Commodity Modeling and Pricing: Methods for Analyzing Resource Market Behavior

CHAPTER 9

Dynamic Quadratic Programming in Process Control

Bruce A. Bancroft

INTRODUCTION

In the coal industry, real-time blending is in many cases required to satisfy contractual requirements on coal quality, for example, ash. Continuous nuclear analyzers are used to obtain real-time feedback of the quality of the blended product and produce a quality generally at a rate of one per minute. The product typically consists of two sources of coal: one that has a quality higher than the target quality and one that is lower than the target quality. The object is to control the proportions of the two sources to achieve the target quality while maximizing the usage of the lower quality, which is typically a lower-cost source. This presents some problems because the two sources are each autocorrelated in time, the proportions of the sources are measured with error, and the blended product quality measured by the analyzer, although free of bias, is subject to significant measurement error. This chapter describes a methodology to blend coal to meet a barge specification.

PROCESS CONTROL MODELS COMPARED

In process control, the workhorse methodology for feedback control is the proportional-integral-derivative (PID) controller. Mathematically it is given by:

(9.1)

where

(9.2)

SP = setpoint(desired ...