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(c) Using Routh test, find the locations (if any) at which the loci cross into the unstable region. [8+4+4]
Figure 2:
Figure 3: 6. The above figure 3 liquid level system has a cross-sectional area of 3.0 f t2 . If the value is such that , calculate the time constant for this system if the average operating level is 9 f t2. [16] 7. For the control system shown below figure 4, determine the controller settings using Ziegler-Nichols method. [16] 8. An ideal PD controller had the transfer function P = K c (τ D s + 1) ε An actual PD controller had the transfer function s+1) P = K c (τ (τ /β ε )s+1 D
D
Where β is a large constant in an industrial controller. If a unit-step change in error is introduced into a controller having the second transfe r function, show that P (t) = K c (1 + A exp(−βt/τ D ) Where A is a function of β which you are to determine. For β = 5 and K c = 0.5, plot P(t) versus t/τ D . As β → ∞, show that the unit-step response approaches that for the ideal controller. [16] 2
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Figure 4:
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Set No. 4
III B.Tech II Semester Regular/Supplementary Examinations,May 2010 PROCESS DYNAMICS AND CONTROL Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Explain process identification. Explain any one method used for the identification of a process. (b) Explain the criteria for good control along with corresponding equation. [10+6] 2. Using the Bode stability criterion, determine if the open loop transfer function is 3e− stable G(s) = (0.1s+1)(2s+1) . [16] .5s
3. For the control system in the figure 5: (a) Write the characteristic equation. (b) Use the Routh test to determine if the system is stable for K c = 4. (c) Determine the ultimate value of K c , above which the system is unstable. [16]
Figure 5: 4. A manometer of length 1.2 m and diameter 6 mm shown below in the figure 6 is filled with water to the extent of 30 cm length in the manometer. The manometer is subjected to a step change of 3000 N/m2. Find (a) Overshoot. (b) Decay ratio. (c) Rise time. Is the manometer length enough for the step change given? Data: ρwater = 1000 kg/m3 , viscosity of water = 1 x 10 3 N/m. −
4
[16]
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Figure 6: 5. A cascade control system is shown below figure 7. Calculate the maximum gain and the critical frequency of the primary controller. Eliminating the inner loop, compare these values with the single-loop system. [16]
Figure 7: 6. For the block diagram shown below figure 8, derive transfer functions for Y(s)/D(s) and Y(s)/Ysp(s). [16]
Figure 8: 7. A liquid storage system is shown below. The normal operating conditions are q¯1 = 10ft3 / min, q¯ 2 = 5ft3 / min, h = 4 ft. The tank is 6 ft in diameter, and the
5
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Figure 9: density of each stream is 60 lb/f t3 . Suppose a pulse change occurs in q 1 as shown below figure 9: (a) What is the transfer function relating H to Q1 ?
(b) Derive an expression for h(t) for this input change. (c) What is the new steady state value of liquid level h?
[6+6+4]
8. A two tank chemical-reactor control system is given below figure 10. A first order reaction A→ R is carried out, tanks are maintained at different temperatures T 1 and T 2 (T 1 T 2 ). The purpose of the control system is to maintain C 2 , the concentration of A leaving tank 2, at some desired value in spite of variation in inlet concentration C 0 , which is accomplished by adding a stream of pure A to tank 1 through a control valve. Develop a block diagram, with approximate transfer functions in each block. [16]
Figure 10:
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Set No. 4
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Set No. 1
III B.Tech II Semester Regular/Supplementary Examinations,May 2010 PROCESS DYNAMICS AND CONTROL Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. The transfer functions of P, PI, PD and PID are of the form U(s)/E(s), where U(s) is the laplace transform of u(t), the controller output, and E(s) the laplace transform of e(t), the actuating error signal. Discuss and sketch u(t) vs t curves for each of these controllers when the actuating error signal is: (a) e(t) = unit-step function. (b) e(t) = unit ramp function.
[8+8]
2. (a) Derive the unit ramp response of first - order systems. Discuss for this, what is ’Steady state error’. (b) A thermometer requires 1 min to indicate 98% of the response to a step change input. Assuming the thermometer to be a first order-system, find the time constant. If the thermometer is placed in a bath, the temperature of which is changing linearly at a rate of 100/min, how much error does the thermometer show? [6+10] 3. (a) The transfer function of a system is input, find the output y(t). (b) What is the final value of y(t)?
Y (s) R(s)
=
5(s+100) . s2 +60s+500
If r(t) is a unit step [8+8]
4. (a) Explain the concept of root locus. Give the procedure for plotting the root locus diagram along with the rules proposed by Evans. Consider the following open loop transfer function as an example. K G = (s+1)(s+2)(s+3) . (b) Discuss the limitations of Routh test.
[10+6]
5. Derive the closed loop transfer function relating a secondary disturbance to the primary output for a cascade control system. [16] 6. Explain in detail the characteristics of the ultimate response of a linear system with a transfer function G(s) to a sustained sinusoidal input. [16] 7. The block diagram 11 of a special feed back control system is shown below. Derive an expression for the closed loop transfer functions Y(s)/D(s) and Y(s)/Ysp(s). [16] 8. For the control system shown below figure 12, determine the controller settings using Ziegler-Nichols method. [16] 8
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Set No. 3
Figure 11:
Figure 12: III B.Tech II Semester Regular/Supplementary Examinations,May 2010 PROCESS DYNAMICS AND CONTROL Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Find the number of poles in the left-half plane, the right half plane and on the jω - axis for the system given below figure 13: (b) Determine the stability of the system which has the following characteristic equation. 1 + (s+1) (s+4) = 0 (s+2)(s+3) Also find the frequency ω, where the system has sustained oscillation. [6+10] 2
2. Explain the following: (a) Band width. (b) Reset ratio. (c) Anticipatory control. 9
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Figure 13: (d) Positive feed back.
[16]
3. (a) Explain the operation of a feed forward control with an example. State the advantages and disadvantages. (b) Explain the design of ratio control with an example. 4. Sketch the Bode plot for the following system: 1 1 G p (s) = 5s +2s+6 ; Gc (s) = 10 1 + 0.5s ; gm(s) = 2
[8+8]
1 ; s+1
Gf (s) =
10 . s+10
[16]
5. The two-tank liquid - level system shown in the figure 14 is operating at steady state when a step change is made in the flow rate to tank 1. The transient response is critically damped, and it takes 1.0 min for the change in level of the second tank to reach 50 % of the total change. (a) If the ratio of the cross-sectional areas of the tanks is A1 /A2 =2, calculate the ratio of the resistances R 1 /R2. (b) Calculate the time constant for each tank. (c) How long does it take for the change in level of the first tank to reach 90% of the total change? [16]
1 τ I s
6. For the system below in figure 15, with G c = K c 1 + , derive the response for a unit step change in the load variable. Explain all the terms involved in the answer. [16] 7. For the control system shown below figure 16, determine the controller settings using Ziegler-Nichols method. [16] 8. (a) Discuss the importance of linearization in process dynamics and control. (b) A thermometer is immersed in a liquid which is heated at such a rate that its temperature is increasing at the rate of 0.1 degree centigrade per second. If both thermometer and liquid are initially at 300 C, what rate of passage of liquid over the thermometer bulb is required, if the error in the thermometer 10
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Figure 14:
Figure 15:
Figure 16:
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Set No. 3
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reading is to be not more than 0.5 0 C. The mass of mercury in bulb is 10 g. Heat transfer coefficient (h) is given by, where ’u’ is the velocity of fluid in m/s, h in watt/m2-0 C. The surface area of bulb is 0.01 m2 and specific heat of mercury is 1.38 kJ/kg- 0 C. [6+10]
12
