P controller

Why does a P controller have steady state error?

Pout=Kp(Sp-Pv)

A steady error implies that (Sp-Pv) is not zero but there got to be instance where the setpoint (sp) = Process variable (Pv). If there isn't an instance where Sp =Pv, why?

Per your formula if SP=PV the output is zero. You need an offset to have an output
greater then zero.

http://www.documentation.emersonpro...ments/tech_bulletin_monograph/d350406x012.pdf

yes there is an instance where the error is zero.
imagine your are driving on a straight road.
error is zero so Pout is also zero.
however when in a turn the error is not zero and depending on the sharpness of the turn the steer has to turn, but for that the error must be bigger, so when turning you will see the that the car is not in middle of road.

david90 said:

Why does a P controller have steady state error?

Pout=Kp(Sp-Pv)

A steady error implies that (Sp-Pv) is not zero but there got to be instance where the setpoint (sp) = Process variable (Pv). If there isn't an instance where Sp =Pv, why?

Click to expand...

In a frictionless, perfectly linear system with infinite resolution, all you would need is a P controller to get you to zero error.

But that world doesn't exist. P controllers are great to get you moving but as you get closer to your target, the error gets smaller and smaller. Therefore, your control output (the thing driving you to your destination) is getting smaller and smaller.

There will come a point when the error gets so small that the signal out from your P controller is not large enough to move your actual value anymore. This could be due to friction or some minimum threshold at your system or being under the analog resolution of part of the system. But in all cases, it means, you can't get to the set point.

So you think, increase my P gain. This can work to a point but usually the friction kills you because it is non-linear. Say you have a block on the floor and you are trying to push it into a position. You get close and the force you can push with is less than the sliding friction. So you increase the P gain to get get the block moving. BUT, as soon as you start moving the kinetic friction is much less than the static friction was so the block (having no other choice than to follow F=ma) lunges forward past your set point. The issue is the same in the other direction.

This isn't a perfect example but hopefully helps you visualize why P gain usually cannot get Pv=Sp

One of our esteemed forum members Ron Beaufort created a series of threads on this forum a few years back that covered this topic in some detail. Rather than re-invent the wheel so to speak, and since no one makes it seem so simple better than Ron does, take the time to read them and then follow up with any additional question you might have.


Proportional-only control – why won’t it work right?

What is P in PID?

what is "I" in pid ?

What is “D” in PID? ... fundamentals of Derivative

You can also find PDFs of these same articles and a lot more on Ron's website at http://www.ronbeaufort.com/main_frame_page.htm

I use the terms type 0 ( non-integrating ) and type 1 ( integrating ). Type 0, 1 and 2 are what text books use to indicate the number of integrators in a system.

Velocity and temperature control are non-integrating systems. Non-integrating systems will return to a steady state value like 0 speed or ambient temperature. Integrating systems are systems like level control,pressure control, and position control where the output is integrated. In position control the velocity is integrated to get position. In a water level control the flow is integrated to get level.

Type 0 or non-integrating systems must have a controller with a integrator to reach the set point. Type 1 or integrating systems do no in an ideal world as Norm pointed out but in reality an integrator is needed anyway if the set point is going to be reached exactly.

Thanks all! Now I can PIDed with confidence:nodi: