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Consider flow ratio control with no ratio feedback correction. The PV is the ratio of the secondary flow to independent flow. The zero-gain PID output is the feed-forward for the required secondary flow computed as the ratio setpoint multiplied by the independent flow. This feed-forward-only ratio controller is used when there is no online composition measurement available for feedback correction. The secondary flow measurement is used in the ratio measurement that is the PV for ratio control. The ratio control setpoint is used in the inverse of the model that is the ratio controller output. The responsibility for the secondary flow PID to follow its setpoint is solely the responsibility of the secondary flow PID. The performance of the secondary flow loop is ignored by the PID for ratio control.
A feed-forward-only controller is also used to regulate internal reflux within a distillation column. The model for the internal reflux PID PV is the measured external reflux flow corrected by the heat capacity of this external stream and the latent heat of vaporization of the vapor stream within the column. The tower overhead vapor temperature and the external reflux temperature are used in the calculation. The inverse of the model is used to set the secondary loop for external reflux flow. Again, for stability, the setpoint rather than the PV of this feed-forward-only controller must be used in the model whose inverse is the internal reflux controller output.
The heat transfer to the reboiler can be controlled instead of just the heating stream flow. The model for the heat duty is simply the heating stream flow multiplied by the stream heat capacity and the difference between the inlet and outlet temperatures (hot oil supply and return temperatures).
This powerful concept can be used for any model-based control, no matter how complex, as long as it can be algebraically inverted. I have used it in inferential control where the model came from statistical regression, and I have used it in dynamic model control, such as a Smith predictor, where the inputs are reconciled with the outputs dynamically.