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2003 Course Process Dynamics & Control

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Total No. of Questions : 12] [Total No. of Pages : 6 [3864] - 321 P 1088 B.E. (Chemical) PROCESS DYNAMICS & CONTROL (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answers to the two sections should be written in separate answer books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) a) b) i) With neat sketch explain feedback control strategy for controlling temperature of liquid inside a steam-heated stirred-tank heater by manipulating flow rate of steam. Identify CV, MV, DV for this system. [8] ii) If a direct-acting controller is used, whether you will select a airto-open or air-to-close type control valve on steam line. [2] With reference to the control system described in Q.1-a, explain the objectives of the control system. [8] OR Q2) a) b) Q3) a) Explain mathematical languages (methods) used for analysis and design of control systems in China, Russia, England, Greece and German. Also state the types of mathematical models used for analysis as the outcome of these languages. [8] For a stirred-tank heater system explained in Q.1-a, sketch and explain the following i) The control system for controlling level of liquid inside the tank by manipulating the flow rate of exit liquid stream. ii) The control system for controlling flow rate of liquid entering the tank. [10] A cylindrical liquid tank has 1 m2 cross-sectional area with a control valve with resistance 10 min/m2 installed in the liquid outlet line. Liquid enters into the tank at a rate 0.2 m3/min. [8] P.T.O. i) b) Find steady-state level of liquid in the tank corresponding to flow rate of 0.2 m3/min. ii) Find the transfer functions of the system. H(s) Q i (s) & Q o (s) Q i (s) where Qi, Qo & H represent inlet, outlet flow rates and level of liquid in deviation form. iii) If input flow rate is given unit step change (increase), derive the time-response equations for liquid level and outlet flow rate. Also find level of water after 30 seconds and new level attained. iv) Find the time required for achieving 80% change in level. A cylindrical liquid tank A having cross-section area 1.2 m2 is connected to another cylindrical tank B having cross-section area 0.8 m2 in the non-interacting arrangement. If the resistances in the flow lines between the tanks and that leaving from tank B are 8 m2/min & 6 m2/min respectively. Then find [8] i) Individual transfer functions G1(s) & G2(s) of tanks A & B in the form H (s) Q i (s) . ii) The overall transfer function of the combined non-interacting tank system. Also find the poles of this transfer function and hence predict the nature of its dynamic response for step change in input flow rate to tank A . iii) If initial input flow rate Fi to tank A is 0.3 m3/min, find the corresponding steady-state levels of liquid in tanks A & B . iv) If a unit step change (decrease) is given to input flow rate Fi find the expression for time-response of liquid level in tank B . OR Q4) a) b) A mercury thermometer having time constant 30 sec. shows steady-state temperature of 27oC which is suddenly immersed in hot liquid maintained at 200oC. [8] i) Assuming unit static gain, state the transfer function T m (s) T(s) for the thermometer system where T & Tm are temperature outside the bulb and measured temperature respectively. (In deviation form). ii) Find the temperature reading after 10 sec. iii) Find time required for 90% change in temperature reading. i) What are inverse response systems? Explain inverse response of liquid level in a boiler system. ii) If a first-order process having transfer function G1 (s) = K 1 1s + 1 is connected in opposition to a pure integrator process having transfer function G2(s) = K2/s, find the overall transfer function G(s). Also find the boles & zeros of G(s). Derive the condition for inverse response behaviour. [3864] - 321 -2- iii) Sketch the step responses of outputs of the individual processes having transfer functions G1(s), G2(s) and the combined process G(s). [8] Q5) a) Figure-1 A liquid tank system shown in Figure 1 has cross-section area A. For this system. [8] i) Derive differential equation model based on mass balance around the tank. ii) Derive the Laplace domain open-loop model for the system in the form h (s) = G P (s) F i (s) + G d F d (s) , b) Where h , F , F are deviation variables corresponding to h, Fi & i d Fd respectively. iii) If liquid level in the tank is to be controlled at set-point hsp using feedback controller having transfer function GC = KC, construct block diagram for this system assuming unity transfer functions for the measuring element and final control element. Find servo and regulator transfer functions for this closed-loop system. For liquid level control system shown in Figure 1, if P-controller having gain KC is used find time response equation for height h of liquid for a unit step change in i) Set-point hsp. ii) Disturbance