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Jan
11

Universal Concept – Bias

The simplest correction to models and measurements turns out to be the most widely applicable correction. Whether you are correcting a model for feedforward control, model predictive control, or a neural network prediction or correcting a measurement of composition, flow, level pressure, pH, or temperature the simple bias rules.

I am a biased when it comes to how you correct a feedforward signal. While theoretically a feedforward multiplier would be used for a slope correction on a plot of the manipulated variable versus the disturbance variable, I have gotten into trouble using this approach. The choice of scaling factors is unforgiving with very little guidance to keep you out of trouble. Second, it turns out that the largest and most important feedforward measurement error is typically a bias. Even if there was a slope error, it would take quite a range of operation to see a significance disadvantage from a bias versus a span correction. Additionally, a feedforward summer does not introduce nonlinearity. A feedforward multiplier might correct for the change in process gain for plug flow. However, for the more common case of composition, pH, or temperature control of volume with some back mixing due to agitation or boiling or recirculation, the change in process gain with flow is cancelled by the change in process time constant with flow in terms of the effect on the maximum controller gain setting. Lastly, we live in a nonlinear world with complex process relationships and nonlinearities where a bias correction is the most foolproof solution. I am biased against being a fool.

For model predictive control, a difference between the current and predicted controlled variable could be due to a mismatch between the actual and modeled process gain, deadtime, or time constant. For neural networks, it would be quite a challenge to decipher which node weight was causing the inevitable difference between a predicted composition and a lab measurement. All models are wrong it is just a matter of how much.

All measurements especially composition measurements in the field and lab, have offset errors due to extraneous effects, resolution, sensitivity, and drift. For pH measurements, I have gotten into chasing calibration errors by removing electrodes and doing 2 point buffer calibrations especially for high ionic solutions and solid references where the liquid junction potential and time to equilibration is large. A pH standardization (pH offset correction by a simple bias) with a process sample taking into account solution pH changes with temperature has been the more effective in my book. If you think about it, a slope error of 10% means the process gain has changed by 10%, which is a lot less than the changes due to process nonlinearities. However, a 10% offset will result in a 10% error in the setpoint, which is a greater consideration for higher level loops such as composition, pH, and temperature. An offset can be a problem for any loop operating close to a safety instrumentation system (SIS) trip point. Consequently, eliminating offset errors is generally more important than eliminating slope errors.