Problems of Process Control

Chemical Engineering Department Subject Process Control for undereducated students instructor Dr. Karima Marogi Typical Questions & Answers Process Control problems Problem (1) etymon a) Energy balance for the thermocouple, where m is mass of thermocouple C is foment capacity of thermocouple h is heat transfer coefficient A is surface area of thermocouple t is time in sec Substituting numerical values in (1) and noting that victorious Laplace modify, Problem (2) A thermometer having a time constant of 0. min is placed in a temperature bath and after the thermometer comes to equilibrium with the bath, the temperature of the bath is increased linearly with time at the rate 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 occurs. (d) plot the forcing function and the response on the same graph. After the long enough time buy how umteen minutes does the response lag the input?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 maintain 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 equation Subtracting and writing in terms of deviation Taking Laplace transformsWe have trio 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 equipment shown in fig. consists of tow tanks, one nested insi de the other. Heat is transferred by convection through the wall of inner tank. 1. Hold up volume of each tank is 1 ft3 2. The cross 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 fluid 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 outer tank and the contents of the outer tank are equal to 100 oF. Contents of inner tank are ab initio at 100 oF. the flow of heat to the inner tank (Q) changed according to a step 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 thither is no change in temp of feed stream to outer tank. Which gives For inner tank Problem (6)The input (e) to a PI controller is shown in the fig. Plot t he 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. There is no lag in the mensuration element. (a) Draw a block diagram of the control system with the appropriate transfer function in each block. Each transfer function should have 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 grade point. (c ) Find 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 is 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) Deter mine value of k above which the system is unstable. (b) Determine the value of k for which the two 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