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Lambda Tuning Equations PDF

This document discusses two types of self-regulating processes: integrating processes and near-integrating processes. It provides equations to calculate the process gain, controller gain, and controller integral time for tuning a PID controller for each type of process. Key parameters in the equations include the process time constant, dead time, and lambda factor.

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209 views4 pages

Lambda Tuning Equations PDF

This document discusses two types of self-regulating processes: integrating processes and near-integrating processes. It provides equations to calculate the process gain, controller gain, and controller integral time for tuning a PID controller for each type of process. Key parameters in the equations include the process time constant, dead time, and lambda factor.

Uploaded by

GMCA
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Self-Regulating Process

Process Variable or
Controller Output (%)
%PV
Kp = ∆%PV / ∆%CO
Self-regulating process gain (%/%)

%CO

∆%PV

0.63∗∆%PV
∆%CO

θp τp Time (seconds)
dead process
time time constant

Lambda (closed loop time constant) is defined in terms of a Lambda factor (λf):
λ = λ f ∗τ p
Self-Regulating Process

Self-Regulation Process Gain:


∆ % PV
Kp =
∆ %CO

Controller Gain
Ti
Kc =
K p ∗ (λ f ∗ τ p + θ p )

Controller Integral Time


Ti = τ p

“Near Integrating” Gain Approximation


Kp
Ki =
τp
Integrating Process

Process Variable or
Controller Output (%)
%PV
Ki = { [ ∆%PV2 / ∆t2 ] − [ ∆%PV1 / ∆t1 ] } / ∆%CO

Integrating process gain (%/sec/%)

%CO

∆%CO

ramp rate is ramp rate is


∆%PV1 / ∆t1 ∆%PV2 / ∆t2

Time (seconds)
θp
dead
time

Lambda (closed loop arrest time) is defined in terms of a Lambda factor (λf):
λ = λ f / Ki
Integrating Process

Integrating Process Gain:


∆ % PV2 / ∆t2 − ∆ % PV1 / ∆t1
Ki =
∆ %CO

Controller Gain
Ti
Kc =
K i ∗ [(λ f / K i ) + θ p ]2

Controller Integral Time


Ti = 2 ∗ (λ f / K i ) + θ p

The above tuning automatically insures the following inequality is satisfied


to prevent slow rolling oscillations from too low of a gain or integral time.
4
K c ∗ Ti >
Ki

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