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Re: Stability in PID Controllers

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Tim Wescott <tim@seemywebsite.really> writes:

> On Fri, 12 May 2017 11:17:05 -0400, Randy Yates wrote:
>
>> I know next-to-nothing about this topic, but the following question has
>> popped into my mind several times.
>> 
>> It seems like folks generally (and perhaps this is totally wrong) design
>> PID controllers by basically selecting what they think are "good"
>> constants for the proportional, integral, and derivative terms. That is,
>> they just sorta play with their systems and tweak the terms until it
>> seems to work smoothly.
>> 
>> However, how do you know that a particular configuration is stable?
>
> If you are tuning informally, then the informal way of making sure the 
> system is stable is to make sure that it is neither singing nor dancing.  
> Telling the difference between an autonomous oscillation and some 
> external signal being amplified is a matter of experience.
>
> If you're doing formal loop tuning (which is _not_ a matter of randomly 
> choosing values, but rather measuring or deriving a plant model from 
> first principles, and then doing real live math on the model), then there 
> are a number of ways which are appropriate to the methods you're using.
>
> If you're going by swept-sine measurement of the plant response, then 
> Bode and/or Nyquist charts.
>
> If you're going by a Laplace-domain model (i.e., transfer functions), 
> then you work out the transfer function of the overall system and decide 
> if its stable (or you decide on the pole locations of the finished system 
> and get your PID gains from that).
>
> If you're going by a linear state-space model, then you check the 
> eigenvalues of the model of the overall system, or you do your design by 
> pole placement.
>
> If you're using a nonlinear plant model, then you use an appropriate 
> nonlinear method (I don't know what's popular -- I rarely have to do 
> this, and it seems that each problem has its own correct method).

Hey Tim,

Thank you for such a comprehensive response. 

I was probably not clear in my question. I wasn't asking how to formally
determine stability - that I have had a small amount of experience in,
and certainly have studied some methods in the control system classes
I've had (although I've forgotten much of it).

I guess what I'm asking (which may have been a bit of a dumb question)
is, is there some inherent property of PID controllers that makes them
unconditionally stable, or at least stable in a wide variety of
situations? I.e., is it unneceessary for folks who just sort of "tweak"
such systems to be concerned about their stability?

I'm pretty sure the answer to that last question is: no. 
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com

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Stability in PID Controllers Randy Yates <randyy@garnerundergroundinc.com> - 2017-05-12 11:17 -0400
  Re: Stability in PID Controllers rickman <gnuarm@gmail.com> - 2017-05-12 12:40 -0400
    Re: Stability in PID Controllers Tim Wescott <seemywebsite@myfooter.really> - 2017-05-12 16:19 -0500
  Re: Stability in PID Controllers danielot@gmail.com - 2017-05-12 09:41 -0700
  Re: Stability in PID Controllers Tim Wescott <tim@seemywebsite.really> - 2017-05-12 13:38 -0500
    Re: Stability in PID Controllers Randy Yates <yates@digitalsignallabs.com> - 2017-05-13 12:53 -0400
      Re: Stability in PID Controllers Tim Wescott <tim@seemywebsite.really> - 2017-05-13 13:14 -0500
      Re: Stability in PID Controllers rickman <gnuarm@gmail.com> - 2017-05-13 15:47 -0400
        Re: Stability in PID Controllers Tim Wescott <seemywebsite@myfooter.really> - 2017-05-14 19:06 -0500
          Re: Stability in PID Controllers rickman <gnuarm@gmail.com> - 2017-05-15 00:22 -0400
            Re: Stability in PID Controllers Tim Wescott <tim@seemywebsite.really> - 2017-05-15 00:03 -0500
              Re: Stability in PID Controllers rickman <gnuarm@gmail.com> - 2017-05-15 01:18 -0400
                Re: Stability in PID Controllers Tim Wescott <tim@seemywebsite.really> - 2017-05-15 10:53 -0500
              Re: Stability in PID Controllers Les Cargill <lcargill99@comcast.com> - 2017-05-15 20:03 -0500
                Re: Stability in PID Controllers Tim Wescott <seemywebsite@myfooter.really> - 2017-05-15 23:54 -0500
  Re: Stability in PID Controllers gyansorova@gmail.com - 2017-05-13 12:57 -0700
  Re: Stability in PID Controllers Kevin Neilson <kevin.neilson@xilinx.com> - 2017-05-13 13:10 -0700
    Re: Stability in PID Controllers Kevin Neilson <kevin.neilson@xilinx.com> - 2017-05-13 13:18 -0700
    Re: Stability in PID Controllers gyansorova@gmail.com - 2017-05-20 23:35 -0700

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