$state Response

Now from the steady$-$state expressions obtained from problem$-3$ for armature current $i_a$ and motor speed $,$ you will be able to determine certain critical parameters of the motor $($i$.$e$.$ No$-$load speed, no$-$load current, stall torque, and stall current$).$ These critical parameters are defined as follows:

No$-$load speed: It is the motor speed when the load torque is zero $($i$.$e$.$ you need to put $T_L=0$ in the steady$-$state expression of $).$ This is the highest motor speed for a given input voltage.

No$-$load current: It is the generated armature current when the load torque is zero $($i$.$e$.$ you need to put $T_L=0$ in the steady$-$state expression of $i_a).$ This is the current generated in the motor when it is rotating at corresponding no$-$load speed.

Stall torque: It is the value of the torque that produces zero motor speed $($i$.$e$.$ you need to set $=0$ in the steady$-$state expression of $,$ and find $T_L).$ Remember, this found $T_L$ is so high that the motor can not rotate at all!

Stall current: It is the generated armature current when the load torque is equal to the Stall torque $($i$.$e$.$ you need to put the found expression for stall torque in the steady$-$state expression of $i_a).$

In this problem, assume the parameter values for a certain armature$-$controlled motor are:

$K_b=K_T=0\mathrm{.}2N*\frac{m}{A}$

$b=5{10}^{-4}N*m*\frac{s}{r}ad,R_a=0\mathrm{.}8$

The manufacturer's data states that the motor's maximum speed is $3500$ rpm $,$ and the maximum armature current it can withstand without demagnetizing is $40$ A $.$ Now we want to know whether the motor can be operated with a certain applied voltage. In order to ensure that, you need to compute those steady$-$state parameters mentioned above for that input voltage. Therefore, compute a$.$ No$-$load speed, b$.$ No$-$load current, c$.$ Stall torque, and d$.$ Stall current and determine whether the motor can be operated with an applied voltage of $v_a=10V.$ Hint: Remember, for an input voltage, No$-$load speed must be lesser than the maximum speed, and No$-$load current and Stall current must be lesser than the demagnetization current declared by the manufacturer. PLEASE DO IN MATLAB CODE