Question

I need help with this question for my Experimental Measures class. I will rate whoever can help with the answer!

Show that the equations below are solutions to the 2d order system with a constant input driving function. φ sin-1 (VE)

Answer 1

SOLUTION:

Here, a constant input driving function, u(t)=KA is given to the system.

Let a constant input as follows be given to the system yu(t) = {kA t greaterthanorequalto 0 0 t < 0 Laplace transform L(u(t)) = kA/s = u(s) we know, the transfer function of a second order dynamical system is G(s) = w_n^2/w_0^2 + s^2 + 2 sigma w_n s y(s) = kA/s w_n^2/w_0^2 + 2 sigma w_ns + s^2 = k_1/s + k_2s + k_3/w_n^2 + 2xigma w_ns + s^2 ie kAw_n^2 = k_1(w_n^2 + 2 sigma w_ns + s^2) + (k_2s + k_3)s kAw_0^2 = k_1w_n^2 + (k_1 + k_2)s^2 + (k_1 2 sigma w_n + k_3)s comparing coefficients, k_1 = kA k_2 = -k_1 = -kA k_3 = -k_1 2 sigma w_nA = -2 sigma w_n kA \r\n Rightarrow y(s) = kA/s - kA_s + 2 sigma w_n kA/w_n^2 + 2 sigma w_n s + s^2 = kA[1/delta - kA_delta + 2 sigma w_n kA/w_n^2 + 2 sigma w_n s + s^2

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