Question

2 In the block diagram below, G(s) -1/s, P(s)P(s) s-+2 s+2 D(s)- k-oo Ше-ks[1-e-s/1001. The inverse Laplace transforms of these equations are g(t), p(t),p(t), and d(t), respectively. The parameter K scales the feedback k-0 D(s) R(s) G(s) P(s) C(s) P(s) A Consider for a moment, D(s)- 0. Simplify the block diagram in terms of G(s), P(s), P(s) and find the transfer function by substituting the equations given above B What are the zeros and poles of the system you obtained in part 2A in Cartesian coordinates and polar coordinates? C For which values of K is the system stable? D Now we consider D(s), which is an approximated train of δ-functions. Using the Laplace Transform table, find the inverse Laplace transform, d(t). Sketch the relation as a function of t. Label axes Set the input R(s)-0 and write the transfer function C(s)/D(s). Do not substitute for G(s), P(s) P(s), yet Determine the inverse Laplace transform of the transfer function C(s)/D (s) by substituting and de- composing with partial fractions when again R(s) 0 and K-2 E F

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