FC 154 - Adaptive Parameter Scheduler

The adaptive parameter scheduler function allows process characteristics such as a measured or calculated index variable to be used to adjust the tuning parameters for the associated inferential smith controller (ISC function code 160). This feature optimizes controller performance for predictable changes in process operation and prevents periods of potentially unacceptable control while the ISC controller is being retuned by the model parameter estimator (function code 152) via the ISC parameter converter (function code 153).

 

The adaptive parameter scheduler can automatically establish the relationship between an ISC tuning parameter and a measured or calculated index variable using linear regression. The adaptive parameter scheduler uses this relationship to automatically adjust the specified ISC tuning parameter based on the value of the specified index variable.  Alternatively, this function can automatically determine the correction bias required for a pre-established gain schedule.  This permits a nonlinear relationship between the ISC tuning parameter and the index variable, with automatic correction of the relationship for design inaccuracies and changes in process behavior.

 

Outputs:

Blk

Type

Description

N

R

Output Value of Function

N+1

R

 

N+2

B

 

 

 

 

Specifications:

Spec

Tune

Default

Type

Range

Description

S1

N

5

I

Note 1

Block address of index variable

S2

N

5

I

Note 1

Block address of fixed gain schedule

S3

N

5

I

Note 1

Block address of scheduled parameter

S4

N

0

I

Note 1

Block address of reset trigger

S5

N

5

I

Note 1

Address block containing specification to be adapted

S6

N

0

I

0 - 255

Specification to be adapted

S7

N

0.000

R

Full

Minimum index value

S8

N

0.000

R

Full

Maximum index value

S9

Y

0.000

R

Full

Spare real parameter

S10

N

0

I

Note 1

Block address of coefficient update hold:

0 = update A and B

1 = hold updates of A and B

 

NOTES:

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

 

 

154.1   Explanation

 

When a process controlled by an inferential smith controller (function code 160) shifts from one operating point to another,  the inferential smith controller (ISC) is automatically retuned to maintain the desired controller performance at the new operating point. However, during self-tuning, the ISC controller performance can be temporarily less than desirable. In applications where the specific value of an ISC tuning parameter (process gain or lag time) is related to some process variable or discrete event (an index variable), these periods of suboptimum controller performance during self-tuning can be eliminated by adaptive scheduling of the tuning parameter.

 

The adaptive parameter scheduler utilizes a least-squares technique to automatically correlate a preselected index variable with one controller tuning parameter output by the ISC parameter converter. Once an effective linear correlation has been established, the adaptive parameter scheduler adjusts the tuning parameter for the ISC controller as a function of this index variable. If more than one tuning parameter must be scheduled, more than one adaptive parameter scheduler must be used.

 

The adaptive parameter scheduler utilizes a bin data structure for regression of the linear relationship between the index variable and the correction bias. The range of the index value is divided into ten bins, and when a valid data set becomes available, it goes into the bin corresponding to the value of the index variable for the data set. Only one data point is stored in each bin. As new data becomes available for a bin, the old data is replaced and the regression is recalculated. To facilitate commissioning of the adaptive parameter scheduler when there is only one data set, a line passing through the data point with zero slope is assumed.

 

Scheduled tuning parameter = Output from fixed gain schedule <S2> + correction bias

 

Correction bias = Ax + B

 

Where:

x = Value of the index variable <S1>

A and B coefficients are updated by the regression algorithm.

 

 

154.1.1  Specifications

 

S1

(Block address of index variable) Identifies the index variable used by the adaptive parameter scheduler.

 

S2

(Block address of fixed gain schedule) Identifies the output of the associated fixed gain schedule. If not using a preestablished gain schedule, this specification should be set to block address five (default value), which provides a constant value of zero.

 

S3

(Block address of scheduled parameter) Identifies the estimated value of the scheduled tuning parameter. This value determines the relationship between the tuning parameter and index variable. The instantaneous correction bias (S2-S3) is used with the index variable (S1) as a data point set for regression determination of A and B.

 

S4

(Block address of reset trigger) Identifies an external trigger used to reset the regression data. When the trigger changes from zero to one, all historic data used for determining the correlation equation is erased and the correction bias is set to zero.

 

S5

(Address of block containing parameter to be adapted) Identifies the block address for the parameter adjusted by the adaptive parameter scheduler.

 

S6

(Specification to be adapted) Identifies which specification of the identified block is adjusted by the adaptive parameter scheduler.

 

S7 and S8

(Minimum and maximum values for the index variable) Define the allowable range for the index variable.

 

S10

(Block address of coefficient update flag) Allows suspension of the recalculation of the A and B coefficients. The correction bias will still be computed and the output updated. Also, the parameter in the target block and specification continue to update.

 

 

154.2   Applications

 

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

 

Figure 154-1 shows an advanced self-tuning configuration with deadtime scheduling and adaptive gain/lag scheduling. For more application information on self-tuning control, reference the Self Tuning Control application guide.