Ch1355 Process Instrumentation, Dynamics & Control

1 CH2354 PROCESS INSTRUMENTATION & CONTROL

UNIT-I

Part-A (Questions & Answers)

1. Write down the Laplace transform of f(t) = e-2t sin(3t) The given equation is of the form f(t) = e-at sin(kt), then its Laplace transform is f(s) = k/[(s+a)2 + k2]. Therefore, the transform for the given equation is 3/ [(s+2)2 + 32].

2. Obtain the Laplace transform of f(t) = R u(t) + Rl [du(t)/dt] The transform for the given equation is f(s) = R/s + Rl [s u(s) – u(0)]. Where u(s) = L{u(t)} and u(0) is u(t) evaluated at t = 0.

3. What is the Laplace transform of the function f(t) = e-2t t2? The given equation is of the form f(t) = e-at tn, then its Laplace transform is f(s) = n!/(s + a)n+1. Therefore, the transform for the given equation is 2!/(s+2)2+1 = 2/(s+2)3.

4. Linearize the function f(x) = x3 at x = 2. By Taylor series of expansion, we get f(x) = f(xs) + f’(xs) (x - xs) 3 2 2 For the Given f(x) = x at xs = 2, we get f(x) = 2 + 3 (2 ) (x – 2) = 8 + 12 (x – 2) = 12x - 16

5. Give the transforms of step function and exponential function.  For the step function f(t) = 1 (unit-step), its transform is f(s) = 1/s  For the exponential function f(t) = e-at, its transform is f(s) = 1/(s+a)

6. Write the transforms of ramp function and sine function.  For the ramp function f(t) = t, its transform is f(s) = 1/s2  For the sine function f(t) = sin (kt), its transform is f(s) = k/(s2+k2)

7. State initial and final value theorems.  Initial value theorem: If f(s) is the Laplace transform of f(t), then lim [f(t)] = lim [s f(s)] t→0 s→∞  Final value theorem: If f(s) is the Laplace transform of f(t), then lim [f(t)] = lim [s f(s)] t→∞ s→o Provided that [s f(s)] does not become infinite for any value of ‘s’ satisfying Re(s) ≥ 0. If this condition does not hold, f(t) does not approach a limit as t→∞.

8. Define open loop system. A system which generates output signals but which depends on the integrity of the system to execute them, without feedback for monitoring or comparison purposes. Open-loop systems ignore error signals and operate on the assumption that no errors occur.

1 2 9. Define transfer function and explain its properties. The transfer function relates two variables in a physical process; one of these is the cause (forcing function or input variable) and the other is the effect (response or output variable). Thus, the transfer function G(s) is defined as G(s) = Laplace transform of the output deviation variable, Y(s) Laplace transform of the input deviation variable, X(s)

10. What is a first order system? Any physical system for which the relation between Laplace transforms of input and output deviation variable is of the form Y(s)/X(s) = 1/( s + 1) is called a first order system. Where ‘’ is the time constant of the system and has the units of time.

11. What are the assumptions used in developing the transfer function for thermometer? The following assumptions are used in developing the transfer function for thermometer;  All the resistance to heat transfer resides in the film surrounding the bulb (the resistance offered by the glass and mercury is neglected)  All the thermal capacity is in the mercury. Furthermore, at any instant the mercury assumes a uniform temperature throughout.  The glass wall containing the mercury does not expand or contract during the transient response.

12. List different forcing functions. The different forcing functions are  Step function: X(t) = A u(t). Where ‘A’ is the magnitude of step input and u(t) is the unit-step function.  Impulse function: X(t) = A δ(t). Where δ(t) is the unit-impulse function.  Sinusoidal input: X(t) = A sin(ωt).

13. Define resistance and capacitance of a first order system.  Resistance is defined as the ratio of the change in driving force to the change in flow.  Capacitance is defined as the ratio of the change in storage to the change in driving force.

14. Write the units of resistance and capacitance in a thermometer.  Resistance = 1/(h A), has the SI unit of [oK-s/kJ]  Capacitance = m C, has the SI unit of [kJ/ oK]

15. Explain linearization of non-linear systems. Most of the physical systems are non-linear. The process dynamics of a particular system is characterized by its transfer function. To obtain the transfer function for liquid level system, linear resistance to flow was considered. In practice, the relationship between the flow rate and liquid head is square root relationship, which is non-linear. The non-linear systems are approximated by the linear system. The accuracy of approximation is good, if the control system is operating around the steady state

2 3 point. Under such conditions, these relations may be linearized by using Taylor’s series at or near its steady state point. Therefore, any non-linear system operated at or near its steady state conditions can be assumed as linear systems.

16. Write the variables in second order transfer function. The second order transfer function is Y(s)/X(s) = 1/[ 2 s2 + 2 ξ  s + 1] The variables are ‘τ’ is the time constant (has the units of time) and ‘ξ’ is the damping coefficient (represents the characteristics of the second order control system).

17. Define critically damped system and write the transfer function for the same. In a second order control system, if ξ (damping coefficient) = 1 then the system is said to be critically damped system (and allows most rapid approach of the response without oscillation). Its transfer function is Y(s)/X(s) = 1/[ 2 s2 + 2  s + 1] = 1/(  s + 1)2.

18. “Two first order system connected in series is an over-damped second order system” – Justify. The transfer function for two first order system connected in series is given by

Y(s)/X(s) =1/[( 1 s + 1) (2 s + 1)]. It behaves as over damped system (ξ>1, the response is non-oscillatory and becomes more sluggish as ‘ξ’ increases) because the roots s1 and s2 are real and the equation 2 s2 + 2 ξ  s + 1 may be factored into two linear factors. Therefore, 2 2 Y(s)/X(s) =1/[( 1 s + 1) (2 s + 1)] = 1/[  s + 2 ξ  s + 1].

