PID Control on Micro with PWM

Liam wrote:

Use units in the equations you write. The units of your pressure
transducer reading is [PSI (or bar or mmHg)/volt]. Presumably, your
input, also a pressure (else, subtraction wouldn't be legitimate) uses
the same unit.

What translated 1 to 2? If there's a scaling gain somewhere, that has to
be non-dimensional.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF

I think I can convert the volts to a corresponding pressure. I can
then calculate the Error = (Input - Output) ; the units will be
pressure units (PSI or equiv).

From this error value, how do I know at what duty cycle I have to
drive the system? I have a pressure but I need a % duty cycle for the
PWM?

Liam wrote:

   ...

What does the PWM output do? Control the speed of a pump? Pressure some
function of speed? Matlab notwithstanding, the world is made out of
things, not numbers.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Fri, 14 Mar 2008 01:35:57 -0700, Liam wrote:


¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Just knowing the error value doesn't mean that you do know how to drive
the pump.  If the immediate value of the error were enough information
then you'd just need proportional control, or perhaps some nonlinear but
memoryless mapping between error and duty cycle.

At any rate, for the purposes of keeping your dimensions straight your
controller gain would need to be in (duty cycle)/(psi).  In the real
world your controller gains are going to be buried deeper -- in an analog
system they'd be volts/volt for proportional, volts/volt-second for
integral, and volts/(volts/second) for derivative.  This would be
preceded by a sensor with a gain whose dimensions are in volts/PSI,
followed by a driver with a gain in duty cycle/volt, then probably a
filter, then a pump whose gain involves PSI in the numerator and volts in
the denominator, and probably some interesting time dependencies.

I'm with Peter -- write the differential equations.  If you have trouble,
check back here & someone will probably help.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

Jerry is just trying to get you to think about the problem.
I am more blunt and direct.

This is easy stuff.  I see only one problem.
The input and the feed back is pressure.
The gain of the controller is %Control Output per pressure unit.
Easy so far.  Here is the problem.
Does the pump pressure integrate?   A fixed displacement pump pumping
fluid in a fixed space without any leakage will integrate the
pressure.  Otherwise the pressure will bleed off a some rate.  Usually
it is proportional to the square root of the pressure drop across the
orifice or valve.
The pump gain is pressure rate per % control output.
If the object you are pumping the fluid into doesn't leak it will
integrate the rate of change in pressure.  If the object leaks the
pressure rate will have a negative term that is proportional to the
square root of the pressure drop across the valve or orifice. You
haven't told us about what happens to the fluid.  Don't you think it
is important that we know if the pressure will decay or not?

In any case the (system) will have a steady state pressure/control
output if the system leaks or integrated (pressure/control output) if
it doesn't leak.  Note, most things leak at least a  little.

Now heed Jerry's advice and write the ( differential ) equations.
I provided a lot of good information ( hints ).


All the time.  If we told you the answer would you understand?  How
can you when you don't understand the problem?  It is best if you
struggle though this at least until you understand the problem.  You
didn't pick an easy one to start with.

Peter Nachtwey

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