Masters Theses

Date of Award

8-1988

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

J. M. Bailey

Committee Members

James J. Downs, Ernest F. Vogel

Abstract

Today's faster, more powerful, and affordable computers have made it possible for engineers to solve today's multivariable control problems through the use of predictive control algorithms. These control algorithms, which require thousands of numerical calculations per second, can solve control problems that can be described or approximated by a set of linear equations. Dynamic Matrix Control is an example of a predictive control algorithm, and in this paper the author intends to document his design and testing of a multivariable Dynamic Matrix Controller.

The design of the Dynamic Matrix Controller may be subdivided into the following parts: 1. design of the internal model; 2. design of the optimizer; and 3. design of the constraint handler. The internal model generates a template representing the process dynamics from step response data. It uses this template, the process inputs, and past history to predict what the process will do in the future. The dynamic matrix is a combination of these templates. It represents the relationship between a change in each of the controller's moves and the corresponding response to each of the process outputs. The optimizer uses singular value analysis to decompose the process dynamic matrix and create its pseudoinverse. The responsiveness of the controller is determined primarily by the number of singular values retained. This pseudoinverse matrix multiplied by the process output error results in a set of optimal controller moves. The constraint handler updates the prediction projection given the optimizer's control moves and determines if any constraints will be violated. If so, the constraint handler calculates the minimum correction to the optimizer's control moves that are needed to insure the moves and their responses will satisfy the constraint requirements.

Testing of this design is performed through a series of simulations. The process model used in these simulations represents a 2x2 distillation column. The simulations are designed to demonstrate DMC's response to set point changes and load disturbances. Further simulations are used to illustrate various features such as input and output constraint handling, output weighting, and set point anticipation. DMC's response to a process with unequal number of inputs and outputs is also studied.

The design proved successful throughout the testing. The controller produced very fast response to process upsets and was very successful in decoupling process interaction. Further the controller demonstrated the ability to compensate for input and output constraints and output weighting. The controller's ability to simultaneously operate many inputs and outputs and choose which are the most important may provide the economic incentives necessary to implement advanced control algorithms such as DMC.

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