A feedback control sys tern is shown in Figure P6.4. The controller and process transfer functions are given by
Gc(s) = K and G(s) = s + 40 / s(s + 10)
and the feedback transfer function is H(s) = l/(s + 20).
(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 half 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 -1 and -2.
Figure P6.4
Non unity feedback system.

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Controller Process Y(s) Sensor H(s)