PID Without a PhD, Finally

On Tue, 26 Apr 2016 00:30:18 -0700, Paul Rubin wrote:

> Tim Wescott <tim@seemywebsite.com> writes:
>> D'oh -- why, of course I'll include an appendix or something on how to
>> do this with op-amps.  It should have occurred to me immediately.
> 
> Indeed I've been wondering whether this stuff was ever done with purely
> analog electronics.  I don't know how far back it goes historically but
> I imagine quite a way.  Optimal control is from the 1940s and I'd expect
> PID to be much older?  I'm clueless though.

The first PID controllers, to my knowledge, were purely mechanical 
systems.  The seminal papers were written in the 1860's, but they were to 
describe and analyze what had already been in use in industry.  

Pneumatic systems were a great innovation in the 1930's (or 20's, or 
teens).

Electronics doing PID control is a johnny come lately.

Here's Maxwell's paper (yes, James Clerk Maxwell of E&M fame).  There was 
a Russian -- Tchebychev, I think.  I can't remember who, nor have I found 
any papers.

https://upload.wikimedia.org/wikipedia/commons/b/b1/On_Governors.pdf

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On Thu, 14 Apr 2016 17:03:53 -0500, Tim Wescott
<seemywebsite@myfooter.really> wrote:

>Embedded Systems Design (or whatever they call themselves) kept moving 
>this around -- so I've revamped it, updated it, and posted it on the web.
>
>Take a gander.  Please comment on anything you like/don't like.  I'm not 
>sure if the way that I'm setting off the math is a Really Good Idea or a 
>Really Bad Idea -- I'm trying to make it easy for the math-averse to skip 
>over it, without breaking up the flow too much for folks who can read 
>math without breaking stride.
>
>http://wescottdesign.com/articles/pid/pidWithoutAPhd.pdf

I think that PID control originated in the pneumatic controller days,
before there were many (or any) PhDs in control theory. One story that
I read suggests that the derivative term was discovered accidentally,
the result of a leaky bellows or something.

I designed a state-of-the-art digital boiler/throttle control system
for the Navy's LHA helicopter assault ships. The Navy couldn't
maintain it so they ripped it out and substituted pneumatics.


-- 

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement 

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

On Tue, 26 Apr 2016 11:12:45 -0700, John Larkin wrote:

> On Thu, 14 Apr 2016 17:03:53 -0500, Tim Wescott
> <seemywebsite@myfooter.really> wrote:
> 
>>Embedded Systems Design (or whatever they call themselves) kept moving
>>this around -- so I've revamped it, updated it, and posted it on the
>>web.
>>
>>Take a gander.  Please comment on anything you like/don't like.  I'm not
>>sure if the way that I'm setting off the math is a Really Good Idea or a
>>Really Bad Idea -- I'm trying to make it easy for the math-averse to
>>skip over it, without breaking up the flow too much for folks who can
>>read math without breaking stride.
>>
>>http://wescottdesign.com/articles/pid/pidWithoutAPhd.pdf
> 
> I think that PID control originated in the pneumatic controller days,
> before there were many (or any) PhDs in control theory. One story that I
> read suggests that the derivative term was discovered accidentally, the
> result of a leaky bellows or something.
> 
> I designed a state-of-the-art digital boiler/throttle control system for
> the Navy's LHA helicopter assault ships. The Navy couldn't maintain it
> so they ripped it out and substituted pneumatics.

PID -- or at least PI -- control has been around longer than that: 
http://rspl.royalsocietypublishing.org/content/16/270.full.pdf+html

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On 04/26/2016 03:30 AM, Paul Rubin wrote:
> Tim Wescott <tim@seemywebsite.com> writes:
>> D'oh -- why, of course I'll include an appendix or something on how to do
>> this with op-amps.  It should have occurred to me immediately.
>
> Indeed I've been wondering whether this stuff was ever done with purely
> analog electronics.

Sure thing.  About three weeks ago for me. ;)

Cheers

Phil Hobbs

On Thu, 14 Apr 2016 19:09:26 -0400, DJ Delorie <dj@delorie.com> wrote:

>
>You leave out math but include C code, I think that's defeating the
>purpose.  If you can't explain it in non-technical words or a simple
>picture... well, try harder :-)
>
>You spend only one page on tuning, and give no examples of "If you see
>this, try this" which is much more useful to the practical user.


Engineers tend to do

  Actuator = error * (Kp + Ki + Kd)

whereas old-time analog controllers did

  Actuator = Kp * (1 + Ki + Kd)

with the idea being that it's easier to tune on-site.


