8.C) ZIEGLER-NICHOLLS METHOD :This technique also called ‘Ultimate Cycling Method’ is based on adjusting a closed loop until steady oscillations occur. Controller settings are then based on the conditions that generate the cycling. This method is based on frequency response analysis.

Unlike the process reaction curve method which uses data from the open-loop response of a system, the Ziegler-Nichols tuning technique is a closed-loop procedure. It goes through the following steps:

i)Bring the system to the desired operational level

ii)Reduce any integral and derivative actions to their minimum effect

iii)Using proportional control only and with the feedback loop closed,introduce a set point change and vary proportional gain until the system oscillates continuously.The frequency of continuous oscillation is the cross over frequency ‘⍵0’.Let ‘M’be the amplitude ratio of the system’s response at the cross over frequency.

iv)Compute the following two quantities :

Ultimate gain ¿Ku=1/M

Ultimate period of sustained cycling =Pu =2π/⍵c 0min/cycle

v)Using the values of Ku & Pu, Ziegler & Nichols recommended the following settings for feedback controllers.

Mode K p T I(Min) T d(Min)

Proportional K u/2 ¿¿ ¿¿

Proportional-Integral K u/2.2 Pu/1.2 ¿¿

Proportional-Integral-Derivative

K u/1.7 Pu /2 Pu/8

The settings above reveal the rationale of the Ziegler-Nichols methodology.

i)For proportional control alone,use a gain margin equal to 2

ii)For PI control use a lower proportional gain because the pressure of the integral control mode introduces additional phase lag in all frequencies with destabilizing effects on the system.Therefore lower K p maintains approximately the same gain margin.

iii)The presence of the derivative control mode introduces phase lead with strong stabilizing effects in the closed-loop response.Consequently the proportional gain K p for a PID controller can be increased without threatening the stability of the system.

10.a)DESCRIBE THE CONSTRUCTION & WORKING PRINCIPLE OF PNEUMATIC CONTROL VALVE :

The pneumatic valve is the most commonly used final control element.It is a system that exhibits inherent second order dynamics.

Consider a typical pneumatic valve shown in Fig. The position of the stem(or equivalently of the plug at the end of the stem)will determine the size of the opening for flow and consequently the quantity

of the flow(flow rate).The position of the stem is determined by the balance of all forces acting on it.These forces are

Fig.1.33pneumatic valve

pA=Force exerted by the compressed air at the top of the diaphragm;pressure ’p’ is the signal that opens or closes the valve & ‘A’ is the area of the diaphragm.

Kx=Force exerted by the spring attached to the stem & the diaphragm ‘K’ is the Hooke’s constant for the spring & ‘x’ is the displacement,it acts upward.

C*dx/dt=Frictional force exerted upward & resulting from the close contact of the stem with valve packing;C is the friction coefficient between stem & packing.

Applying Newton’s law,we get

pA - Kx – C*dx/dt = (M/gc)*d2 x/dt OR (M/K gc)*d2 xd t 2

+C/K* dx/dt+x = A/K*p

Defining τ 2=M/K gc, 2ζτ=C/R & Kp = A/K

We get τ 2∗c+, 2ζτ*dx/dt+x=KpP

The last equation indicates that the stem position’x’ follows inherent second-order dynamics.The transfer function is

G(s) = X(s)/P(s) = A/K/(M/gc)s2+C/K*s+1

G(s) = Kp/τ 2 s2+2ζτs+1

10.b)AT ARE Cv & Kv?EXPLN THEIR RELATIONHIP.

One of the most useful factors to determine the size of a control valve in the ‘flow coefficient’ or Cv factor(or Kv factor).Practically all control valve manufactures supply Cv factors for their valves.These factors form the basis for all calculations.The flow coefficient indicates the amount of flow the control valve can handle under a given pressure drop across the control valve.

Cv factor : The flow coefficient (Cv)is defined as the flow rate of water in gallons per minute at 60⁰F through a valve at maximum opening with a pressure drop of 1 psi measured in the inlet & outlet pipes directly adjacent to the valve body.

Kv factor :Whenever the flow coefficient is mentioned in metric units,it is denoted by the symbol Kv which is defined as the flow rate of water in m3/hour at about 30⁰C flowing through the fully opened control valve at a pressure drop of 1kg/c m2 across the control.

The following relationship between Cv & Kv can generally be used.

Cv = 1.17Kv ; Kv = 0.86Cv

The flow coefficient is determined by the manufacturer for various types & sizes of valves by actual experiments with water.The flow coefficient for 100% valve opening is termed as Cv (or Kv) of the particular valve size & the variation of Cv (or Kv) at different valve openings is given in the form of a graph,which is termed as valve characteristic.

12.b) VALVE POSITIONER : The main purpose of having a valve positioner is to gurantee that the valve does move to the position where the controller wants it to be.By adding positioner one can correct for many variations including changes in packing friction due to dirt,corrosion,or lack of lubrication;variations in the dynamic forces of the process sloppy linkages or non linearities in the valve actuator .The effective dead band of a valve/actuater combination can be as much as 5% with the addition of a positioner it can be reduced to less than 0.5%.It is job positioner to protect the controlled variable from being upset by any of the variations.In addition the positioner can be used for split-ranging the control signal between more than one valve,for increasing the actuator speed for modifying the valve characteristics by cams or electronic function generators.But these reason do not necessitate the use of positioners as they can be achieved by other means without using positioner also.

The valve positioner is a high-gain plain proportional controller which measures the valve stem position compares that measurement to its set point & if there is a difference corrects the error.The open-loop gain of positioners ranges from 10 to 200 (proportional band of 10% to 0.5% )& their periods of oscillation range from 0.3 10 10 seconds(frequency response of 3 to 0.1 Hz).In other words the positioner is a very sensitively tuned proportional only controller.

12.d) I/P CONVERTER : The current to pressure converter or simply I/P converter is a very important element in process control.Often when we want to use the low-level electric current signal to do work it is much easier to let the work to be done by a pneumatic signal.The I/P converter gives us a linear way of translating the 4-20mA current into a 0.2 to 1kg/c m2 signal (3 to 15 psi signal).There are many designs for these converters,but the basic principle almost always involves the use of a flapper/nozzle system.Fig. illustrates a simple way to construct such a converter.Notice that the current through a coil produces a force that will tend to pull the flapper down & close off the gap.A high current produces a high pressure so that the device is direct acting.Adjustment of the springs & perhaps the position relative to the pivot to which they are attached allows the unit to be calibrated so that 4mA corresponds to 0.2kg/c m2 (or 3psi)& 20mA corresponds to 1kg/c m2(or 15 psi).

Fig.4.5