HW11soln

HW11soln - ME 375 PROBLEM 1(35 HOMEWORK 11 SOLUTION Spring...

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ME 375 HOMEWORK 11 SOLUTION Spring 2009 PROBLEM 1 (35%) In many chemical processes the temperature in a tank has to be maintained within a good degree of accuracy. The block diagram of an open-loop temperature-control system is shown in Fig. (a) and that of a closed-loop system in Fig. (b). Assume that the nominal value of K is 1 for both cases. Fig. 2(a) Open-loop temperature-control system. Fig. 2(b) Closed-loop temperature-control system For each system: a. Determine and sketch the variation of θ (in degrees C) with time t (in seconds) if r(t) is a unit step and the disturbance d(t) is zero. b. Determine the steady-state temperature for a unit step reference input when the disturbance d(t) is zero c. What time must elapse before the temperature reaches 63.2 percent of its final value with d(t) = 0? After the temperature in the tank has reached the steady-state value, a disturbance occurs due to a sudden increase in the volume of fluid in the tank. This is equivalent to d(t) being a step input of size 0.1. Normalized temperature θ (t) Temperature sensor d(t) + + Heating System Reference temperature r(t) K 11 0 s + Normalized temperature θ (t) Reference temperature r(t) Heating system Amplifier + a K1 0 0 = K 0 s + T = + + d(t)
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2 d. Determine the effect of this disturbance on the temperature and sketch the response for both cases.
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This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue.

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HW11soln - ME 375 PROBLEM 1(35 HOMEWORK 11 SOLUTION Spring...

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