-- 

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement 

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

On 4/26/2016 8:07 PM, John Larkin wrote:
> On Thu, 14 Apr 2016 19:09:26 -0400, DJ Delorie <dj@delorie.com> wrote:
>
>>
>> You leave out math but include C code, I think that's defeating the
>> purpose.  If you can't explain it in non-technical words or a simple
>> picture... well, try harder :-)
>>
>> You spend only one page on tuning, and give no examples of "If you see
>> this, try this" which is much more useful to the practical user.
>
>
> Engineers tend to do
>
>    Actuator = error * (Kp + Ki + Kd)
>
> whereas old-time analog controllers did
>
>    Actuator = Kp * (1 + Ki + Kd)
>
> with the idea being that it's easier to tune on-site.

I think you mean,

Actuator = error * Kp * (1 + Ki + Kd)

In other words, the Ki and Kd terms were normalized to Kp.

-- 

Rick C

Paul Rubin wrote:
> Tim Wescott <tim@seemywebsite.com> writes:
>> D'oh -- why, of course I'll include an appendix or something on how to do
>> this with op-amps.  It should have occurred to me immediately.
>
> Indeed I've been wondering whether this stuff was ever done with purely
> analog electronics.  I don't know how far back it goes historically but
> I imagine quite a way.  Optimal control is from the 1940s and I'd expect
> PID to be much older?  I'm clueless though.
>


The first PID was used for steering ships and was mostly mechanical:

http://www.pcbheaven.com/wikipages/PID_Theory/

-- 
Les Cargill

John Larkin wrote:
> On Thu, 14 Apr 2016 19:09:26 -0400, DJ Delorie <dj@delorie.com> wrote:
>
>>
>> You leave out math but include C code, I think that's defeating the
>> purpose.  If you can't explain it in non-technical words or a simple
>> picture... well, try harder :-)
>>
>> You spend only one page on tuning, and give no examples of "If you see
>> this, try this" which is much more useful to the practical user.
>
>
> Engineers tend to do
>
>    Actuator = error * (Kp + Ki + Kd)
>

Uhhhhh... no.

Actuator = (error * Kp)
            + ( filter1(sum(error)) * Ki )
            + ( filter2(delta(error,lastError)) * Kd)

> whereas old-time analog controllers did
>
>    Actuator = Kp * (1 + Ki + Kd)
>
> with the idea being that it's easier to tune on-site.
>
>

Because trimpots are awesome.

-- 
Les Cargill

Tim Wescott wrote:
> On Tue, 26 Apr 2016 00:30:18 -0700, Paul Rubin wrote:
>
>> Tim Wescott <tim@seemywebsite.com> writes:
>>> D'oh -- why, of course I'll include an appendix or something on how to
>>> do this with op-amps.  It should have occurred to me immediately.
>>
>> Indeed I've been wondering whether this stuff was ever done with purely
>> analog electronics.  I don't know how far back it goes historically but
>> I imagine quite a way.  Optimal control is from the 1940s and I'd expect
>> PID to be much older?  I'm clueless though.
>
> The first PID controllers, to my knowledge, were purely mechanical
> systems.  The seminal papers were written in the 1860's, but they were to
> describe and analyze what had already been in use in industry.
>
> Pneumatic systems were a great innovation in the 1930's (or 20's, or
> teens).
>
> Electronics doing PID control is a johnny come lately.
>
> Here's Maxwell's paper (yes, James Clerk Maxwell of E&M fame).  There was
> a Russian -- Tchebychev, I think.  I can't remember who, nor have I found
> any papers.
>
> https://upload.wikimedia.org/wikipedia/commons/b/b1/On_Governors.pdf
>


The writing on that is superb. Thanks for the link.

-- 
Les Cargill

rickman wrote:
> On 4/26/2016 8:07 PM, John Larkin wrote:
>> On Thu, 14 Apr 2016 19:09:26 -0400, DJ Delorie <dj@delorie.com> wrote:
>>
>>>
>>> You leave out math but include C code, I think that's defeating the
>>> purpose.  If you can't explain it in non-technical words or a simple
>>> picture... well, try harder :-)
>>>
>>> You spend only one page on tuning, and give no examples of "If you see
>>> this, try this" which is much more useful to the practical user.
>>
>>
>> Engineers tend to do
>>
>>    Actuator = error * (Kp + Ki + Kd)
>>
>> whereas old-time analog controllers did
>>
>>    Actuator = Kp * (1 + Ki + Kd)
>>
>> with the idea being that it's easier to tune on-site.
>
> I think you mean,
>
> Actuator = error * Kp * (1 + Ki + Kd)
>
> In other words, the Ki and Kd terms were normalized to Kp.
>


No, he didn't do that properly. Otherwise, there'd be no need
for three Kx constants.

The integrator term accumulates the error per sample by some law/filter
and the Kd is multiplied by a filtered version of the difference
between the error this sample and the error of the previous sample.

Actuator = (error * Kp)
            + ( filter1(sum(error)) * Ki )
            + ( filter2(delta(error,lastError)) * Kd)

where the filters are very likely extremely stateful and not very 
filter-ey.

Forms exist for continuous linear PID and they're about what you'd expect.


-- 
Les Cargill