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Chemical Engineering Department Subject matter: Process Control for undereducated students Teacher: Dr . Karima Marogi Normal Questions , Answers Process Control Challenges Problem (1) Solution a) Energy harmony for the thermocouple, where m is usually mass of thermocouple C is heat capacity of thermocouple they would is heat transfer pourcentage A is surface area of thermocouple big t is time in sec Substituting numerical ideals in (1) and observing that Choosing Laplace enhance, Problem (2) A thermometer having a period constant of 0. min is placed in a temperature bath and after the thermometer comes to equilibrium while using bath, the temperature from the bath is increased linearly with time on the rate of I degrees C as well as min precisely what is the difference between indicated temperature and bathroom temperature (a) 0.

one particular min (b) 10. min after the enhancements made on temperature starts. (c) What is the maximum deviation between the suggested temperature and bath temp and when does it occurs. (d) plot the forcing function and the response on the same graph. After the lengthy enough time purchase how a large number of minutes will the response lag the suggestions?

Solution Consider thermometer to be in balance with temperature bath for temperature (a) the difference involving the indicated temp and bath temperature Problem (3) Decide the copy function H(s)/Q(s) for the liquid level shown in figure listed below Resistance R1 and R2 are linear. The circulation rate from tank 3 is managed constant at b using a pump, the flow rate from container 3 is independent of head they would. The tanks are noninteracting. Solution and balance in tank 3 gives publishing the regular state equation Subtracting and writing when it comes to deviation Taking Laplace transforms

We have 3 equations and 4 unknowns (Q(s), H(s), H1(s) and H2(s). Therefore we can exhibit one in terms of other. From (1) Combining equation 4, a few, 6 Trouble (4) Determine Y (4) for the machine response stated by Difficulty (5) Temperature transfer products shown in fig. involves tow storage containers, one nested inside the additional. Heat is transferred by simply convection through the wall of inner container. 1 . Hold up volume of every tank is usually 1 ft3 2 . The cross sectional area intended for heat transfer is you ft2 a few. The overall temperature transfer coefficient for the flow of warmth between the storage containers is 15 Btu/(hr)(ft2)(oF) 4. Heat capacity of smooth in every single tank is 2 Btu/(lb)(oF) 5.

Denseness of each smooth is 60 lb/ft3 In the beginning the temperature of supply stream towards the outer fish tank and the contents of the outer tank happen to be equal to 75 oF. Material of inner tank happen to be initially for 100 oF. the stream of heat for the inner reservoir (Q) transformed according into a step alter from 0 to 500 Btu/hr. (a) Attain an expression pertaining to the laplace transform in the temperature of inner container T(s). (b) Invert T(s) and obtain To for t= 0, 5, 10, U Solution (a)For outer reservoir Substituting statistical values Today Ti(s) = 0, because there is no change in temperature of feed stream to outer tank. Which gives To get inner reservoir Problem (6)

The insight (e) to a PI control mechanism is shown in the fig. Plot the output of the controller if KC = 2 and XI = zero. 5 min Solution Problem (7) The thermal system shown in fig S 13. 6th is managed by PD controller. Data, w = 250 lb/min,? = sixty two. 5 lb/ft3, V1 = 4 ft3, V2=5 ft3, V3=6ft3, C = 1 Btu/(lb)(F) Alter of 1 pound-force per square inch from the control mechanism changes the flow price of heat of by 500 Btu/min. the temperature of the inlet stream may vary. You cannot find any lag in the measuring aspect. (a) Draw a stop diagram from the control program with the appropriate transfer function in every single block. Each transfer function should include a numerical ideals of the parameters. b) From your block picture, determine the overall transfer function relating the temperature in tank a few to a difference in set point. (c ) Find the offset to get a unit steo change in inlet temperature in case the controller gain KC can be 3psi/F of temperature error and the derivative time can be 0. your five min. Fig. (1) (b) Problem (8) for the control shown, the characteristics equation is s 4 +4 s3 +6 s 2 +4 s +(1 + k) =0 (a) Identify value of k previously mentioned which the system is unstable. (b) Determine the significance of k for which the two with the roots are recorded the mythical axis. Remedy s some +4 s3 +6 h 2 +4 s +(1 + k) =0 Intended for the system to become unstable