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This lecture is from Process Control course. Some key points for this lecture are: Development, Material, Energy Balances, Flow Dynamics, Physical Properties, Thermodynamics, Step Input, Dye Injection, Random, Sinusoidal
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Black Box Models
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Fitting of 1st-Order Model
( ) ( )
( ) (^) ( )
( )
/
0
t
t
τ
τ
τ
τ
−
=
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FOPDT and SOPDT Models
( )
( ) (^2 )
s
s
θ
θ
−
−
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For a 1st order model, we note the following characteristics in step response:
There are 3 generally accepted graphical techniques for determining the first-order system parameters τ and θ.
( ) 1
s Ke G s s
θ
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Method 1: Sundaresan &
Krishnaswany (1978)
1 2
y t KM y t KM
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Method 2: Numerical Fitting
( )
( )
t
θ
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is virtually indistinguishable from the step response of the integrating element
K G s s
=
In the time domain, the step response of an integrator is
Hence an approximate way of modeling a first-order process is to find the single parameter
(^2) τ (7-25)
K K =
that matches the early ramp-like response to a step change in input.
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Figure 7.10. Comparison of step responses for a FOPTD model (solid line) and the approximate integrator plus time delay model (dashed line).
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Harriot’s Method
1.
0.
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0.
0.
τ 1 ≥τ 2
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Smith’s Method
( )
( )
60
20 20 60
ζ τ
20