19. What is loading in an interacting system? The term ‘Interacting’ is often referred to as ‘Loading’. That is, the second tank is said to load the first tank. The effect of interaction on a system containing two first order systems is to change the ratio of effective time constants in the interacting system.

20. What is overshoot? Overshoot is a measure of how much the response (step response of under damped system) exceeds ultimate value following a step change. The over shoot for a unit step is relate to ‘ξ’ by the expression Over shoot = exp[-π ξ/(1 – ξ)1/2]

21. Define decay ratio. Decay ratio is defined as the ratio of the sizes of successive peaks (in the step response of under damped system) . The decay ratio is related to ‘ξ’ by the expression Decay ratio = exp[-2π ξ/(1 – ξ)1/2] = (Overshoot)2

22. Define rise time and response time. Rise time: It is the time required for the response to first reach its ultimate value (in the step response of under damped system). Response time: This is the time requires for the response to come within ± 5 percent of its ultimate value and remain there (in the step response of under damped system).

3 4 Part-B (Questions)

1. (i) Solve the following by Laplace transform [d2x/dt2]+ x = sin(t) (ii) Obtain the inverse Laplace transform of Y(s)/X(s) = 10 (s + 1)/[s (s + 2) (s + 3)].

2. (i) Develop a transfer function for mercury thermometer. Obtain the dynamic response for a step change in y\the input variable. (ii) A thermocouple of time constant of 2 min is placed in a bath at 150 oC. The bath temperature increases linearly at the rate of 1.5oC/min. Sketch the response of the system.

3. (i) Derive the transfer function of a mixing tank. (ii) A thermometer having a time constant of 1 min is placed in a temperature bath, T1 of 60oC and after the thermometer comes to equilibrium with the bath, the temperature of the bath is suddenly increased to 80oC for a period of 0.3 min and the bath is brought back to 60oC. Plot the temperature response of the thermometer.

4. (i) If a forcing function f(t) has the Laplace transform f(s) = (1/s) + [(e-s – e-2s)/s2] + (e-3s/s). Graph the function f(t). {The function f(t) has the Laplace transform f(s) = (1 – 2e-s + e-2s)/s2. Obtain the function f(t) and graph f(t).} (ii) A process of unknown transfer function is subjected to a unit-impulse input. The output of the process is measured accurately and is found to be represented by the function y(t) = t e-t. Determine the unit step response of the process.

5. (i) Derive the response of a first order system to a pulse input. (ii) Derive the transfer function H/Q for the liquid level system shown below; [H and Q are the deviation variables in ‘h’(m) and ‘q’ (m3/min) respectively, Area A = 0.75m2].

R1 = 1 R1 = 2

6. (i) Derive the response of a first order system to a unit ramp input. (ii) A liquid level process is operating at steady state and the input to the tank is 10m3/min. At t = 0, 1m3 of water is added suddenly (unit impulse) to the tank; at t = 1, 2m3 of water is added suddenly to the tank. The resistance at the exit is 0.5 and the time constant,  = 1. Plot the response of the level in the tank and determine the level at t = 0.5, 1 and 1.5 4 5

7. (i) For a typical reactor, write the balance equations and obtain the transfer function for the same. (ii) A liquid level system has a cross sectional area of 3 m2. The valve characteristics are q = 8 h1/2; where ‘q’ is the flow rate in m3/min and ‘h’ is the level in ‘m’. Calculate the time constant for this system if the operating level is 3 m and 9 m.

8. For two interacting (or non-interacting) liquid level tanks connected in series, Derive the transfer function relating the level in the second tank to the inflow to the first tank.

9. A step change of magnitude 4 is introduced into the system having the transfer function G(s) = 10/(s2 + 1.6s + 4). Determine (i) Percent overshoot (ii) Decay ratio (iii) Period of oscillation (iv) Rise time and (v) Settling time.

10. There are ‘N’ storage tanks of volume ‘V’ arranged so that when water is fed into the first tank, an equal volume of water overflows form the first tank into the second tank, and so on. Each tank initially contains component ‘A’ at some concentration ‘Co’ and is equipped with a perfect stirrer. At tine zero, a stream of initial concentration is fed into the first tank at a volumetric rate ‘q’. Find the resulting concentration in each tank as a function of time.

5 6 UNIT-II

1. What are the components of feedback control system? The components of feedback control system are (i) Process (ii) Measuring element (iii) Controller (iv)Final control element

2. Explain negative and positive feedback system. If the signal to the comparator (the controlled variable is, measured and, compared with the desired value or set point) were obtained by the difference between measured variable and set point, then the system is said to be Negative feed back system (ensures that the difference between measured variable and set point is used to adjust the control element so that the tendency is to reduce error). If the signal to the comparator were obtained by adding the measured variable and set point, then the system is said to be Positive feed back system (which is inherently unstable).

3. Why negative feedback is invariably preferred in closed system? Negative feed back systems ensure that the difference between measured variable and set point is used to adjust the control element so that the tendency is to reduce error, and are stable. But the positive feed back systems are inherently unstable. That is why the negative feedback is invariably preferred in closed system.

4. Write the closed loop equation for a feedback control system. The closed loop equation (transfer function of the negative feed back system is C(s)/R(s) = G(s)/[1 + G(s) H(s)] Where G(s) = Gc(s).Gv(s).GP(s) Gc(s) = transfer function of the controller Gv(s) = transfer function of the control valve (final control element) GP(s) = transfer function of the process H(s) = transfer function of the measuring element

5. Draw the block diagram for a positive and negative feedback control system.

6 7 6. Define load and set-point variable. The load variable is represented by ‘U’, its response is obtained by setting R = 0 (represents the solution to the regulator problem). The set-point variable is represented by ‘R’, its response is obtained by setting U = 0 (represents the solution to the servo problem).

