7 Sate space modellingConsider a mechanical system based on a pendulum rotation on a metal axis, theequation is as follows:20(t) + 30(t) + 50(t) = 13u(t)1. What would he the simplified differential equation if we consider that the angle bpendulum and the normal is below 10°2. Calculate the transfer function of this system using two methods.

Given: To find: Transfer function

Answered: Sate space modelling Consider a…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.6P

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HW # 2-3 : Consider the following inverted pendulum. a) Obtain the differential equation describing the system. e sin 0 b) Find the transfer function. m c) Obtain the state equation in terms of vector-matrix form. e cos 0 mg the center of gravity of the pendulum as (xG, YG). Then P XG = x + l sin 0 M YG I cos e %3D
Problem Consider the following mechanical system consisting of a massless rod of length L connected to a ball of mass m. The system has a rotational damper b, a spring constant k, and is subject to gravitational acceleration g. The input into the system is a torque u(t). 4 torque input u(t) 10 L Lamb.. 'm k Derive and fully simplify the transfer function: gravity (s) U (s) G(s) Make sure to expand/cancel terms such that the numerator and denominator are each a polyno- mial in terms of s (with coefficients in terms of the constants of the problem: k, m, b, L as needed). Use small angle approximations.
Q5: Given the rotational system shown in below, find the transfer function G(s)= 01(s)/T(s) D K2 Please help ASAP. Pls show all steps and calculations. Make sure to find theta1(s)/T(s)
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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
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