consider the transfer function Y(s)/U(s) = G(s) = b/(s+a) Now find a and b
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2. (20 points) Consider a second-order system whose transfer function is G(s) = Y(s)/U(s) = 10/((s+1)(s+2)), where U(s) and Y(s) are the Laplace transforms of the input u(t) and the output y(t), respectively. The initial conditions are zero, i.e., y(0) = 0 and y'(0) = 0. (a) (10 points) Suppose that the input u(t) = A+5e^-t (A : constant) is applied to this system. Determine the value of A such that the final output (y(∑) = lim y(t) as t→∑) is 50. (b) (10 points) Now, the input u(t) = sin(t) is applied to this system. Determine the maximum amplitude of the steady-state output (i.e., the output after a sufficiently large amount of time).
Adi S.
For the system shown: a. Find the transfer function Y(s)/X(s) in terms of G1 and G2. b. For G1(s) = (4s + K) / s^2 and G2(s) = 1 / (s + 2) find the characteristic equation of the closed-loop system. c. Determine the condition on the gain K for stability.
Madhur L.
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