Question

The block diagram of a series cascade control system (with time in minutes) is shown in the figure: a primary PI controller $(K_{c})^{m}\cdot (τ_{Is}+1)/(τ_{Is})$ sets the setpoint for a secondary proportional controller $(K_{c})^{s},$ whose output drives the inner process 1/(2s+1), followed by the outer process 2/[(8s+1)(4s+1)]. For $τ_{I} = 8$ min and $(K_{c})^{s} = 1,$ the maximum value of $(K_{c})^{m},$ below which the cascade control system is stable, is ____ (rounded off to the nearest integer).

Official answer: 10