7. Briefly explain or Distinguish between servo and regulator problem. The study of the variation of the controlled variable with set point ‘R’ with time for constant value of the load variable (dU/dt = 0) is known as Servo problem. The study of the variation of the controlled variable with the variation in the load variable ‘U’ with time for constant value of the set point (dR/dt = 0) is known as Regulator problem.

8. Explain the mechanism of control valve. Control valve (pneumatic) is hardware component of the control loop, which is most commonly used final control element that implements the control action. It receives the pneumatic output pressure of a controller, which acts on the diaphragm of the control valve and adjust the valve of the manipulate variable. The pneumatic control valve has spring and diaphragm actuator. The function of the actuator is to convert the controller signal to valve opening. The output of the controller has to be converted to the corresponding change in the valve opening. So, a control valve is opened or closed by the actuator. The actuator converts the controller signal to a mechanical movement to position the valve plug to give the desired flow rate of air flowing through the orifice of the control valve.

9. Distinguish quick opening and equal percentage valve characteristics.  The linear (quick opening) valve is one for which the sensitivity is constant and the relation between flow and lift is linear. For linear valve, the relation between flow ‘m’ and lift ‘x’ is (Sensitivity) dm/dx = α. Where ‘α’ is constant.  The equal percentage valve is of the increasing sensitivity type and the relation between flow and lift is non-linear. A valve that does shut tight is said to be equal percentage. For linear valve, the relation between flow ‘m’ and lift ‘x’ is (Sensitivity) dm/dx = β m. Where ‘β’ is constant

10. Define rangeability of a control valve. In order to express the range over which an equal percentage valve will follow the equal percentage characteristics, the term ‘Rangeability’ is used. Rangeability is defined as the ratio of maximum flow to minimum controllable flow over which the valve characteristic is followed. Rangeability = mmax/mmin, controllable

11. List any two disadvantages of pneumatic controller. The disadvantages of pneumatic controller are;  The cost of the controller is more  It cannot be used for very long distance because of the transportation lag in the transmission line.  The knob calibrations for the various controller parameters like gain, integral time and derivative time are essential. 7 8

12. What is proportional band? Explain reset rate. The proportional band (pb) is defined as the error (expressed as a percentage of the range of measured variable) required to move the valve from fully closed to fully open. A frequently used synonym is bandwidth.

Reset rate is defined as the reciprocal of the integral time ‘I’ and is given by Reset

rate = 1/I.

13. Give the importance of integral mode in a PI controller. The addition of integral mode to a proportional controller eliminates the offset; the controlled variable ultimately returns to the original value. This advantage of integral action is balanced by the disadvantage of a more oscillatory behavior.

14. Give the importance of derivative mode in a PD controller. The addition of derivative mode to a proportional controller gives a definite improvement in the response. The rise of the controlled variable is arrested more quickly and it is returned rapidly to the original value with little or no oscillation.

15. Write short notes on On-Off control. A special case of proportional control is on-off control. If the gain ‘Kc’ is made very high, the valve will move from one extreme position to the other, if the pen deviates only slightly from the set point. This very sensitive action is called on-off action because the valve is either fully open (on) or fully closed (off); that is, the valve acts like a switch. This is a very simple controller and is exemplified by the thermostat used in a home- heating system. The bandwidth of an on-off controller is approximately zero.

16. Define offset. What type of controller eliminates offset? With proportional action only, the control system is able to arrest the rise of the controlled variable and ultimately bring it to reset at a new steady-state value. The difference between this new steady-state value and the original value is called ‘Offset’. The PI controller eliminates this offset, because the addition of integral mode to a proportional controller eliminates the offset.

17. Write the transfer function of a PID controller. The transfer function of PID controller is

P(s)/ε(s) = Kc [1 + D s + (1/I s)].

Where Kc = controller gain, D = derivative time and I = integral time

18. Explain transportation lag or delay.

A phenomenon that is often present in flow systems is the Transportation lag ‘d’. Synonyms for this term are distance velocity lag and dead time. It is simply the time needed for a particle of fluid from the entrance of the pipe to the exit, and it can be calculated from the expression d = volume of the pipe/volumetric flow rate. The transfer function of a transportation lag is Y(s)/X(s) = e- ds

19. Define stability of linear system. A control system is defined to be stable, if the bounded inputs (which is a function of time and has a definite value within fixed bound) produce the bounded outputs. Or A stable system will be defined as one for which the output response is bounded for all bounded inputs. A control system is defined to be unstable if it produces the unbounded or unlimited output response for every bounded input. Or A system exhibiting an unbounded response to a bounded input is unstable.

20. State Routh’s stability criterion. The Routh’s procedure is used to determine the locations of roots off the polynomial characteristic equation, lie in the right of the imaginary axis of the complex plane without actual calculations of the values of the roots of the characteristic equation to determine the stability of the closed-loop control system.  If all the roots of the characteristic equation lie in the left half of the complex plane and the roots have negative real parts (coefficients of polynomial must be positive), then all the elements of the first column are non-zero and positive indicating a Stable control system.  If any coefficient of polynomial is negative, the system is definitely unstable.

Part-B (Questions)

1. (i) Discuss various controller modes. (ii) A proportional controller is used for two non-interacting liquid level system, time constants for the tanks are 1 and 0.5. The value of the gain of controller is 5. Assume unity feedback control system. The set point of control system is given step change of magnitude 0.4. Determine the offset.

2. (i) Discuss the closed loop response of a PI controller to first order process for a step change in load. Also, evaluate the offset. (ii) Discuss the characteristics of P, PI and PID controllers and list the advantages of PID controller over other controllers.

3. Load ‘U1’ and ‘U2’ enter at two different points as shown below. Show that for the closed loop the response frequency is same for both load changes, but the offset is different.

