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PLC and Inverter Forum
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Re: PID Questions








Mr. Edwards,








I placed your inquiry on our Web Forum in hopes of soliciting additional input. 


So far, no one has been “brave” (or interested) enough to post a reply.  Rather than


leave you “hanging”, I thought I would at least throw in my 2 cents worth.








I am a Senior Member of the ISA (over 20 years), so hopefully my comments will come close. 


Just from your wording, I surmise you need this information for a training course you are taking. 


Because the terms seem “exact”, I deduce that your instructor has referenced a particular book or manual. 


Therefore, I have footnoted some documents supporting the material I present.








Dampening, is an element of “Second Order Response”. 


The terms of which you inquired, have to do with the value of the “dampening ratio”  (indicated


by the symbol ξ.











  1. When


    ξ < 1.0, the system is said to be “under-damped” and will overshoot the final steady-state value. 


    If ξ < 0.707, the system will not only overshoot but will oscillate about the final steady-state value.








  2. When


    ξ > 1.0, the system is said to be “over-damped” and will not oscillate or overshoot the final steady-state position. 








  3. When


    ξ = 1.0, the system is said to be “critically damped” and yields the fastest response without overshoot or oscillation.












Error Detection, is a rather nebulous term, in my humble opinion. 


In its simplest form, ERROR = Set Point – Measured Variable.  The meaning (of Error


Detection) is solely based upon the context in which it is used.  Your tea water may be boiling,


but your thermometer may only indicate 98°C.  In


this instance, the “error detector” is your eyes and brain.  Just as valid, is the concept


that “Error Detection” (sometimes referred to as a Comparator
)


is the heart of all feedback control systems.  The error signal, which is the output of the


comparator, becomes the input to the feedback controller,  Based on the error signal, the


controller calculates a signal to the final control element – which is typically a control valve – and this in turn controls the


manipulated variable input to the process.








Lastly, unless I have missed your point, the term “dead band”, “dead zone”,


“differential gap”, and “neutral zone” are often used synonymously.   “Sensitivity”


is defined as “the smallest change in measured variable to which an instrument properly responds
.” 


“Dead Band”, is then the opposite of  Sensitivity. 


It is defined as, “The largest change in a measured variable which is not detected by an instrument
.” 


In conventional practice, it is not possible to build a device that is sensitive to the sign of extremely small deviations – and


more importantly – it is not desirable to do so.  Such an excessively sensitive controller


would undergo needless wear and tear on its moving parts and contacts and would keep the process very unsteady.  The solution in most commercial two-position controllers (on-off), is to establish a dead zone of about 0.5% to 2.0% of


full range.  The   Dead Band  straddles the set-point; no control action takes place when


the control variable lies within the dead zone itself.   This seems to be one of those


topics that an entire semester of study could be devoted.  There are even control strategies


that incorporate Dead Band.  An example of this is a variant of two-position (on-off) control


with differential gap; called appropriately enough, “Three-Position Control”.  Here, the


controller responds with an intermediate output when the controlled variable lies within the neutral zone.








I hope that even if I have not ‘hit the mark’, I have at least gotten you close.








Good Luck with your project.




Timothy Davis  




 




p.s. The ideas, views, and/or opinions expressed here are mine, and are not necessarily


reflective of those of my employer.

























Béla G. Lipták Instrument Engineers Handbook Chilton Book Company, Radnor Pennsylvania 1969, p 13


















Paul W. Murrill Fundamentals of Process Control Theory Instrument Society of America 1981, p 26


















Norma R. Whitaker Process Instrumentation Primer Petroleum Publishing Company Tulsa, Oklahoma 1980, p 5


















Ibid., p. 5





















--- --- --- --- --- --- --- --- ---

Replying to:

Sent: Tuesday, April 23, 2002 4:54 AM




with regard to P,I,D control can you explain trhe terms:




underdamped


overdamped


critically damped




can you also explain the principles behind error detection and demonstrate the significance of deadband.




i would be very grateful as at the moment i hvent a clue