Sketch the Nyquist diagram for a system with open-loop transfer function GH(s) = K(s-2) %3D (s+1)2 Discuss the range(s) of the gain K with system stability according to Nyquist criterion.

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3. In this problem, use the two closed loop systems given in the figure to answer the questions below. 4 R(s) K₁ 0.0099 In thin K₂ Y(s) R(s) K₁ 4 S(s) = 0.09 K₂ 0.09 (a) Show that these two systems have the same transfer function for K₁ = K₂ = 100 (b) Using the definition of sensitivity, S(s), for each system calculate the sensitivity to the parameter K₁ with K₁ and K₂ as variables. Recall: Y(s) OG G OG Gal (c) Substitute K₁ = K₂ = 100 into each S(s) and compare the sensitivities to parameter K₁.