The behaviour of any process is indicated by the states of output variables, which are dependent on the operating conditions and the adjustments made to the process. However, productivity is quantified by a subset of these output variables; normally the specifications upon which the product is sold, e.g. purity, physical or chemical properties. These so called primary variables are often the ones that are difficult to measure on-line.

Inferential measurement systems are designed to overcome such measurement problems. The other outputs, (for example temperatures, flows and pressures) are called secondary variables and these are easily measured on-line.

Due to the nature of chemical and process engineering systems, the states of many of the secondary variables reflect the states of primary variables. For example, liquid composition is defined by pressures and temperatures while biomass growth is linked to CO₂ evolution and feed rate. Thus it should  be possible to use the readily available secondary variables to infer the state of a quality or primary variable.

In developing inferential measurement systems, therefore, the objective is to model the relationship between a primary output and secondary outputs and inputs. The model can then be used to generate estimates of the difficult to measure primary output at the frequency at which the easily measured inputs and secondary variables are measured. So instead of waiting 30 minutes for a gas chromatograph to complete its analysis, the inferential measurement system could be returning estimates of compositions every 5 minutes, using measurements of temperatures and flows, as shown in the diagram:

If sufficiently accurate, the inferred states of primary outputs can then be used as feedback for automatic control and optimisation. The underlying concepts of inferential measurement systems are thus closely tied in to conventional manual control practises and in the application of parallel cascade control.

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