Where the transfer functions of the controller and plant are given byhc(s) =s+ 1sandhp(s) =1s+ 2respectively. letx(t) =au(t) for parts () below.(a) show that limt→[infinity]y(t) =a.(b) determine the error signale(t) =x(t)−y() does the system track the input signal (i. e., does limt→[infinity]e(t) = 0) if the transferfunction, hc(s), of the controller is changed tohc(s) =1s−2? justify your answer.

For the closed feedwater heater below, feedwater enters state 3 at a pressure of 2000 psia and temperature of 420 °f at a rate of ix10 ibhr. the feedwat extracted steam enters state 1 at a pressure of 1000 psia and enthalpy of 1500 btu/lbm. the extracted er leaves at an enthalpy of 528.7 btu/lbm steam leaves as a saturated liquid. (16) a) determine the mass flow rate of the extraction steam used to heat the feedwater (10) b) determine the terminal temperature difference of the closed feedwater heater