A dc motor develops 9 N-m of torque at a speed of 5400 rac/min when 20 volts is applied. Att voltage, the motor rotates at a rate of 13,500 rad/min when no load is connected to it. Find the transfer function, G(s) = 0,(s)/E,(s). Eal0) Motor I.

A dc motor develops 9 N-m of torque at a speed of 5400 rac/min when 20 volts is applied. Att voltage, the motor rotates at a rate of 13,500 rad/min when no load is connected to it. Find the transfer function, G(s) = 0,(s)/E,(s). Eal0) Motor I.

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

See similar textbooks

Similar questions

1) Guess the form and solve for the particular solution of a driven oscillator described by the equation: mx" + cx' + kx = Fosin(wt) 2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is driven by a force following the function Focos(at); where FO = 2 N. Find the driving frequency that causes practical resonance and find the amplitude. 3) Suppose there is no damping in a mass and spring system with m = 5, k = 20, and Fo= 5. Suppose is chosen to be precisely the resonance frequency. a) Find a b) Find the amplitude of the oscillations at time = 100, given that the system is at rest at / = 0.
Find the transfer function 04(s)/T(s). T(t) 04(1) 26 N-m-s/rad D4 = 3 J4 = 6 N1 = 26 N4= 120 Jj = 2 Dj = 1 N2 = 110 J2 = 1 D2=2 3 kg-m? N3 = 23 J3 = 1 D3 = 3
Consider the following spring system. m, C3 Cy m₂ C₂ Write the stiffness matrix K Write the matrix M ¹K C₁ = 6, m₁ = 6, C₂ = 12, m₂ = 3 Find the eigenvalues and eigenvectors of M ¹K: Smaller eigenvalue = with eigenvector • Larger eigenvalue = with eigenvector C3 = 18, C₁=6 If this spring system oscillates without any external forces present, then the position of each mass satisfies the following general formula: X 8 u(t) = (a₁ cos( t) + b₁ sin(t)) + (a2 cos (t) + b2 sin(t)) If the system begins oscillation with initial position u(0) = [] | and initial velocity (0) = [] then the position of the masses at time t is given by u₁(t): u₂(t):
6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
On rubber wedges modeled as spring and damperelectric motor with mass M placed in damped free vibrationit has been observed to oscillate 6 in 1 second when released, and the degree of damping is known to be 0.15.a) calculate the natural frequency of the system.b) calculate the mass of the engine, given as K=50000N/m.c) Moe imbalance in the rotor while the engine is rotating at 1000 rpmbecause of its value, the engine was observed to vibrate at an amplitude of 4 mm.Calculate the moe imbalance value of the rotor?d) the amplitude of the force transmitted to the ground while the engine is rotating at a speed of 1000 rpmcalculate.
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
Determine the settling time of the system having the transfer function O Ts = 0.1250 s O Ts = 0.4890 s O Tg = 0.2747 s O Tg = 0.7824 s c(s) 20 R(s) S+8
QUESTION 1 Consider the equations of motion of an armature controlled DC motor given by Jw(t)+bw (t) Ki (t) = di (l) L + Ri (t) + Kw (t) = -Tfriction - Tload (t) Vin (t), dt where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t). When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution. What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific notation. The constants are given below: Nominal voltage, Vin(t) = 17 V Moment of inertia of the rotor, J = 0.02 kg-m² Motor viscous friction constant, b = 0.009 N-m-s Friction torque, Tfric = 0.003 N-m Armature inductance, L = 0.1 H Armature resistance, R = 0.35 Back emf constant and motor torque constant, K = 0.21 N-m/A. **Recall that the time constant (or relaxation time) is…
1. Find the transfer function, c(s) - X;(s)/F(s), for each of the system shown In the figure below. a. K-5 Nim Ad, = 5 kg -3Nslm K=4 Nim M=4 ky M =5 kgAn K=4 N/m Siy - 2 N-sm Frictionless Sy =4N-s/m K-5 N/m e = 4N-s/m M4 kg 00O -M2 = 4 kg foy=4 N-s/m Sv4 N-s/m
T C We consider a rotating shaft. A torque T is applied, resuting in a rotation of the shaft. The bearing system and the output connections yield a viscous damping torque D. T: input torque 2: output angular velocity Dan: viscous damping = J: moment of inertia Governing equation (obtained using Euler equation for rotating solids): JN+an = T αΩ
A mass-spring system is driven by the external force g(t) = 2 sin3t + 10 cos 3t. The mass equals 1, the spring constant equals 5, and the damping coefficient equals 2. If the mass is initially located at y (0) =-1, with initial velocity y' (0) = 5, find its equation of motion to find y (1). Round up the answer to the second decimal place point.
9. Derive the transfer function X₂ (s)/F(s) for the mechanical system shown in Figure 2. Assume the following values: M₁ = 3 kg, M₂ = 2 kg, K₁ = 5 N/m, K₁= 3 N/m, D₁ = 1 N.s/m, wwwwwwww K₁ oooo Fo M₁ 0000 K₂ Figure 2 M₂ m 1(1)