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BDAC system representation

BDAC Subtopics:

 

This page examines BDAC system representation, as part of
BDAC - Big Data Approximating Control

Overview of BDAC system representation

BDAC uses a discrete time representation for dynamics. At any time step, measured values (or other features extracted from sensor data) are indicated with a vector y. The subset of measured variables in y that are process inputs (measured disturbances) are referred to with a vector d. Controller outputs (which are process inputs) are indicated by a vector u.  This is shown in the following data flow diagram (Click for full-sized image)

BDAC System Representation - Click for full-sized image

When emphasizing the values of these vectors at a particular time step k, the time step k is placed in brackets: y[k], u[k], d[k]. A trajectory is the full set of sensor values y (including measured disturbances) and control outputs u, over a time window looking back nH steps in time and ahead nH steps in time. A collection of trajectories {si} is stored as the row of a matrix S. This is illustrated in the following diagram (Click for full-sized image)

BDAC Trajectories - Click for full-sized image  

As noted in the figure, values for future controller outputs are converted into an incremental form - the changes in controller output. This better aligns the representation with the goals in subsequent pattern matching, where future controller output changes are penalized. Future values of process output variables lacking setpoints are also converted to incremental form for the same reason: The incremental changes should decay to 0 for stability, even if there are no targets.

Variations on this representation might be appropriate in some cases. For instance, some chemical batch control applications have the goal of either reproducing a prespecified trajectory or just achieving an end composition. There, the window size might be the entire time from the start of the batch to the end of the batch. There wouldn’t necessarily be targets of 0 on incremental control outputs, so the future controller outputs wouldn’t be converted to incremental form. As a new batch progresses, the current time would not be centered - it would just be the actual time into the entire window. Based on early deviations from the training set conditions, corrections could be made to achieve the target end compositions. These mid-course corrections could be an improvement over some existing batch controls that just follow preprogrammed steps without any correction. At the end of the batch run, off-spec product must either be blended off or discarded, after waiting for lab sample results or slow analyzer results.

The general approach of pattern matching in BDAC does not require there to be any control at all. At the end of each time step, there is a full trajectory available, which can be used to extract current value estimates, or predictions of future values.

Copyright 2017, Greg Stanley

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