4. (i) Explain PID control and obtain the transfer function for it. (ii) A PI controller indicates an output of 12 mA when the error is zero. The set point is suddenly increased to 14 mA and the controller output is recorded and is given below; Time, t (sec) 0 10 20 30 Output (mA) 14 16 15 20

Find KC and τI.

5. (i) Explain Routh stability method. (ii) The set point of the control system shown below is given a step change of 0.1unit.

Determine (1) The maximum value of ‘C’ and the time at which it occurs. (2) The offset (3) The period of oscillation (4) Sketch C(t) as a function of time.

6. (i) Compare Pneumatic and Electronic controller. (ii) For a unit step change in set point, find the response ‘C’ for the system given below and represent graphically.

7. (i) Discuss Servo and Regulator problem. (ii) For the control system shown below;

(1) Obtain the closed loop transfer function C/U (2) Evaluate the proportional gain for which the closed loop damping coefficient is 2. (3) Find the offset for a unit step change in ‘U’, if KC = 2.

8. Consider the feed back control of a first order process with a transfer function G(s) = 1/(s + 1). Let the controller be PI controller with GC(s) = KC/ 1 + (1/ τI s)]. Assuming the transfer functions of final control element and measuring instrument to be unity, compute the overshoot, decay ratio and period of oscillation for a step change in set point for KC = 1 and τI = 0.5. Also show that the feed back system has zero offset.

9. For the system shown below, check the value of KC for which the system is stable.

10. A feed back control system has the following transfer functions; Process: Gp(s) = 5/[(2s + 1) (s + 1)] Measurement: H(s) = 1/(0.5s + 1) Valve: GV(s) = 0.2/(0.1s + 1) Controller: GC(s) = KC Using Routh’s stability criteria, find out the value of KC for which the system is stable.

UNIT-III

1. What is frequency response? Frequency response is a valuable tool in the analysis and design of control systems. The design of control systems using frequency response is based on the characteristic of the frequency response analysis which determines the features of the output sinusoidal wave, when a linear system is subjected to a sinusoidal input. It also helps us to select the optimum values of the parameters like gain, integral time and derivative time in the design of controller.

2. Give the expressions for Amplitude ratio and Phase lag for the transfer function G(s) = 1/(s + 1)3 From the given transfer function, we get  = 1. Amplitude Ratio, AR = 1/(2ω2 + 1)3/2 = 1/(ω2 + 1)3/2 Phase angle, φ = 3 tan-1(-ω) = 3 tan-1(-ω)

3. For a system with transfer function G(s) = e-2S/(5S + 1), calculate Amplitude ratio and Phase lag.

From the given transfer function, we get  = 1 and d = 2 Amplitude Ratio, AR = 1/(2ω2 + 1)1/2 = 1/(25ω2 + 1)1/2 (For transportation lag, AR = 1) -1 -1 Phase angle, φ = tan (-ω) -57.3ωd = tan (-5ω) -114.6ω

4. What is Resonant frequency? The frequency at which the maximum AR is attained is called the resonant frequency 2 1/2 and is given by ωr = (1/) (1 - 2ξ )

5. What do you mean by Bode diagrams? Bode diagram is known in then honor of H. W. Bode and it is a convenient tool for analyzing the frequency response of a linear control system. Bode diagrams are the graphical representation of the AR and phase angle, dependence on frequency. It consists of two graphs – logarithm of AR vs. logarithm of frequency ‘ω’ and phase angle ‘φ’ vs. logarithm of frequency ‘ω’.

6. Define corner frequency. The frequency where the low frequency asymptote and high frequency asymptotes

intersect is known as the corner frequency. It is given by ωc = 1/.

7. Define ‘Decibels’ in control theory. The decibel in control theory is defined by Decibels = 20 log10(AR) Thus, an AR of unity corresponds to zero decibels and an AR of 0.1 corresponds to -20 decibels.

12 13 8. Write the rules applied to the asymptotes on the Bode diagram. The following rules apply to the asymptotes on the Bode diagram;  The overall AR is obtained by adding the individual AR’s. For this graphical addition, an individual AR that is above unity on the frequency response diagram is taken as positive; an AR that is below unity is taken as negative.  The overall phase angle is obtained by addition of the individual phase angles.  The presence of constant in the overall transfer function shifts the entire AR curve vertically by a constant amount and has no effect on the phase angle.

9. Explain the frequency response for transportation lag. The transfer function of a transportation lag is Y(s)/X(s) = e- ds. Then, AR = 1 φ = -ω (radians) = -57.3 ω (degrees)

10. State Bode stability criterion. Bode stability criterion states that “A control system is unstable if the open-loop frequency response exhibits an AR exceeding unity at the frequency for which the phase lag is 180o”.

11. Define cross-over frequency. Explain its significance. The frequency at which the phase lag is 180o, in the Bode diagram, is called Cross- over frequency ‘ωco’. At ωco,  if AR < 1thEn the system is stable.  if AR = 1 then the system will continue to oscillate with constant amplitude even if there is no change in the load variable or in the set point.  If AR > 1then the system is unstable and the system exhibit oscillatory response because of the increase in the amplitude of the system.

12. Define gain and phase margin. o If the AR at which the phase lag is 180 (at ωco) is ‘A’ then the gain margin is defined as Gain margin = 1/A Phase margin is the difference between the phase lag 180o and the phase lag at 0 AR = 1. It is defined as Phase margin = 180 – φAR=1

13. What do you mean by Nyquist diagram? The Nyquist diagram is a polar plot of the frequency response for the open-loop transfer function G(s). The gain is plotted as the radius vector and the phase shift is plotted in degrees clockwise from the right-hand abscissa. There is a separate points for each frequency; the frequencies are indicated next to a few of the points, or an arrow is used to show the direction of increasing frequency. Some times a dotted line is used for negative frequencies, and the result from ω = -∞ to ω = +∞ form a closed curve.

