A feedback control loop is used to control the temperature of a process fluid exiting a heat exchanger by manipulating t

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A feedback control loop is used to control the temperature of a
process fluid exiting a heat exchanger by manipulating the flow
rate of cooling water. The transfer functions of the process
(G p) and other components of the feedback loop
(G m, G v and
G c) are given as:
G p =
-5/(10s +1), G m =
1.5/(3s +1), G v =
-0.05/(5s +1), G c =
K c
The process has negative steady state gain, the control valve is a
linear air-to-close valve, and a proportional controller with gain
K c is used. Use the direct substitution
method to determine the upper limit on the value of
K c for stability of the feedback control
loop.
Kc = _________