Try to use eigenfunctions to solve please 5. Consider the inverted pendulum in Fig. 1 In this case, the input to the system is the torque x(t) at time texerted by the motor connected to the end of the pendulum. The output y(t) is the angle of the pendulum fromthe vertical line.The following differential equation, describes a linearization for the input-output characterization of such apendulum around = 0 (for simplicity, parameters of the system including pendulum mass, pendulum length,and g are all assumed to be 1):d²y(t) dy(t)+- y(t) = x(t).dt2dtCompute the transfer function H(jw) of this linearized system.y(tx(t)Figure 1: The schematic view of an inverted pendulum system connected to a motor.

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Answered: 5. Consider the inverted pendulum in…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

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Q1) Figure below shows two pendulums suspended from frictionless pivots and connected at their midpoints by spring. Assume that each pendulum can be represented by a mass M at the end of massless bar of length L. Also assume that the displacements small and linear approximations can be used for sin (0) and cos (0). The spring located in the middle of the bars is unstreched when 0, = 02. The input force is represented by f(t), which influences the left-hand bar only. (a) Obtain the equations of motion, and sketch a block diagram for them. (b) Determine the transfer function T(s) = 0, (s)/F(s). [P.S. For small angle, sin (0) × 0 , cos (0) z 1] L/2 fin Q2) A robot includes significant flexibility in the arm members with a heavy load in the gripper. A two mass model of the robot is shown in the figure below. Find the transfer function Y(s)/F(s). Fuy м т
. You are given the following First Order Differential Equation. The current ? is in Amps and the time t in seconds. Calculate the time constant T. 20 dit+60i(t) = 200 Put your answer in milli-seconds in box below with no units.
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2. A DC motor has the angular displacement-to-applied armature voltage transfer function: Om(s) 1 E„(6) s(s+) %3D Ea(s) 15 a. If a 75Vdc step input is applied to armature at t=0.0s, what will the final motor speed equal? b. Write the differential equations relating the angular displacement, 0m (t) to the applied armature voltage, ea(t). c. Using 2b, write the state equations describing the dynamics of the system. с.
Please solve with steps
The damping ratio and peak overshoot are measures of: Speed of response Steady state error O Relative stability O Absolute stability
Determine the differential equation for the following mechanical system
A rotating load is connected to a DC motor with negligible inductance. A test result shows that the load reaches a steady-state speed of 60 rpm (revolutions per second) in 5 seconds when a constant voltage of 12 V is applied to the motor terminals. Let the input be the terminal voltage v(t), and the output be the angular velocity w(t) of the load. (a) Determine the DC gain and the time-constant of the system. (b) Obtain the transfer function of the system.

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