14. State Nyquist stability criterion. A control system is unstable if the plot encircles the (-1) point in a clockwise direction. This occurs if the plot for positive frequencies passes to the left of the (-1) point, which just means that the overall gain is greater than 1 at 180o phase lag. Or

The closed-loop control system is stable if the number of denominator roots of G(s) with positive real parts is equal to the number of counterclockwise encirclements of the (-1) point.

15. Draw the Nyquist diagram for a first order system.

For GP(s) = KP/(s + 1), the Nyquist diagram is

16. What is a direct acting controller? If the controller output decreases as the measured variable increases then the controller is said to be Direct acting. If the controller output increases as the measured variable increases, then it is called Reverse acting. In other words, the controller is Direct acting if the gain ‘Kc’ is positive and Reverse acting if the gain ‘Kc’ is negative.

17. What is meant by tuning of controllers? The adjustment of the controller parameters to achieve satisfactory control is called ‘Tuning’. The process of ‘Tuning’ can vary from a trial-and-error attempt to find suitable control parameters for ‘good’ control to an elaborate optimization calculation based on a model of the process and a specific criterion of optimal control.

18. Define ultimate gain and ultimate period. According to the Bode criterion, the gain of a proportional controller which would cause the closed-loop control system to be on the verge of instability is (1/A); this is said to be the ultimate gain ‘Ku’. Thus, Ku = 1/A. The ultimate period ‘Pu’ is defined as the period of the sustained cycling that would occur if a proportional controller with gain ‘Ku’ were used. It is given by Pu = 2π/ωco, (time/cycle).

19. Name any two experimental methods available for tuning of controller settings. The experimental methods available for tuning of controller settings are;  Zeigler-Nichols method (closed-loop tuning method)  Cohen-Coon method (open-loop tuning method)

20. Write the Zeigler-Nichols controller settings for PID controller. The Zeigler-Nichols controller settings for PID controller are;

 Controller gain, Kc = 0.6 Ku

 Integral time, I = Pu/2

 Derivative time, D = pu/8 Where ‘Ku’ and ‘Pu’ are the ultimate gain and the ultimate period.

14 15 Part-B (Questions)

1. For the transfer function G(s) = [s2 (s + 10)]/[(s + 5)2 (s + 0.1)], sketch the Bode magnitude plot.

2. A control loop contains first order lags with time constants 10 and 30 secs and a time delay of 6 secs. Plot the open loop Bode diagram and determine the value of K C to give 30o phase margin. Only a proportional controller is used in the loop.

3. (i) Discuss Bode’s criterion for stability of a control system. (ii) Compare different stability criteria’s available for analysis of control system. (iii) Enlist the Zeigler-Nichols controller settings for different modes of control, indicating the significance of the parameters involved.

4. Plot the Bode diagram for the system whose overall transfer function is given by -0.3s [Kc e ]/[(s + 1) (s + 5) (s + 6)]. What value of KC leads to instability?

5. The transfer function of the process and measuring element connected in series is given by [e-0.75s]/[(4s + 1) (2s + 1)]. Sketch the open loop Bode diagram. Determine the ‘P’ and ‘PI’ controller parameters by Zeigler-Nichols method.

6. The transfer functions of the process. Control valves, measuring element are 1/ (20s + 1), 1/(4s + 1), 1/(6s + 1) respectively. Sketch Bode plot and calculate ultimate gain and ultimate period. Using Zeigler-Nichols rules, find the controller constants for a PID controller.

7. Consider a feed back control system with open loop transfer function given below; -5s G(s).H(s) = [KC e ]/[(s + 1) (3s + 1)]. Using Bode stability criteria, calculate the value of KC at which the closed loop system becomes unstable.

8. Open loop transfer function of a feed back control system is given below; -5s G(s).H(s) = KC e /[(s + 1) (2s + 1) (3s + 1)]. Using Bode stability criteria, calculate the value of KC for which the system is stable.

3 9. Prepare a Nyquist plot given G(s) = KC/(s + 1) . Find KC for stability, with a gain margin of 2.

10. Consider a feed back control system with open loop transfer function given below; G(s).H(s) = KC/[s (s + 1) (2s + 1)]. Sketch the Nyquist plot. Using Nyquist stability criteria, calculate the limiting value of KC at which the closed loop system is unstable.

15 16 UNIT-IV

1. When to go for advanced control schemes? If the response of the simple feedback system is unsatisfactory because of large uncontrolled load changes (even if the minor changes such as reducing a time delay or one of the smaller time constants was done) then advanced control (multi-loop systems) schemes can be considered.

2. Write briefly on ‘Cascade control’. Cascade control is often used to regulate the flows, temperatures and compositions (that are load variables or inputs to the process) by using additional controller. For example, the flow rate and temperature of the feed to a distillation column are often controlled by separate feedback systems to make it easier to achieve close control of product composition. The output of the primary controller (master controller) is used to adjust the set point of a secondary controller (Slave controller), which in turn sends signal to the control valve. The process output is fed back to the primary controller, and a signal from an intermediate stage of the process is fed back to the secondary controller.

3. Give an example for cascade control. Cascade control is often used for temperature control of chemical reactors because a slight deviation in temperature may lead to poor product quality and sometimes to a runway reaction. The primary controller acts on the difference between the set point and the measured variable, and the output is a pressure signal to the set point bellows of the secondary controller (In most newer pneumatic controllers, the set point is changed by changing the air pressure in a bellow rather than by moving a mechanical linkage). The secondary controller adjusts the flow of coolant to keep the jacket temperature at the value determined by the primary controller.

4. Explain the importance of Cascade control. Cascade control is especially useful in reducing the effect of a load disturbance that is located far from the control variable and which moves through the system slowly. The presence of the inner loop reduces the lag in the outer loop with the result that the cascade system (which has a high natural frequency) responds more quickly to a load disturbance.

