numerical time constant

1
h PV -1 PV o PV 1 t o t 1 t -1 old s.s. base line T d h T nss = data points New s.s. base line Numerical formulation for time constant, T c : Based on the fact that any point along a straight line has similar slope’s value; hence, * (T nss , PV nss ) T c d nss c T T T = 1 1 1 1 1 1 = t t PV PV t T PV PV nss nss ( ) + = 1 1 1 1 1 1 PV PV t t PV PV t T nss nss ) , ( ) , ( 1 1 PV t at slope PV T at slope nss nss = Numerical Analysis on openloop process response data **UNPUBLISHED MATERIAL**- INTERNAL USE ONLY

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Numerical Time Constant

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∆h

PV-1

PVo

PV1

to t1t-1

old s.s.base line

Td

∆ h

Tnss

= data points

New s.s. base line

Numerical formulation for time constant, Tc:

Based on the fact that any point along a straight line has similar slope’s value; hence,

*(Tnss , PVnss)

Tc

dnssc TTT −=

11

11

1

1

−−

=−−

ttPVPV

tTPVPV

nss

nss

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−+=−

11

1111 PVPV

ttPVPVtT nssnss

),(),( 11 PVtatslopePVTatslope nssnss =

Numerical Analysis on openloop process response data

**UNPUBLISHED MATERIAL**- INTERNAL USE ONLY