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Homework Help: Reverse-acting proportional pressure controller

  1. Oct 1, 2017 #1
    1. The problem statement, all variables and given/known data

    A 5 to 20 bar reverse acting proportional pressure controller has an output of 4 to 20 mA. The set point is 11 bar. Determine:
    (a) the measured value pressure which gives an output of 15 mA when the proportional band setting of the controller is 40%
    (b) the proportional band setting which will give an output of 8 mA when the measured value is 14 bar and the desired value is 11 bar.


    2. Relevant equations


    3. The attempt at a solution
    Can anyone help me with my findings whether i am in the right direction?
    Part (b) should be a figure or a %? Thanks

    (a)

    PB = 40% = 0.4
    Controller output (Co) = initial control valve + (error x gain)
    Gain Comax - Comin / PB = -(20-4) / 0.4= - 40

    error e(t) = SP - MP
    Controller output = Comax + Gain (SP - MP) 15 = 20 - 40 (11 - MP) MP = 10.9 bar


    (b)
    Controller output = Comax + Gain (SP - MP) 8 = 20 + Gain (11 - 14) Gain = 4

    4 = 16 / PB = 4
     
  2. jcsd
  3. Oct 6, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Feb 1, 2018 #3
    Hi, have you resolved your problem yet?
     
  5. Nov 3, 2018 #4
    I'm struggling with this.

    So far I've got 4ma = 5 bar and 20ma=20bar..... So, 15ma is equal to 4ma +11ma which is an increase of 68.75%. 68.75% of 5-20bar is 10.3125bar.

    So, a 15mA signal will give 10.3125 bar if the PB were 100%???? I'm not sure how to work in the PB of the controller being 40%
     
  6. Nov 4, 2018 #5

    Tom.G

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  7. Nov 9, 2018 #6

    David J

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    Does 4mA = 20 bar and 20mA = 5bar ?? (Reverse acting)
     
  8. Nov 9, 2018 #7

    Tom.G

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    Yes.
     
  9. Nov 10, 2018 #8

    David J

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    Thanks for that, I am trying to work this out based on examples given in lessons but they are not clear.

    Can you look at the attachment. This contains 2 examples from the lesson I am following.

    There are 2 diagrams each with 3 proportional bands, 30%, 50% and 100%. They are all centered at 50% of the measured value.

    I understand from this that the proportional band is always associated with the measured value, the input which in the case of this question, is the pressure, 5 - 20 bar. This will be the x axis

    The controller output is 4 - 20 mA. This is the y axis

    So for this question I think that I could create a graph similar to the attached examples with the 5 - 20 bar input on the x axis and the 4 - 20 mA as the Y axis.

    The scaling of the pressure would have to be reduced (squeezed) to 40% on the x axis, centered around 50% of the measured value.

    From this I should be able to strike a line from the 15 mA mark on the y axis and find the approx pressure required to generate a value 15 mA from the x axis

    Does this make sense ??

    Or should the PB be centered around the set-point or desired value, which in the case of this question, is 11 bar
     

    Attached Files:

    Last edited: Nov 10, 2018
  10. Nov 10, 2018 #9

    Tom.G

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    I think it will be easier to see if you start by drawing a graph similiar to the first one in your attachment, but with the axes labelled with the actual pressure and the actual current output of the controller. Start both axes at Zero and initially draw the graphed line for the full working range of the pressure with the controller covering 100% of the pressure range.
     
  11. Nov 10, 2018 #10

    David J

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    Hello again, I worked on this yesterday, trying different methods and I have attached my examples. I seem to get a value of approx 9.75 bar in all cases no matter where I position the PB. I am not sure if this is the correct approach or not and I am not able to mathematically verify this value of 9.75 bar. I am not sure how to do that.
    In the first instance could you look at my graphs and advise if this is the correct approach or not please. My "first attempt" is in answer to your advice in the last post
     
    Last edited: Nov 12, 2018 at 10:13 PM
  12. Nov 11, 2018 #11

    Tom.G

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    Hmmm. Your results work ONLY IF YOU CAN CHANGE THE OFFSET to get the (a) and (b) answers.