5. Distinguish between feed-back and feed-forward control. A simple feed back system compares the set point and the measured variable, for any load disturbances, and the control action was taken with respect to difference in the value. A feed-forward control is considered, if a particular load disturbance occurs frequently in a control process. The quality of control can often be improved by the addition of feed-forward control. To provide for load disturbances that cannot be measured or anticipated, feed-forward control is always combined with feed-back control in a particular situation.

16 17 6. When feed forward control is used? Explain its advantages. If a particular load disturbance occurs frequently in a control process, the quality of control can often be improved by the addition of feed-forward control. The main advantage is that it uses information fed forward from the source of the load disturbance.  It reacts before the effect of a load disturbance has been detected.  It is good for system having significant transportation lag.

7. Give some examples of systems where feed forward control is used.  The flow rate of steam on shell side in a heat exchanger can be controlled by feed forward controller (this is frequently done to change the temperature of the tube side fluid).  The pressure in a distillation column is often feed-forward controlled.  Feed-forward temperature control of CSTR.  Feed-forward level control of drum boiler

8. Write the limitations of feed forward control. The limitations of feed forward control are;  The feed-forward control is usually restricted to correcting for only one load variable.  The success of using a feed-forward control depends on accurate knowledge of the process model, a luxury that may not be available in many applications.  The change in the parameters of a process cannot be compensated by a feed- forward controller because such change many times cannot be detected immediately.

9. Explain ‘Ratio control’. Ratio control is widely used in industry in the blending of two component streams (A and B) to produce a mixed stream of desired composition. It is essentially a flow- control problem in which the flow measurement of stream ‘A’ (the wild stream) is used to compute the set point for the flow of stream ‘B’ so that the desired ratio of components will be obtained.

10. What are the controlled variables in a binary distillation column? The controlled variables in a binary distillation column are;  Feed rate  Composition of both overhead and bottom product  Liquid level in the reflux drum and in the re-boiler  Column temperature, includes change in temperature at each plate  Column pressure

11. Write short notes on feed forward control of distillation column. The control objectives are the composition of the overhead and the bottom product. The feed-forward control of distillation column depends on two principle load disturbances, feed flow rate and feed composition. These two disturbances are measured and the signal is transmitted through the feed-forward controller, which adjusts the steam pressure in the re-boiler and the reflux ratio (manipulated variables).

17 18 12. Explain the cascade control of distillation column. The cascade control is used to maintain the temperature and composition of the bottom product of the distillation column. The temperature at the bottom of the column is measured and the signals are transmitted through the primary controller, which is PI or PID. The secondary (proportional) controller is used to compensate for the change in the flow rate of bottom product, which is coming out from the re-boiler. The secondary or the flow control loop is always cascaded with the primary temperature control loop.

13. List the controlled variables in a double heat exchanger. The controlled variables in a double heat exchanger are;  Steam and condensate flow rate  Inlet temperature of the hot fluid

14. Write short notes on feed forward control of heat exchanger. The control objective is to keep the outlet temperature of the cold fluid, by adjusting the steam pressure (manipulated variable). The feed-forward control of distillation column depends on two principle load disturbances, steam (hot fluid) flow rate and cold fluid inlet temperature. If any changes in the disturbances are detected in the inlet stream, these disturbances are immediately measured and the signals are transmitted through the feed-forward controller, which adjusts the control valve (for steam flow) in such a way to prevent any change in the outlet temperature of the cold fluid, so as to keep the controlled variable near its desired value.

15. Explain the cascade control of heat exchanger. The control objective is to maintain the outlet temperature of cold fluid at a desired value. The exit temperature of the cold fluid is measured and the signals are transmitted through the primary controller. The flow rate of steam (hot fluid) is measured and the signals are transmitted to the secondary controller, which is used to compensate for change in the flow rate of steam and the output signal acts on the diaphragm of the control valve to regulate the changes in the flow rate. The secondary flow control loop is cascaded with the primary temperature control loop, in which generally PI or PID controller is used as a primary controller and proportional (P) controller is used as the secondary controller. Here the offset caused by proportional controller in the secondary loop does not affect in controlling the output of the secondary controller of the cascade control system.

16. Distinguish between analog and digital controllers. In analog controllers, the signals are pneumatic (3 – 15 psig). The energy needed to operate these pneumatic components is a source of clean, dry air at a pressure of about 20 psig. In digital controllers, both electronic and pneumatic powers are required to operate the components. A transducer or converter is needed between the controller and the control valve to convert current (4 – 20 mA) to pressure (3 – 15 psig).

17. List out the tasks of a microprocessor based controllers. The tasks of a microprocessor based controllers are to;  Implement classical and advanced control algorithms  Provide static and dynamic displays on the monitor 18 19  Provide process and diagnostic alarms  Provide mathematical functions  Provide data acquisition and storage (archiving)

18. List out the advantages of a microprocessor based controllers. The modern microprocessor based control plants have several advantages, such as  The high speed of computations with large information storage capacity  Reduction in the function cost  Process safety for the control system It provides unlimited intelligence allowing to use advanced control techniques such as adaptive, inferential, direct digital control, supervisory computer control and programmed computer control. The term microprocessor is synonymous with the computer and therefore microprocessor based control is known as computer based control system.

19. Give the elements of a computer control system. The elements of a computer control system are;  Process  Measuring element  Transducer (or ADC)  Microprocessor based controller (linked with Monitor, Keyboard and Printer)  Transducer (or DAC)  Control valve

20. What is an analog to digital converter? It is represented as ADC or A/D converter, which converts the continuous (analog) signal to a digital signal that can be used in the computer. Since the output from the computer is a digital signal, a DAC or D/A converter is needed on the output of the computer so that a continuous (analog) signal is available to operate the control valve. Typical analog signals associated with the A/D and D/A converters range from 4 – 20 mA or 1 – 5 V.

