FC 152 - Model Parameter Estimator

The model parameter estimator function block uses a recursive least-squares algorithm to identify a mathematical model of a process. This function block calculates the parameters for a linear, first-order dynamic model with deadtime of the specific form.

 

Yt = -aYt-1 + but-k + c

 

Where:

Yt

=

Value of the process variable at time t.

Yt-1

=

Value of the process variable at one sample time before time t.

ut-k

=

Value of the control output one process deadtime (expressed as k sample time increments) before t.

a,b,c

=

Model Parameters

 

 

 

 

Outputs:

Blk

Type

Description

N

R

Model parameter a

N+1

R

Model parameter a

N+2

R

Model parameter a

N+3

R

Residual between actual and calculated process variabledata

N+4

 

Quality of model parameter estimates:

0 = parameter estimator locked on

1 = new parameter estimation in progress

 

 

 

Specifications:

Spec

Tune

Default

Type

Range

Description

S1

N

5

I

Note 1

Block address of controlled process variable

S2

N

5

I

Note 1

Block address of control output

S3

N

0

I

Note 1

Block address of reset trigger (resets on a 0 to 1 transition)

S42

Y3

0.250

R

0.25 - 9.2E18

Sample time (secs)

S52,4

Y3

1.000

R

0.25 - 9.2E18

Process deadtime (secs);

seconds must be < S4 x 40

S6

Y3

0.000

R

0.25 - 9.2E18

Expected noise level in process variable (p-p)

S7

Y

0.000

R

Full

Spare real parameter

S8

N

0

I

Note 1

Spare boolean input

 

 

NOTES:

  1. Maximum values are:9,998 for the BRC-100, IMMFP11/12 31,998 for the HAC

  2. The relationship between S4 and S5 must be valid for proper operation. If adding this block with an inferential smith controller (ISC) (function code 160) the sample time S4 must be greater than the ISC deadtime (function code 160, S8) divided by 40.

  3. The initialization routine in the ISC parameter converter (function code 153) automatically specifies S4, S5 and S6.

  4. Specification S5 is used only when

 

 

 

152.2   Specifications

 

S1

Block address of the process variable. This identifies the controlled process variable used by the model parameter estimator.

 

S2

Block address of the control output. This identifies the controller output used by the model parameter estimator.

 

S3

Block address of the reset trigger. When this trigger changes from zero to one, the model parameter estimator is initialized.  The reset trigger also updates the ISC parameter converter (function code 153) to the default settings (process gain and process lag) stored in NVRAM of the inferential smith controller (function code 160). These settings can be updated manually by tuning the corresponding ISC specifications.

 

NOTE: The estimator does not stop when the loop is in manual or the process is shut down. Reset trigger must be used on startup of process.

 

S4

Sample time. This provides time scaling for the estimation algorithm. To assure proper operation of the model parameter estimator, the sample time should be selected so that it is between 20 percent and 50 percent of the process lag time.  Because of the strong dependency of the calculated model coefficients on the selected sample time, when the sample time is changed more than ten percent or in excess of 0.5 seconds, the model coefficients are automatically initialized.

 

S5

Process deadtime. This defines the deadtime or transport delay exhibited by the process. Underestimation of deadtime adversely affects parameter estimation more severely than  overestimation. When the model parameter estimator is linked with an ISC parameter converter (function code 153), the process deadtime is automatically updated by the ISC parameter

converter.

 

S6

Expected process noise level. The model parameter estimator uses S6 in its identification of process upsets. This value indicates the maximum deviation from set point that can be attributed to noise in the process. The model parameter estimator treats deviations greater than this value as process upsets.

 

152.3   Applications

 

The specialized function blocks required for self-tuning of the inferential smith controller (function code 160) are the model parameter estimator (function code 152) and the ISC parameter converter (function code 153). The use of an adaptive parameter scheduler (function code 154) is optional.

 

The model parameter estimator configuration is shown in the applications section of function codes 153 and 154. The ISC parameter converter (function code 153) application is a self-tuning configuration. The adaptive parameter scheduler (function code 154) application is advanced self-tuning configuration with deadtime scheduling and adaptive gain and lag scheduling.

 

For more application information on self-tuning control, refer to the Self Tuning Control application guide.