    Given the problem statement, I would design on the basis of 20 bar pressure always gives 4mA output, and then, if possible, to use one PB that could cover both parts (a) and (b). If more than one PB is needed for the two questions, then state/show the two different values.

    Does the original problem, or its context, say anything about offsets? The problem statement given in this thread refers only to the "proportional band setting" with no mention of even the concept of "offset."

    It would be a big help if someone can copy and paste the original problem.

    Optional:
    If you want to generate a formula for a final answer rather than a graph, I suggest that the graph 'Y' axis start at Zero current. This will make it more obvious when generating the formula that there is an offset. (it's easy to forget otherwise :biggrin:)

    Cheers,
    Tom

    p.s. This has got me thinking some too; it has been a few decades since I've used these!
     
  13. Nov 11, 2018 #12

    David J

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    Hi

    The original problem is copied below. It does not mention offsets so I have to assume tat the control loop is stable and the controller is set up properly. The 3 graphs I posted were my attempts, varying the position of the PB with respect to the measured value. I am wondering if I am looking to deeply into this because part B of the question seems to be written in a way that can be calculated if I knew of the equation

    A 5 to 20 bar reverse acting proportional pressure controller has an output of 4 – 20 mA. The set point is 11 bar. Determine:

    (a) The measured value pressure which gives an output of 15 mA when the proportional band setting of the controller is 40%
    (b) The proportional band setting which will give an output of 8 mA when the measured value is 14 bar and the desired value is 11 bar


    In the first post of this thread there is an equation (see below) which I think assumes there is an error but the result of that calculation (10.9) does not agree with my graphs so that has kind of thrown me of the route a bit

    PB = 40% = 0.4
    Controller output (Co) = initial control valve + (error x gain)
    Gain Comax - Comin / PB = -(20-4) / 0.4= - 40

    error e(t) = SP - MP
    Controller output = Comax + Gain (SP - MP) 15 = 20 - 40 (11 - MP) MP = 10.9 bar
     
  14. Nov 11, 2018 #13

    Tom.G

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    Perhaps we are interpreting the problem statement differently.
    I am reading that as there being a self-contained pressure controller that reports the measured outlet pressure to the 4-20mA loop.
    Another interpretation could be a proportional pressure valve that is driven by a controller... which seems to be the interpretation you are using.

    The apparent ambiguity of the problem statement in the First Post is why I asked for the ORIGINAL statement, as in a link to where it appeared or at least a copy-and-paste.

    I have put in a request for other any other Advisor to join this discussion to help sort things out.

    Cheers,
    Tom
     
  15. Nov 12, 2018 at 1:38 AM #14

    David J

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    Ok thanks for the update, hopefully we can solve this
     
  16. Nov 12, 2018 at 10:13 PM #15

    David J

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    I was given a small amount of information regarding this, an example which could help.
    As we have said the
    "controller is reverse acting hence 20mA corresponds to 8 bar and 4mA to 14 bar. 6 bar pressure change = 16mA then calculate for output of 15mA (i.e a change of 11mA from 4 to 15)"
    I cant work out how the above statement can be incorporated in this problem but it obviously can be
     
  17. Nov 12, 2018 at 10:35 PM #16

    Tom.G

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    It may help to realize that a straight-line graph can be characterized by its Slope-Intercept form, Y=mX+b. You made use of that in your earlier calculations.
    Y= Dependent variable
    m= Slope of the line
    X= Independent variable
    b= Y Intercept

    Cheers,
    Tom
     
  18. Nov 12, 2018 at 10:44 PM #17

    David J

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    I have been unofficially told that one of my earlier graphs was actually correct although there are other methods of calculating this question. What I am trying to do now is mathematically work out the answer. I know the answer is approx. 9.75 bar for a 15mA signal when the PB is 40%. I am just trying to prove the math now. I need to read up on Y=mX+b as I think there maybe some differential in there which is not my strong point
     