21. Write down the PID controller equation in discrete form. The ideal PID controller equation in time domain is

To discretise the controller, we need to approximate the integral and the derivative terms to forms suitable for computation by a computer. From a purely numerical point of view, we can use:

Therefore, the discrete form of PID algorithm is

Part-B (Questions)

1. Explain, with an example and diagrams, the cascade control system as applicable for a chemical process.

2. Derive the transfer function for the cascade control system and discuss its advantages.

3. (i) Explain the advantages of cascade system over a simple feedback system. (ii) Analyze the concept of feed forward control system and its application in industries.

4. (i) Explain tuning of primary and secondary controllers in the cascade control system. (ii) Sketch and explain typical computer controlled chemical process.

5. (i) Obtain Gf for the feed forward –feedback system, so that the output variable doesn’t change when load disturbance occurs. (ii) If Gf is a lead-lag transfer function, explain the procedure to evaluate the time constant of the lead and lag element using Foxboro’s rule.

6. (i) Discuss the advantages of feed forward control. (ii) Briefly explain on ‘Ratio control’.

7. Discuss various control schemes used for the control of shell and tube heat exchanger.

8. With a neat block diagram, explain how the temperature of process fluid can be controlled in a heat exchanger.

9. With a diagram, explain the application of different control loops (or various control strategies) as applicable for a distillation column control. List your assumptions clearly.

10. (i) Discuss the tasks of a micro-processor based controller. (ii) Discuss in detail the implementation of distributed control system in chemical plants.

UNIT-V

1. Name any two characteristics of measuring instruments and define them. The two (static) characteristics of measuring instruments are (i) Static error (ii) Drift. Static error of an instrument is the difference between the true value of a quantity not changing with time and the value indicated by the instrument. Drift is an insidious quality in industrial instruments, (Zero drift – whi9ch is usually due to simple effect, such as permanent set or slippage; Span drift – involves a gradual change in which the calibration from zero upward changes a proportional amount; A third kind of drift occurs when only one portion of a calibration changes) because it is rarely apparent and must be carefully guarded against by continuous inspection and maintenance.

2. List the static and dynamic characteristics of process control instruments. The static characteristics of process control instruments are;  Static error (Accuracy)  Drift (Reproducibility)  Dead zone (Sensitivity) The dynamic characteristics of process control instruments are;  Lag (Speed of response)  Dynamic error (Fidelity)

3. Define sensitivity and dead zone. Sensitivity denotes the smallest change in value of a measured variable to which an instrument responds (that is, the instrument has a dead zone). On the other hand, it may mean that the instrument produces a given deflection for a given change in value of a measured quantity (that is, the instrument has a given span).

4. Name some instruments for measurement of temperature. The instruments for measurement of temperature are;  Thermocouples  Bimetallic thermometer (0-500oC)  Resistance thermometer (20-600oC)  Vapor pressure thermometer (0-400oC)  Mercury in glass thermometer (0-500oC)  Radiation pyrometer (300-3000oC)  Optical pyrometer (300-3000oC)  Photoelectric pyrometer(500-1500oC)  Platinum resistance thermometer (-200 to 0oC)

5. What is Seebeck effect? In 821 Seebeck discovers that a current flows in a thermoelectric circuit when the temperatures at the junctions are different (hot and cold junctions of simple thermoelectric circuit). There is therefore a thermal e.m.f. generated in the circuit, which causes the current flow. By the principle of conservation of energy, it is

21 22 apparent that this energy under static conditions must come from the absorption of heat from external sources.

6. What is the principle of operation of a thermocouple? A thermocouple is made up of two dissimilar metals joined together resulting generation of a thermal e.m.f (electro motive force). The reference junction of two dissimilar metals is maintained at low temperature at 0OC in an ice box and the measuring junction is the hot junction indicating the temperature of the system. According to Seebeck effect, a current flows in a thermoelectric circuit because of the difference in the temperature at the two junctions and consequently the thermal e.m.f. is generated in the circuit resulting the flow of current in the circuit. The Thomson effect gives the relationship between the e.m.f. generated in the thermoelectric circuit and the difference in temperature between the two junctions of a thermocouple circuit. The generated e.m.f. is proportional to the temperature difference in the wire and depending on the different metals of the thermocouple.

7. What are the commonly used thermocouples? The commonly used thermocouples are;  Copper – Constantan (100-700oC)  Iron – Constantan (0-600oC)  Chromel – Alumel (100-1000oC)  Platinum – Platinum (13% Rhodium or 10% Rhodium) (500-1500oC)

8. State law of intermediate temperatures. Law of intermediate temperatures provides a means of relating the e.m.f. generated under ordinary conditions to what it should be for the standardized constant temperature.

9. Indicate standard temperature scales with their ranges. Centigrade scale (used in scientific literature) – assigns 0OC to the ice point and 100oC to the steam point. Kelvin scale (used in technical literature) – assigns 273.16OK to the ice point and 373.16oK to the steam point. Fahrenheit scale (used in most English speaking countries) - assigns 32OF to the ice point and 212oF to the steam point. Rankine scale (used in Engineering literature) - assigns 491.69OR’ to the ice point and 671.69oR’ to the steam point. Reaumur scale (used in few European countries, especially in alcohol industries) - assigns 0OR to the ice point and 80OR to the steam point.

