Reference no: EM131085845
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].
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