tuning of pid controller
Tom Weyer
I don't know how to adjust the parameters of a pid controller with the
transfer function:
Fc(s) = Kr * ( 1 + 1/(Ti*s) + Td*s/(1+Tv*s) )
Kr: Gain
Ti: Integrator time
Td: Derivative time
Tv: Delay time
The output of a Pt2 plant which is excited by perturbation shall be
controlled to zero. The plant transfer function is:
Fp(s) = Kp/( s/w0)^2 + 2*D*s/w0 +1 )
Kp: Gain
w0: Natural frequency in rad/sec
D: Damping (Lehr)
Thank you for answers !
--
Tom.
Walter Driedger
Tuning parameters are called that because they cannot be reliably
precalculated. That is why they are 'tuned'. That is, they are
adjusted during operation for optimum response. It is a total waste
of time to attempt to precalculate them. The reasons are these:
1 - Almost all controls math, including yours, is linear. Almost all
control systems are non-linear.
2 - The actual, physical parameters of your system are only
approximately known. They do NOT agree with the ones you are using in
your calculations.
3 - The exact nature of the disturbances your system will experience
are unknowns both in magnitude, spectral composition and point of
influence. Pure mathematics cannot handle this sort of mess.
4 - All the above will change with time in an unpredictable manner.
5 - Every application has its own definition of 'good' tuning. No
single formula can provide a universally satisfactory result. Very
good tuning for a steam drum is very bad tuning for a surge drum.
The purpose of the controller, and its tuning parameters, is to
concentrate all the unknowns into a single point in your process and
to make that point adjustable. If you knew enough to fully
predetermine the tuning constants, you wouldn't need a controller.
For more information you may refer to a booklet
"Controller Tuning and Control Loop Performance, a
Primer, Second Edition", which is available in the US at the
cash discounted price of $16, postpaid if prepaid. It has
sold 27,803 copies to date. Control Engineering Magazine
has referred to it as "PID Without the Math".
Information is available at
http://members.aol.com/pidcontrol/booklet.html. There is a link
from there to a page about companion software ($10).
If you wish, I could e-mail you a brochure on either.
Walter.