Question

Please help me with QUESTION 2.

1. Consider the electrical system shown below, for which the input variable u, the output variable y, and the state variables xi and x2 have been specified. R L + C (a) Determine the state-space model of the system (b) Show that the transfer function (from u to y) has the form bis H(s)=2+ajs+ a0 by relating (ao, ai, bi) to (R, L, C) (c) Show that the frequency response function (from u to y) has the form Н jw) - 1 +jq by relating (wo, q, y) to (R, L, C) (d) Discuss how H(jw) varies with w, especially for values of w near wo Q000 2. Problem 1 provides various related models of the given system's physics. In this problem will add feedback to this system to improve its damping we (a) To add damping to the system, apply feedback of the form u to the model in Problem 1(a). With this feedback, and k is an adjustable coefficient. The units on k and R are identical; since this type of feedback adds virtual resistance, it is called damping injection. Determine the new state-space model obtained for this new "compensated" system replaces u as the external input 2019 by David G. Taylor. All rights reserved 1 of 2 (b) Show that it is possible to select k such that both eigenvalues of the compensated system are located at a common point of A and k in terms of (R, L, C) the negative real axis, say s -X; provide the values on (c) A nice way to compare the uncompensated system (Problem 1) and the compensated system (Problem 2) is to evaluate the eigenvalues of both systems assuming that the physical system has low damping, i.e. assuming R^ 0. Provide a sketch on the complex plane to illustrate how the uncompensated system and the compensated system have very different eigenvalue locations

Answer 1

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