The plant transfer function for a particular process is G

Chapter , Problem 11.14

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The plant transfer function for a particular process is

                                                 \(G_p(s)=\frac{8-s}{s^2+2 s+3}\)

We wish to investigate the use of proportional control action with this plant.

a. Obtain the root locus and determine the range of values of the proportional gain \(K_P\) for which the system is stable.

b. Determine the value of \(K_P\) required to give a time constant of \(\tau=2 / 3\).

c. Plot the unit step response of the plant for \(K_P=1\). A process containing a negative sign in the numerator of its transfer function is called a "reverse reaction" process. What is the effect of the negative sign in the numerator of \(G_p(s)\)?

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