Problems of Process Control

Chemical Engineering discussion section Subject change Control for undereducated students Instructor Dr. Karima Marogi Typical Questions & Answers Process Control Problems Problem (1) dissolver a) Energy fit for the thermocouple, where m is push-down store of thermocouple C is take fire force of thermocouple h is lovingness transfer coefficient A is surface area of thermocouple t is meter in sec Substituting numeral hold dears in (1) and noting that pickings Laplace transform, Problem (2) A thermometer having a time constant of 0. bit is pose in a temperature bath and subsequently the thermometer comes to equilibrium with the bath, the temperature of the bath is increase linearly with time at the direct of I deg C / min what is the difference between the indicated temperature and bath temperature (a) 0. 1 min (b) 10. min after the change in temperature begins. (c) What is the maximum deviation between the indicated temperature and bath temperature and when does it occ urs. (d) bandage the forcing ope judge on and the result on the same graph. After the long teeming time buy how many minutes does the response lag the arousal?Solution Consider thermometer to be in equilibrium with temperature bath at temperature (a) the difference between the indicated temperature and bath temperature Problem (3) Determine the transfer function H(s)/Q(s) for the liquid level shown in figure below Resistance R1 and R2 are linear. The flow rate from tank 3 is maintained constant at b by means of a pump the flow rate from tank 3 is independent of head h. The tanks are non-interacting. Solution and balance on tank 3 gives writing the steady state equality Subtracting and writing in scathe of deviation Taking Laplace transformsWe have ternary equations and 4 unknowns (Q(s),H(s),H1(s) and H2(s). So we can express one in terms of other. From (1) Combining equation 4,5,6 Problem (4) Determine Y (4) for the system response expressed by Problem (5) Heat transfer equi pment shown in fig. consists of tow tanks, one nested inside the other. Heat is transferred by convection through the wall of upcountry tank. 1. Hold up volume of each tank is 1 ft3 2. The torment sectional area for heat transfer is 1 ft2 3. The overall heat transfer coefficient for the flow of heat between the tanks is 10 Btu/(hr)(ft2)(oF) 4. Heat capacity of quiet in each tank is 2 Btu/(lb)(oF) 5.Density of each fluid is 50 lb/ft3 Initially the temp of feed stream to the out tank and the contents of the outer(a) tank are equal to blow oF. Contents of intimate tank are initially at deoxycytidine monophosphate oF. the flow of heat to the inner tank (Q) changed according to a mensuration change from 0 to 500 Btu/hr. (a) Obtain an expression for the laplace transform of the temperature of inner tank T(s). (b) Invert T(s) and obtain T for t= 0,5,10, U Solution (a)For outer tank Substituting numerical values Now Ti(s) = 0, since there is no change in temp of feed stream to oute r tank. Which gives For inner tank Problem (6)The input (e) to a PI control condition is shown in the fig. Plot the output of the controller if KC = 2 and XI = 0. 5 min Solution Problem (7) The thermal system shown in fig P 13. 6 is controlled by PD controller. Data w = 250 lb/min ? = 62. 5 lb/ft3 V1 = 4 ft3, V2=5 ft3 V3=6ft3 C = 1 Btu/(lb)(F) Change of 1 psi from the controller changes the flow rate of heat of by 500 Btu/min. the temperature of the inlet stream may vary. in that location is no lag in the measuring element. (a) Draw a handicap diagram of the control system with the appropriate transfer function in each block. Each transfer function should contain a numerical values of the parameters. b) From the block diagram, determine the overall transfer function relating the temperature in tank 3 to a change in set point. (c ) happen upon the offset for a unit steo change in inlet temperature if the controller gain KC is 3psi/F of temperature error and the derivative time i s 0. 5 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) Determine value of k above which the system is unstable. (b) Determine the value of k for which the dickens of the roots are on the imaginary axis. Solution s 4 +4 s3 +6 s 2 +4 s +(1 + k) =0 For the system to be unstable