Sundaresan-Krishnaswamy Technique for Estimation of Process Parameters

time delay θ

FE`\:03b8$$385648202467573113638082558848836737311

time constant τ

FE`\:03c4$$385648202467573113638082558848836737311

Consider a first-order plus delay model defined by the transfer function

G(s)=

K

-θs

e

τs+1

, where

K

,

τ

, and

θ

are the gain, time constant, and time delay, respectively. In order to find

τ

and

θ

, Sundaresan and Krishnaswamy [1, 2] use the normalized response

y

KM

of the model to a step-forcing function:

U(s)=M/s

at two different times,

t

1

and

t

2

. These times are selected such that the normalized response reaches 35.3% at

t

1

and 85.3% at

t

2

. The recipe gives the estimated values of the time constant and delay time by

τ

est

=0.674803(

t

2

–

t

1

)

and

θ

est

=1.29382

t

1

–0.293815

t

2

.

The Demonstration plots the normalized response for user-set values of

τ

and

θ

. Perfect agreement is observed between the estimated values

τ

est

and

θ

est

and actual values (

τ

and

θ

).