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A feedback control system has the open-loop transfer function, GOL(s) = 0.5Kce–3s / (10s + 1). Determine the values of Kc for which the closed-loop system is stable using two approaches:

(a) An approximate analysis using the Routh stability criterion and a 1/1 Padé approximation for e–3s.

(b) An exact analysis based on substitution of s = jw.

A process control system contains the following transfer functions:

(a) An approximate analysis using the Routh stability criterion and a 1/1 Padé approximation for e–3s.

(b) An exact analysis based on substitution of s = jw.

A process control system contains the following transfer functions:

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