flow Fd. Find the offset in both the cases. [8] OR Q6) a) Consider a second-order system having transfer function KP y(s) . G P (s) = = 22 m(s) s + 2 s + 1 [3864] - 321 -3- i) If a P-controller having transfer function KC is used to maintain output y near to the set-point ysp, find closed-loop servo transfer function assuming Gm = Gf = 1. ii) Find output response y (s) for unit step change in set-point y sp (s) . Find the closed-loop response characteristics and compare them with open-loop response characteristics Kp, & . iii) Find the value of offset in the value of y. b) [8] 1 is feedback 10s + 2s 2 + s 5 controlled using a P-controller having gain KC. i) Find the characteristic equation assuming Gm = Gf = 1. ii) Find the range of values of KC that produce stable closed-loop responses (using Routh-Hurwitz criterion). iii) Also find the value of gain KC at which the closed-loop system is at the verge of instability. Find corresponding roots of characteristic equation and hence the frequency of oscillations. [8] A system having transfer function G P (s) = 3 SECTION - II Q7) a) b) The output of a process having transfer function G P = 1 is s 2 + 2s feedback controlled using a P-controller with the measuring element having transfer function G m = 1 . Assuming Gf = 1. [10] s +1 i) Find closed-loop servo transfer function of the control system. ii) Draw block diagram. iii) Sketch root locus for the system. iv) Find the range of values of gain KC for which the system will be stable and unstable. v) Find the value of KC at which the system undergoes sustained oscillations. Also find the corresponding frequency of oscillations. i) Sketch asymptotic Bode plot for the control system having open- ii) 5e 5s . loop transfer function G 0L = (2s + 1)(s + 1) Find the phase margin & gain margin alongwith corresponding crossover frequencies. On the basis of these values, comment on stability of the system. [8] OR [3864] - 321 -4- Q8) a) b) Q9) a) b) Draw the root locus of a closed-loop system with k GH = [8] 2 s(s + 4)(s + 4s + 20) i) Sketch the Bode plot for a control system consisting of a process having K = 1, = 1, td = 1 the measuring element having K = 0.95, = 0.01 , the P-controller having gain 10 and the final control element having unity transfer function. ii) Find the values of PM & GM with corresponding cross-over frequencies with these values comment on stability of the system. [10] Explain split-range control system for controlling the pressure inside the gas phase reactor by manipulating flow rates of reactant and product streams. Draw neat graph showing % opening of the valves on inlet and outlet sides at different controller output signals. [8] i) Compare the performance of feedforward and feedback controllers. ii) Explain feedforward control of a jacketed CSTR to achieve constant temperature and composition within the reactor by controlling feed stream temperature and concentration with manipulation of coolant flow rate entering jacket and the rate of product withdrawal from the reactor. [8] OR Q10)a) b) Q11)a) Two reactants streams A & B enter the CSTR in certain fixed proportion R. Draw and explain ratio control system for CSTR which will maintain the ratio of A & B constant at the desired value RD by manipulating flow rate of B, while A is used as wild stream. [8] What is adaptive control system? State its applications in chemical processes. Draw and explain block diagram of programmed adaptive control system used for changing controller parameters based on auxiliary process measurement. [8] Draw and explain control system for batch reactor used to control the following variables [8] i) Flow rates of reactant streams A & B. ii) Pressure inside the reactor by manipulating the flow rate of vent stream. iii) Temperature inside the reactor is controlled using split-range control system on the hot and cold water flow lines entering the jacket. Explain how the temperature is achieved and maintained during start-up, reaction period and shut-down period. [3864] - 321 -5- b) i) ii) Explain feedback control strategy for controlling temperature of cold fluid outlet from a counter-current shell and tube heat exchanger by manipulating flow rate of entering hot fluid. Explain cascade control strategy consisting a primary temperature controller described above along with a secondary controller for controlling flow rate of entering hot fluid. What are the advantages of using cascade control over single-loop feedback control? [8] OR Q12)a) b) Explain control scheme for a two-product distillation column used to control the following [8] i) Flow rate of binary feed (A + B, A being more volatile component). ii) Level of liquid in the condensate accumulator. iii) Composition of top product. iv) Level of liquid in the reboiler. v) Composition of bottom product. Write short note on the following : [8] i) Selective control systems. ii) Cohen-Coon method of tuning of controllers. [3864] - 321 -6-

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