10. Name few instruments for measurement of pressure. The instruments for measurement of pressure are;  Liquid-head manometers [U-tube (< 30psi), Differential (<30psi), Inclined (small pressure difference), Inverted U-tube (< 30psi)and Ring manometer (< 10000psig)]  Bellows pressure element (< 100psi)  Bellows differential pressure gauge (< 200psig)  Bell differential pressure gauge (< 1000psig) 22 23  Inductance pressure meter (30 to 2000psig)  Pneumatic balance pressure meter (up to 600psig)

11. State the various composition measuring instruments. The various composition measuring instruments are;  Mass spectrometer (used in petroleum refining, in rubber analysis, isotope analysis)  Infrared analyzer (used in pharmaceutical industry – organic and inorganic compounds)  Emission spectrometer (used for the analysis of the metallic compound)  Polaragraph (used in the analysis of alloys and ores)  X-ray diffraction (used in the analysis crystalline and amorphous solids, control of dye and filler in rubber, particle size determination in ceramic industry)

 Thermal conductivity cell (used in the analysis of CO2 gas; determination of H2 in nitrogen, air and oxygen; determination of ammonia, hydrocarbon, carbon monoxide, argon and water vapor in air)  Psychrometer, Hygrometer (used in the analysis of moisture in air)  Refractometer (used in the analysis of composition of the miscible solution)

12. Mention the principle involved in the concentration (composition) measurement. Principle involved in Mass spectrometer: In this instrument the sample of gas at 40 microns mercury is introduced into the ionization chamber in which the vacuum is maintained at less than 40 microns mercury, absolute. The gas is combined with electrons emitted from the filament in the chamber and transformed into ions; neutral fragment ions are positively charged, move towards the two plates where the electric potential field accelerate the ions on both the plates resulting a parallel beam. The ion beam deflecting in a circular path because of the presence of the magnetic field in a circular tube. The radius of the circular path is depending on the mass and the velocity of the ion. Numbers of such beams are formed having different specific mass of ions. By accelerating the voltage at the two plates, the selection of a particular beam to strike the collector an be fixed and the ions give the charge to the collector plate, which is amplified and recorded by the potentiometer; the intensity of the ion beam for different mass of the ion is recorded, giving the spectrum. The analysis of the spectrum gives the composition of the gas by comparing the spectrum of a pure substance.

13. What are variable head meters? Give examples. The variable head meters is the most common method used to measure the flow of fluid is closed pipes, which operates by measuring the pressure differential across a suitable restriction to flow. The examples are (i) Venturi meter (ii) Orifice meter

14. List various orifice meter tappings. The various orifice meter tappings are;  Thin-plate square-edge orifice (concentric, eccentric and segmental)  Orifice with flange taps

23 24  Orifice with pipe taps  Orifice with vena-contracta taps

15. Mention any two flow measuring devices.  Volumetric flow rate (Closed channel flow – Orifice meter, Venturi meter, Pitot tube and Rotameter; Open channel flow – Notches and weirs – triangular, rectangular, etc.,)  Mass flow rate (Magnetic flow meter)

16. Distinguish between variable head and variable area flow meters. The variable head meters is the most common method used to measure the flow of fluid is closed pipes, which operates by measuring the pressure differential across a suitable restriction to flow. The examples are (i) Venturi meter (ii) Orifice meter The variable area meters are very oftenly employed, and they operate from the variation in area of the fluid stream. Example: Rotameter

17. Explain the principle involved in the measurement of pH. The most common industrial method of measuring pH is by glass-cell and calomel- cell electrodes, used with a potentiometer instrument. In brief, this method requires that an electrode be immersed in the solution. An electric potential is produced at the electrode which forms an electrolytic half-cell. This the measuring cell. A second electrode is required to provide a standard potential and to complete the cell. This is the reference cell. The algebraic sum of the potentials of the two half-cells is proportional to the concentration of the hydrogen ions in the solution.

18. How the viscosity is measured? List few viscometers. Viscosity is a characteristic sometimes called fluid friction. Consequently, it can be measured by measuring friction or, actually, shear force. The few viscometers are (i) Red-wood viscometer (ii) Saybolt viscometer (iii) Oswald’s viscometer.

19. How humidity of gases can be measured? Dew-point method is used to measure the absolute humidity (weight of vapor per unit weight of dry gas).The instrument consists of a thin metal tube covered with a glass cloth, saturated with lithium chloride. A double winding of silver wire is made over the glass cloth. A power supply of a few volts is connected to the winding. The electrical conductivity between wires is directly proportional to the moisture in the salt taken on from the surrounding gas. When the moisture is low, there is a small current flow, and the temperature rise of the cell due to Joule heating is low. When the moisture is high, the current flow is high and the temperature of the cell is high. Thus, a thermometer bulb placed inside the metal tube will measure the cell temperature and, therefore, absolute humidity.

20. Using electrical conductivity, which parameters can be measured? The parameters that can be measured using electrical conductivity are;  Temperature  pH  Composition of gases  Total dissolved salts or minerals in water 24 25

Part-B (Questions)

1. Explain with principle, the range of application of thermometers commonly employed in chemical industries.

2. Explain the working of a bimetallic thermometer, material of construction and range of operation with neat sketches.

3. (i) Explain the working principle of vapor pressure thermometer. (ii) Write about the principle of temperature measurement using radiation and optical pyrometers.

4. Discuss the properties and types of industrial thermocouples with range of operation & advantages.

5. (i) Compare resistance thermometers and thermocouples with their principle of operation. (ii) Explain why thermal wells are necessary and the various factors that are to be considered in their selection.

6. (i) What are the principles on which pressure measuring instruments work? List out the instruments used for the pressure measurement and indicate their range of operation. (ii) Briefly describe the working of an ionization type vacuum gauge (vacuum pressure) with a neat sketch.

7. (i) What are the methods used for measuring high pressure? (ii) Indicate a method for measuring pressure of a corrosive fluid. (iii) With a neat sketch, explain the working of McLeod gauge and its range of operation.

8. Compare variable head meters and variable area meters in industrial flow metering with their principles of operation.

9. (i) With a neat diagram, explain the principle and working of a spectrometer. (ii) Explain the principle and working of instruments used in process industries for measuring viscosity.

10. (i) Explain the principle and working of a pH meter. (ii) Discuss briefly on the measurement of thermal conductivity. (iii) Write in detail the measurement of humidity of gases.

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