Question

R = 1 ? L = 0.015 H Kt = 0.040 Nm/A Ke = 0.068 V·s/rad c = 0.006 N·s/m I = 10.5 · 10?? Armature Controlled DC Motor Consider this armature controlled DC motor. You can calculate the angular velocity ? of the inertial element with moment of inertia I that is being rotated by the DC motor using the following model. I d?/dt = Kt i - c? L di/dt = -Ri - Ke? + v(t) The parameters L and R are respectively the inductance and resistance of the motor armature (windings on the rotor), while i denotes the current passing through the armature windings. Constants Ke and Kt are the so-called “Back emf” (back electro-magnetic force) and torque constants, respectively. A bearing supports the shaft opposite of the motor and creates a torque due to viscous friction. The resistance torque created by the bearing is proportional to the angular velocity ? of the shaft with the damping coefficient c being the constant of proportionality. Numerical values of all parameters are enclosed next to the figure above. (a) (5 points) Let z1 = ? and z2 = i . Rewrite the above equations in matrix form [?1; ?2] = A [z1; z2] + bv(t) where v(t) is the input voltage into the motor armature. Please note that A is a 2 by 2 matrix, while b is a 2 by 1 vector. You need to determine the 2 by 2 matrix A and 2 by 1 vector b. If you cannot do that, please continue the rest of the problem using A = [1 2; 3 4], b = [5; 6] These are not the correct matrices and if you use them, you will obtain only up to 60% of the points available in this problem.

          R = 1 ?
L = 0.015 H
Kt = 0.040 Nm/A
Ke = 0.068 V·s/rad
c = 0.006 N·s/m
I = 10.5 · 10??

Armature Controlled DC Motor

Consider this armature controlled DC motor. You can calculate the angular velocity ? of the inertial element with moment of inertia I that is being rotated by the DC motor using the following model.

I d?/dt = Kt i - c?
L di/dt = -Ri - Ke? + v(t)

The parameters L and R are respectively the inductance and resistance of the motor armature (windings on the rotor), while i denotes the current passing through the armature windings. Constants Ke and Kt are the so-called “Back emf” (back electro-magnetic force) and torque constants, respectively. A bearing supports the shaft opposite of the motor and creates a torque due to viscous friction. The resistance torque created by the bearing is proportional to the angular velocity ? of the shaft with the damping coefficient c being the constant of proportionality. Numerical values of all parameters are enclosed next to the figure above.

(a) (5 points)
Let z1 = ? and z2 = i . Rewrite the above equations in matrix form
[?1; ?2] = A [z1; z2] + bv(t)
where v(t) is the input voltage into the motor armature. Please note that A is a 2 by 2 matrix, while b is a 2 by 1 vector. You need to determine the 2 by 2 matrix A and 2 by 1 vector b.
If you cannot do that, please continue the rest of the problem using
A = [1 2; 3 4], b = [5; 6]
These are not the correct matrices and if you use them, you will obtain only up to 60% of the points available in this problem.

R = 1 ?
L = 0.015 H
Kt = 0.040 Nm/A
Ke = 0.068 V·s/rad
c = 0.006 N·s/m
I = 10.5 · 10??

Armature Controlled DC Motor

Consider this armature controlled DC motor. You can calculate the angular velocity ? of the inertial element with moment of inertia I that is being rotated by the DC motor using the following model.

I d?/dt = Kt i - c?
L di/dt = -Ri - Ke? + v(t)

The parameters L and R are respectively the inductance and resistance of the motor armature (windings on the rotor), while i denotes the current passing through the armature windings. Constants Ke and Kt are the so-called “Back emf” (back electro-magnetic force) and torque constants, respectively. A bearing supports the shaft opposite of the motor and creates a torque due to viscous friction. The resistance torque created by the bearing is proportional to the angular velocity ? of the shaft with the damping coefficient c being the constant of proportionality. Numerical values of all parameters are enclosed next to the figure above.

(a) (5 points)
Let z1 = ? and z2 = i . Rewrite the above equations in matrix form
[?1; ?2] = A [z1; z2] + bv(t)
where v(t) is the input voltage into the motor armature. Please note that A is a 2 by 2 matrix, while b is a 2 by 1 vector. You need to determine the 2 by 2 matrix A and 2 by 1 vector b.
If you cannot do that, please continue the rest of the problem using
A = [1 2; 3 4], b = [5; 6]
These are not the correct matrices and if you use them, you will obtain only up to 60% of the points available in this problem.

Added by Sheena F.

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