P6.4 A feedback control system is shown in Figure P6.4. The controller and process transfer functions are given by

G(s) K and G(s) = = s+100 s(s+25) and the feedback transfer function is H(s) = 1/ (s + 50). (a) Determine the limiting value of gain K for a stable system. (b) For the gain that results in marginal stability, determine the magnitude of the imaginary roots. (c) Reduce the gain to one-third of the magnitude of the marginal value, and determine the relative stability of the system (1) by shifting the axis and using the Routh-Hurwitz criterion and (2) by determining the root locations. Show the roots are between -4 and -5.