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Problem 1: A system is governed by the ODE 4x + 2x = 3u(t). a) Find the transfer function T(s) from the input U(s) to the output X(s). Tu→x = b) Calculate the time constant T and steady-state gain kss. T = kss = c) Sketch the output x(t) for the input u(t) shown below with an initial condition of x(0) = 0. Each grid line marks 1 unit on both axes. 6 5 x(t) 4 3 2 1 -3 -4 -5 O 3 4 5 6 。 -1 -2 -6 0 Time

Problem 1: A system is governed by the ODE 4x + 2x = 3u(t). a) Find the transfer function T(s) from the input U(s) to the output X(s). Tu→x = b) Calculate the time constant T and steady-state gain kss. T = kss = c) Sketch the output x(t) for the input u(t) shown below with an initial condition of x(0) = 0. Each grid line marks 1 unit on both axes. 6 5 x(t) 4 3 2 1 -3 -4 -5 O 3 4 5 6 。 -1 -2 -6 0 Time

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 1: A system is governed by the ODE 4x+2x=3u(t). a) Find the transfer function T(s) from the input U(s) to the output X(s). Tu-+x= b) Calculate the time constant I and steady-state gain kss- T = kss c) Sketch the output x(t) for the input u(t) shown below with an initial condition of x(0) = 0. Each grid line marks 1 unit on both axes. 6 5 x(t) 4 3 2 1 -1 -2 -3 -4 -5 -6 0 Time d) You would like to make the system response time faster. Which option below is the best strategy for achieving this? (i) Increase the magnitude of the step input u(t). (ii) Introduce a saturation block to limit the magnitude of u(t). (iii) Use closed-loop control and increase the proportional gain Kp. (iv) Use open-loop control and increase the gain F. (ii) Tu→x (iv) (iii) Kp Tu→x F Tu→x
Transcribed Image Text:Problem 1: A system is governed by the ODE 4x+2x=3u(t). a) Find the transfer function T(s) from the input U(s) to the output X(s). Tu-+x= b) Calculate the time constant I and steady-state gain kss- T = kss c) Sketch the output x(t) for the input u(t) shown below with an initial condition of x(0) = 0. Each grid line marks 1 unit on both axes. 6 5 x(t) 4 3 2 1 -1 -2 -3 -4 -5 -6 0 Time d) You would like to make the system response time faster. Which option below is the best strategy for achieving this? (i) Increase the magnitude of the step input u(t). (ii) Introduce a saturation block to limit the magnitude of u(t). (iii) Use closed-loop control and increase the proportional gain Kp. (iv) Use open-loop control and increase the gain F. (ii) Tu→x (iv) (iii) Kp Tu→x F Tu→x
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