Answer the following by hand and without the use of AI. Thank you! 2.The transfer function of a simplified DC motor model is:N(s)=CtorV(s) Kemf Ctor+BRa+JaRaswhere Ctor is the torque constant, Kemy is the back EMF constant, the load rotation is resisted bya torsional damper B, Ja is the equivalent inertia at the armature, and Ra is the armature resistance.With a unit-step input, find a) the D.C. gain of the system, b) the steady-state response, and c)the time when the system response reaches 63.2% of the final value.

Step 1:The time constant is actually τ.

Answered: 2. The transfer function of a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The differential equation of a DC motor can be described by the following equation Find the transfer function between the applied voltage ( Va)and the motor speed (thetadot m). What is the steady state speed of the motor after a voltage (Va = 10V) has been applied. Find the transfer function between the applied voltage (Va) and the shaft angle (thetadot m) .
3. Consider the following system described below (parameters and inputs are in SI units): Im = 0.4 R = 0.18 k=30 b = 0.2 M m = 6 b=20 www Im T(t) = 2 R Mr Bammy Note: b is the damping coefficient between the mass and the ground (it is shown as c in the diagram, but we will use b). Complete the following: a) Find an equation of motion for the simplified equivalent mass system. Assume that the shaft between the inertias is rigid. b) Find the equations of motion in state variable form for this system. You should end up with 2 state variable equations. c) Numerically solve for the state variables and plot each state variable versus time. Assume, that the mass is initially displaced a distance of 0.1 in the positive direction and the mass velocity is initially zero. Also plot the spring force and damping force. d) This system is required to have a maximum displacement overshoot that is less than 15% of the steady state value to avoid the rack impacting another portion of the machine.…
AUTO CONTROLDNO COPIED ANSWERS, SHOW FULL SOLUTION The differential equation of a DC motor can be described by the following equation Find the transfer function between the applied voltage ( Va)and the motor speed (thetadot m). What is the steady state speed of the motor after a voltage (Va = 10V) has been applied. Find the transfer function between the applied voltage (Va) and the shaft angle (thetadot m) .
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Solve the following question by hand and without the use of AI. Use detailed mathematical expressions to solve the problem and please do not use AI. Thank You!
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2. The equations of motion of this system are; 12Y+7Y+24Y-6Z"-122-0 6Z" +6Z"+12Z-6Y-12Y=f(t) 7W+7W+14W-7Y'-14Y=ft) Where Y,Z and W are deformations of the masses and springs. Put these equations into state variable form and express the model as matrix vector equation if output of the system is Y. Energy Storage Element m1 m₂ M3 k₁ k₂ k₂ State Variable X₁ = Y' X₂ = Z' X3 = W' X₁ = Y X5 = Z X6 = W Sea Suspension Wheel Road Datum leve
Answer the following by hand and without the use of AI. Thank you!
Example 3: Find the transfer function of the diagram shown below, which contain of a motor coupled to an inertial load through a shaft with a spring constant K. A non-rigid coupling between two mechanical components in a control system often causes torsional resonances that can be transmitted to all parts of the system. MOTOR Jm Bm m K Om K 0₁. LOAD JL
1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂
2 Problem The transfer function of the mass-spring-damper system discussed above is determined to be: G(s) - X(s) F(s) = 100 s²+5s+100 where x(t) is the displacement of the mass and f(t) is an arbitrary force input. We wish to study how the system responds to changing the frequency of the input, w when the forcing function is a sinusoid f(t) = A sin(wt) with A = 2. As part of your analysis, the following is requested:
2. The equation of motion for a damped multidegree of freedom system is given by Where [m] = [m]{x} + [c]{x} + [k]{x} = {f} [100 = 0 0 0 10 0 10. 1000-4 {f} [c] 8 –4 0 8 – 4 -4 4 0 8 4 = 100 2 0 = Focos(wt) -2 -2 The value of Fo 50N and w 50 rad/sec. Assuming the initial conditions to be zero and using the modal coordinate approach, find out the steady state solution of the system in the modal coordinate for first mode. Plot the steady state solution using the computational tools. 0 −2], [k] = = 2

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