Consider the following functions gs 10ss5s1 sketch the

Question

1. Consider the following unity feedback system:

G(s) = K(s+4)/s²+4s+8

Draw the root locus of the above system 0 < K < Infinity.

2. Consider the following functions,

G(s) = 10/s(s+5)(s+1)

a) Sketch the asymptotes of the Magnitude plot in the Bode diagram.

b) Determine the gain crossover frequency (the frequency at which 20log10|G(jω) = 0 dB) based on (a).

c) Also estimate the bandwidth frequency of this system based on the asymptotes in (a).

3. A feedback control system is shown in the following figure. The process transfer functions are:

G(s) = K(s+45)/s(s+20); H(s) = 1/(s+10)

a) Determine the limiting valued of gain K for a stable system using Routh-Hurwitz criterion.

b) For the gain that results in marginal stability, determine the magnitude of the imaginary roots.

4. A system is represented by the block diagram shown below:

a) Find the closed loop transfer function Y(s)/R(s).

b) Find the value of K required for an allowable steady state error of 3% or less for a step input [i.e. R(s) = 1/s].