7.7 Consider the following first-order systemsSystem I:i+x =rSystem II:2.x +x =rSystem III:5x +x =rEvery system is subject to a unit step input. Assume zero initial conditions.(a) Obtain the step response of each system by Laplace transform.

The Step Response of a system is defined as its response to a unit-step input, u(t), or u(s)=1s. The…

Answered: Consider the following first-order…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Consider the following second-order, nonlinear system of ordinary differential equations, and its initial conditions. A. Linearize the right-hand sides of Eq. (4.1) and Eq. (4.2) about the stated initial conditions and simplify the resulting equations. B. Transform the results in (A) to Laplace space using Laplace transforms and simplify. All X(s) terms and Y(s) terms should be on the left-hand side of both equations and all other terms should be on the right-hand side of both equations. C. Solve for X(s) and Y(s). D. Convert the right-hand-sides of the results in (C) to a form where the individual terms may be transformed back to time space using inverse Laplace transforms. E. Apply inverse Laplace transforms to the result in (D).
Consider the following state equation: A) Design an integral controller u = –Kx + Ke xn to yield a maximum overshoot Mp = 0.05, a 2% settling time ts = 2 s, and a steady-state error ess = 0 in response to a step input. Note: Place one pole in the desired characteristic polynomial at s = –100 (the other two poles are fixed by the desired Mp and 2% ts ).
To this point, the work of days missed per month by workers at a large corporation has average 2.25. A new flexible workday arrangement has been introduced and it is hoped that by introducing this "flex time" that the average workdays miss per month will be reduced. Let alpha=.05 A) defined the appropriate parameter for this problem and then set up the appropriate Null and alternative hypothesis a. The average number of work days missed by all workers at a large corporation. Ho: x bar=2.25; Ha: x bar < 2.25 b. The average number of work days missed by all workers at a large corporation Ho: mu = 2.25; Ha: mu < 2.25 c. The number of work days missed by the workers d. The average number of workdays mess by the 20 workers at a large corporation. Ho: mu =2.25; Ha: mu. 2.25
To this point, the work of days missed per month by workers at a large corporation has average 2.25. A new flexible workday arrangement has been introduced and it is hoped that by introducing this "flex time" that the average workdays miss per month will be reduced. Let alpha=.05 A) Define the appropriate parameter for this problem and then set up the appropriate Null and alternative hypothesis a. The average number of work days missed by all the workers at a large corporation. Ho: x bar= 2.25; Ha: x bar < 2.25 b. the Average number of work days missed by all workers at a large corporation Ho: mu =2.25; Ha: mu < 2.25 c. Number of workdays mess by the workers d. The average number of workdays mess by the 20 workers at a large corporation Ho: mu =2.25 ; Ha: mu> 2.25 B) Flex time is tried out with a sample of 20 workers. The average number of days missed in the next month is 1.83 with a standard deviation of 0.71. Make any necessary assumptions and use the data to (a) calculate…
Let w(x) = 1 and α = β = γ = 1. Find the nontrivial stationary paths, stating clearly the eigenfunctions y (normalised so that C[y] = 1) and the values of the associated Lagrange multiplier.
Use laplace transform to find the initial-value problem of; a) y''-4y'=6e^3t-3e^-t; y(0)=1, y'(0)=-1
Convert the following state variable system differential equations into Single Input-Single Output (SISO) format. Apply Cramer’s rule to express the system as a second order dynamic system in terms of each of x1 and x2 as the output.

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Consider the following first-order systems System I: i+x =r System II: 2x +x =r System III: 5x +x =r Every system is subject to a unit step input. Assume zero initial conditions. (a) Obtain the step response of each system by Laplace transform.