  19. Nov 13, 2018 at 2:06 AM #18

    jim hardy

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    I would venture that
    as @Tom.G suggested
    y = mx + b is the right approach.
    I'd make y be output milliamps
    and x be input bars.
    so as to make the independent variable, pressure, plot on the X axis
    and the dependent one , milliamps, on the y axis.

    x and m and b are not simple single term constants though.
    Look at the units - we have to get from psi to ma,
    so m will be the product of at least two individual m's -
    one for units conversion let's call it munits
    and another for controller gain which is 1/(proportional band) let's call it mgain
    and m's sign will reflect direct or reverse acting..

    Next, since controllers operate on an error signal, namely difference between input and setpoint,
    input x will be that difference namely (pressure - setpoint)
    so x = (bars - setpoint)

    lastly b will take care of the 4ma offset in controller output.
    But there's a sneaky little fact not mentioned in the problem statement, namely,
    ....... in the absence of directions to the contrary you set up controllers so they have 50% output at zero error
    that way they'll control somewhere around mid output and not bang against a limit.
    so our b term also takes care of the fact that at zero error, ie x = zero,. the controller's output will be 50% or 12 ma.
    meaning b is 12 ma not the 4 you'd likely think. .

    y = munits X mgain X (input - setpoint) + 12 milliamps

    so let's step through what we know
    ..
    He didn't state at what proportional band that relation holds so let us assume it's at pb of 100%, meaning it take a fullscale change at input to cause a fullscale change at output.
    So, munits = Δoutput / Δinput = 16 ma / 15 bar
    Furthermore, since it's reverse acting, ie increasing input causes decreasing output,
    Δ's in numerator and denominator have opposite signs
    meaning munits must be negative.
    So munits = -(16/15) ma / bar .




    aha ! Error then will be (pressure -11) bars and that's x .
    x = (bars - 11)


    Great ! He's told us pb is 0.4 which is 1/(controller gain),
    That makes mgain =2.5 ,
    and m = munits X mgain = -16/15 X 2.5 = = -8/3
    and x = pressure - 11
    Now y = mx + b
    and y = 15
    so
    15 = -8/3 X (bars-11) + 12
    (15-12) X 3/8 = -(bars - 11)
    9/8 = 11 - bars
    bars = 11 - 9/8 = 9.875



    okay,
    y = 8
    x is (bars - setpoint) = (14-11) = 3
    b is 12 as before
    solving y = mx + b for m
    8 = m X 3 + 12
    (8 -12 ) / 3 = m = -4/3
    since m = munits X mgain
    mgain = m / munits = ( -4/3 ) / (-16/15) = 5/4 ,

    so pb = 1/mgain = 1/(5/4)= 0.8 = 80%

    [ it's latei= --- i hope i didnt bungle my arithmetic. ]


    Does above make sense ?

    There's no step that is complicated. Just you have to be meticulous.

    let me know if you find a mistake.

    old jim
     
    Last edited: Nov 13, 2018 at 2:20 AM
  20. Nov 13, 2018 at 2:38 AM #19

    jim hardy

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    Wow those would be two different problems with different answers.
    Old adage "A question well stated is half answered... "
    I sure missed that ambiguity. (red faced chagrin icon)

    Seems to me that were this gizmo reporting measured process pressure its setpoint and PB would be superfluous .
    it would be acting as a simple pressure transmitter with simple span and zero adjustments.
    Asking about PB and Setpoint would be a misleading "dirty trick" on students.

    old jim
     
  21. Nov 13, 2018 at 9:30 AM #20

    David J

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    Gents
    Post 18 is correct. It makes a lot of sense to me now. In past lessons I have seen the use of y = mx + b but never connected it with this problem. I had confirmation that my graph was correct and your answer in post 18 mathematically proves that. All I need to do now is revisit the lessons using this and understand how it calculates in this case. I dont think I am finished with this just yet but very close now. Thanks to you both (Tom and Jim) for helping out with this so far
     
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