Reference no: EM133203360

Work the following problems:

1. A unity feedback system has the loop transfer function: L(s) = G_c(s)G(s) = K / ((s(s + 3)(s² + 4s + 7.84)

i. Find the breakaway point on the real axis and the gain for this point.

ii. Find the gain to provide two complex roots nearest the jω-axis with a damping ratio of 0.707.

iii. Are the two roots found in (b) dominant?

iv. Determine the settling time (with a 2% criterion) of the system when the gain of part (b) is used.

2. The loop transfer function of a single-loop negative feedback system is: L(s) = G_c(s)G(s) = K(s + 2.5)(s + 3.2) / (s²(s + 1)(s + 10)(s + 30))

i. This system is called conditionally stable because it is stable only for a range of the gain K such that k₁ < K < k₂. Using the Routh-Hurwitz criteria and the root locus method, determine the range of the gain for which the system is stable.

Please show work and plot this in MATLAB, If possible show the code as well.