R05320803-process-dynamics-and-control

Set No. 1

Code No: R05320803

III B.Tech Supplimentary Examinations, Aug/Sep 2008 PROCESS DYNAMICS AND CONTROL (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Solve the following using Laplace transform. 3 d4 x + ddt3x = cos t x(0) = x′ (0) = x′′′ (0) = 0 dt4 (b) Invert the following Laplace transform

x′′ (0) = 1

1 . s(s2 −2s+5)

[8+8]

2. The two tank system shown in figure 2 is operating at steady state. At time t=0, 10ft3 of water are quickly added to the first tank. Determine the maximum deviation in level in both tanks from the ultimate steady state values and the time at which each maximum occurs. Data: A1 =A2 =10 ft2 , R1 =0.1ft/cfm, R2 =0.35ft/cfm. [16]

Figure 2 3. (a) Specify the Gain of a proportional controller to be used in the control system. (b) With a neat schematic diagram explain about various components of control system. [8+8] 4. For the control system shown in figure 4 given below determine: (a) C(s)/R(s)

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Set No. 1

Code No: R05320803 (b) C(∞) (c) Offset (d) C(0.5) (e) Whether the closed loop response is oscillatory.

[16]

Figure 4 5. (a) Test the stability of the system whose characteristic equation is given by s5 + 2s4 + 5s3 + 10s2 + 4s + 8 = 0. (b) Determine the range of K such that feedback system having characteristic equation s (s2 +s + 1) (s + 4) + K = 0, will be stable. [8+8] 6. (a) ) Explain the substitution rule. Using the substitution rule, find the amplitude ratio and phase angle for general first and second order systems. (b) A control system which is stable for servo operation will be stable for regulator operation also. State true or false and justify the answer. [8+8] 7. Describe in physical terms the concept of dead-time compensation. Why is such a system also called predictor? [16] 8. Discuss the closed loop Zeigler Nichols method of controller settings. Mention the rules and procedures followed in the method. [16] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R05320803

III B.Tech Supplimentary Examinations, Aug/Sep 2008 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 initial value of the function that has the following transform s4 −6s2 +9s−8 x(s) = s(s−2)(s 3 +2s2 −s−2) (b) Find the final value of the function for which the Laplace transform is [8+8] x(s) = s(s3 +3s12 +3s+1) . 2. Develop transfer function for a second order system of your choice.

[16]

3. Derive the Ideal transfer functions for the following Controllers. (a) P Control (b) PI Control (c) PID Control.

[5+6+5]

4. Determine an expression for C in terms of R, U1 and R, U2 respectively for the situation when both set-point change and load change occur simultaneously. As shown in figure 4. [16]

Figure 4 5. In the control system shown in the figure 5, find the value of Kc for which the system is on the verge of instability. The controller is replaced by a PD controller, for which the transfer function is Kc (τD s + 1). If Kc = 10, determine the range of τD for which the system is stable. [16]

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Set No. 2

Code No: R05320803

Figure 5 6. (a) A control system with a P controller has an open loop transfer function Kc G(s) = s(5s+1) 2 where time is in minutes. Obtain the cross over frequency and the ultimate controller gain. (b) Write short notes on resonant frequency & gain margin.

[8+4+4]

7. Describe in physical terms the concept of dead-time compensation. Why is such a system also called predictor? [16] 8. Discuss the criteria for good control. ⋆⋆⋆⋆⋆

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[16]

Set No. 3

Code No: R05320803

III B.Tech Supplimentary Examinations, Aug/Sep 2008 PROCESS DYNAMICS AND CONTROL (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Find Laplace transform of the following: (a) tn e−at u(t) (b) Cosh kt u(t) (c) e−at Sin kt u(t).

[5+5+6]

2. The two tank system shown in figure 2 is operating at steady state. At time t=0, 10ft3 of water are quickly added to the first tank. Determine the maximum deviation in level in both tanks from the ultimate steady state values and the time at which each maximum occurs. Data: A1 =A2 =10 ft2 , R1 =0.1ft/cfm, R2 =0.35ft/cfm. [16]

Figure 2 3. Prove that the combination of process and valve is First-order and state all assumptions involved. [16] 4. Determine the transfer function C/R, C/U1 and C/U2 for the system shown in figure 4. [16]

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Set No. 3

Code No: R05320803

Figure 4 5. (a) State the theorems of Routh test. (b) Use Routh’s stability criterion, ascertain stability for the following case. s6 + s5 - 2s4 - 3s3 - 7s2 - 4s - 4 = 0. [8+8] 6. (a) What is Bode diagram? Bode diagram is a convenient tool for analyzing control problems, discuss. (b) Write short notes on ultimate gain & ultimate period.

[8+4+4]

7. Explain the feedforward control strategy. Compare feedback and feedforward control methods. [16] 8. List out the Z-N rules for application to a real process. ⋆⋆⋆⋆⋆

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[16]

Set No. 4

Code No: R05320803

III B.Tech Supplimentary Examinations, Aug/Sep 2008 PROCESS DYNAMICS AND CONTROL (Chemical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Consider the simple RC circuit shown in the figure 1, in which a voltage source v(t) is applied to a series combination of a resistance R and a capacitance C. For t < 0, ν(t) = νs . Determine the transfer function relating ec (t) to v(t) where ec (t) is the voltage across the capacitor. [16]

Figure 1 2. Define and discuss the following terms with the help of a neat diagram: (a) Overshoot (b) Decay ratio (c) Rise time (d) Response time.

[4×4]

3. Explain the mechanism of Control Valve with a neat diagram.

[16]

4. For the control system shown in figure 4. Determine the response of proportional control and proportional integral control for load change. [16]

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Set No. 4

Code No: R05320803

Figure 4 5. The characteristic equation for a certain feedback control system is given by s4 + a1 s3 + a2 s2 + a3 s + K = 0. If the numerical values of a1 = 22, a2 = 10 and a3 = 2, find K which corresponds to the stable system. [16] 6. For the following transfer functions, sketch the gain versus frequency, asymptotic Bode diagram. Find the actual gain and phase angle at ω = 10. It is not necessary to use log-log paper. Simply rule off decades on rectangular paper. [8+8] (a)

100 (10s+1)(s+1)

(b)

10s . (s+1)(0.1s+1)2

7. What is the effect of dead time in response of simple feedback control loops? Explain in physical terms. [16] 8. Write short notes on (a) Integral of the square of error. (b) Integral of the absolute value of error. ⋆⋆⋆⋆⋆

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[8+8]