A feedback control system is shown in the following diagram.

The pmcess transfer function is G(s) = K(s + 40), s(s + 10)
and the feedback transfer function is H(s) = 1/(s + 20).

(a) DeleTmine the limiting value of gain K for a stable system.
339

(b) FoT the gain that resv.lts in ·marginal stabildy, determine the magnitude of the imaginary roots.

(c) Reduce the gain to 1/2 of the magnitude of the marginal value and determine the relative stability of the system (1) by shifting the axis and us·ing the Routh-H11.Twitz criterion and (2) by determining the mot locations.
Show that the mots are between -1 and -2.
Problem