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me375_sp11_hwk10_soln

# me375_sp11_hwk10_soln - ‘ mosesswmmn" “‘1 E i WWW...

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Unformatted text preview: ‘ mosesswmmn " “‘1 E i % WWW mmmmmpy E ME 375 HOMEWORK #10 Spring 2011 WMWWW [W Out: Apr. 15*, 2011 Due: Apr. 8“: 2011 PROBLEMI 130%! For the system given in the following figure: Bis) .é. gtg (a) Firm. the transfer Motion C(syﬁts) (33mins {3(3) = G}; (17) Find the @2111st ﬁtnction coy-13(5) {sew-me 3(3) x G}. PROBLEMZ {30%} For tire system given in the foitowing ﬁgure: (a) Find the equivalent block that represents the transfer function C(s)/R(s). (b) Derive an equation for the poles of the system. (c) Plot the location of the poles in the complex plane for Kp values between 0 and 1000. (d) Find the value for Kp that corresponds to a critically damped condition. (e) Find the value for Kp that corresponds to a percent overshoot of 16% to a step input for r(_t). 9"" /..,k PROBLEM 3: (40%) In many chemical processes the temperatm'e in a tank has to be maintained within a god degee af accm‘acy. The black diagram 9f an open-imp tenneramre-cnnfmi system is shown in Fig“ 3.1 and that of a dosed-tact: system in Fig. 3.2. Assmne that the naminai value of K is t for both cases. dit} Heating System Reference ’” Nmmzﬂized tampelanne mm... temperature rm an} Fig. 3.1 01332140013 tenqmatnre-cantrol system. (lit) _ Heating Wﬁﬂ gisfgm Refer-mice Normalized tempemtm'e ' temperame fit) at) Taupemnn'e sexism Fig. 3.2 (Staged-loop temez'amrewantml system For each system, ﬁnd gin-fume: ui‘ the unit. step respunse- by answering the: {cunning questions: a) Find unit step response cf 3 in the time domain :13ng ZERO initial munitions and NO diamrbance; b} Determine the resulting steady-state tenmerazure {Nit} disturbance} ; c) What time must elapse before the temperature reaches 63.2 yercent at its ﬁnal value with (Kt)- : 8? After the temperature in the tank has reached the steadyntate value: a disturbance occurs (the to a written increase in the volume: (if ﬂuid in the tank. 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