1. Consider a de electric motor attached to a rotational load with moment of inertia J through a gear box with gear ratio N and subject to an external disturbance torque 74. Then, the equations of motion of the system are described by Jö(1)=NK_J(1)-T₂(1) L di(1) + Ri(1) = v(1)-NK_(1) dt where 0(1), 8(1), and (1) are the load angular position, velocity, and acceleration, respectively, J₁ = J + N²J is the equivalent moment of inertia referred to the load side, J is the rotor moment of inertia, v(1) is the armature input voltage, i() is the current flowing through the armature windings, R and I are the resistance and inductance of the rotor armature, respectively, and K is the back emf (back electromotive force) constant. a) Let the state variables be x₁ = 0, x₂ = 0 and x₂ =i. Construct the state model of the system when the desired output is the angular position of the load 0. b) For the specific values K = 0.05 Nm/A, R=1.22, L=0.05 H, J = 0.0008 kg-m², J=0.02 kg-m² and N = 12, simulate the behavior of the system for zero initial conditions, T, = 0 and input voltage described by v(1)=3 V, 0≤1≤2 seconds and v(1)=-3 V, 2 <1 ≤4 seconds, using the Isim command of Matlab and using Simul ink with ode45 and ode23t solvers with variable sampling. Compare the simulation results.
1. Consider a de electric motor attached to a rotational load with moment of inertia J through a gear box with gear ratio N and subject to an external disturbance torque 74. Then, the equations of motion of the system are described by Jö(1)=NK_J(1)-T₂(1) L di(1) + Ri(1) = v(1)-NK_(1) dt where 0(1), 8(1), and (1) are the load angular position, velocity, and acceleration, respectively, J₁ = J + N²J is the equivalent moment of inertia referred to the load side, J is the rotor moment of inertia, v(1) is the armature input voltage, i() is the current flowing through the armature windings, R and I are the resistance and inductance of the rotor armature, respectively, and K is the back emf (back electromotive force) constant. a) Let the state variables be x₁ = 0, x₂ = 0 and x₂ =i. Construct the state model of the system when the desired output is the angular position of the load 0. b) For the specific values K = 0.05 Nm/A, R=1.22, L=0.05 H, J = 0.0008 kg-m², J=0.02 kg-m² and N = 12, simulate the behavior of the system for zero initial conditions, T, = 0 and input voltage described by v(1)=3 V, 0≤1≤2 seconds and v(1)=-3 V, 2 <1 ≤4 seconds, using the Isim command of Matlab and using Simul ink with ode45 and ode23t solvers with variable sampling. Compare the simulation results.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
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Chapter1: Introduction
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Transcribed Image Text:1. Consider a de electric motor attached to a rotational load with moment of inertia J through a gear box
with gear ratio N and subject to an external disturbance torque Ta. Then, the equations of motion of the
system are described by
JÖ(1)=NK_J(1)-T₂(1)
L di(1) + Ri(1)= v(1)-NK_o(1)
dt
where 0(1), 8(1), and ö(1) are the load angular position, velocity, and acceleration, respectively,
J = J + N²J is the equivalent moment of inertia referred to the load side, J. is the rotor moment of
inertia, v(1) is the armature input voltage, i(t) is the current flowing through the armature windings,
R and L are the resistance and inductance of the rotor armature, respectively, and K. is the back emf
(back electromotive force) constant.
a) Let the state variables be x₁ = 0, x₂ = 0 and x3 =1. Construct the state model of the system when the
desired output is the angular position of the load 0.
b) For the specific values K = 0.05 Nm/A, R=1,2 2, L=0.05 H, J = 0.0008 kg-m², J = 0.02
kg-m² and N = 12, simulate the behavior of the system for zero initial conditions, T = 0 and input
voltage described by v(1)=3 V, 0≤1≤2 seconds and v(1)=-3 V, 2 <1 ≤4 seconds, using the Isim
command of Matlab and using Simulink with ode45 and ode23t solvers with variable sampling.
Compare the simulation results.
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