# RE: PID parameter tuning using Fuzzy Logic

From: P. Sarma (psarma@seas.upenn.edu)
Date: Tue Feb 26 2002 - 12:24:53 MET

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Jayanth,

The fuzzy logic tuning (FLT) of a crisp PID controller is relatively
straightforward. It is a variation on Gain-Scheduling (GS) control,
which serves to make the FLT-PID a nonlinear i/o blackbox controller.

Let K = (P,I,D) represent the vector of gains where the PID is written
with the controller output as

LPID(t) = P*e(t) + I*Ie(t) + D*De(t); Ie and De are obvious. --- (1)

This is valid for the continuous or the discrete case. To account for
nonlinear system behaviour, each of the applicable gains (3 or less) is
externally retuned, using an FLT as a cascade self-tuner or GS. Consider
any one of the gains, say P.

Then we can generate a fuzzy model of P by constructing a fuzzy
rule-base (FRB) based on dynamic error information, namely from (e,e').
An appropriate FRB generated from identification or domain knowledge
will generate a nonlinear dynamically time-varying scheduled gain
P(e(t),e'(t)) = P(t). This can be extended to K(t) as applicable,
leading to the desired

NPID(t) = P(t)*e(t) + I(t)*Ie(t) + D(t)*De(t); Ie and De are obvious (2)

The selection of the FRB's for each gain like the P(e,e') is the key
FLT-PID design issue. The selection of the FLSystem base type for the
FLT, whether Mamdani M-FLS or TSK-FLS is a metalevel design issue.

The great practical utility of this FLT-PID is the ability to add a
relatively simple "fuzzy patch" FLT block (in a DCS or PLC) to an
existing LPID block.

For references, the Web has become a good source. A search engine run
for "fuzzy PID tuning" is quite effective. Checking the Inspec and
Compendex CD-R databases, and typically the IEEE Transactions on Fuzzy
Systems, and the SMC set at the nearest large technical university's
library would produce sufficient data.

Pramit

-----Original Message-----
From: fuzzy-mail@dbai.tuwien.ac.at [mailto:fuzzy-mail@dbai.tuwien.ac.at]
On Behalf Of g jayanth
Sent: Wednesday, February 20, 2002 2:50 AM
To: Multiple recipients of list
Subject: PID parameter tuning using Fuzzy Logic

I am doing a project on the tuning of a conventional PID controller
using fuzzy logic when applied to a superheated steam boiler in a
thermal power plant.However I have not found much literarture on the
topic of fuzzy supervisory & tuning control.I want to explicitly know
how the supervisory works and changes the K,Ti and Td constants.If you
know of any material avilable on the net please help me.

Thanks a lot
JAyanth

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