所屬科目：研究所、轉學考(插大)◆自動控制
(1) (10%) If r(t) = 2cos (t + θ) and y(t) = Acos (t + 45°), obtain values of Oand A.
(2) (20%) Given a unit step input, it is known that. Determine y(t) using the inverse Laplace transform approach without solving differential equations.
3.(26%) With r(t) as the input and y() as the output, this problem considers a linear system that can be represented by where R(s) and Y(s) are the Laplace transforms of r(V) and y(t), respectively. With r(t) = cos21, it is known that the steady-state response of this system can be represented as Acos(at - π). Based on such information, please determine A, d, and T.
4.(24%) This problem considers six transfer functions G1 = 1/(s+1), G2 = 2/(s+2), G3 = 1/(s2+s+1),G4 = 3(s2+s+3), G5 =2/(s2+3s+2), and G6 = (s+10)((s2+s+10). Their step responses (AI, A2 , A6) are amplitude spectra (B1, B2 , B6) are given in the figures shown in the following pages. Please pair each of the transfer functions to one of the step responses and one of the amplitude spectra.(That is, if you think A1 is the step response of G1 and B1 is the amplitude spectrum of GI, write your answer for G1 as G1-A1-B1. Please present your answers in this way for all the six transfer functions considered in this problem.
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. Determine y(t)
using the inverse Laplace transform approach without solving differential equations.
where R(s) and Y(s) are the Laplace transforms of r(V) and y(t), respectively. With r(t) = cos21, it is known that the steady-state response of this system can be represented as Acos(at - π). Based on such information, please determine A, d, and T.
