Open and Closed-Loop Feedback Systems:
Adding Offset (Bias)

Another way to make the gain-only controller usable is to add bias to the algorithm. Bias is also called offset, and it's some value between 0-100% that's added to the output after the gain calculation brings the controller to the steady-state mode. This will help overcome the problem of the gain-only controller not being able to get the PV to SP. The formula for determining the output (M_O) with bias (M_X) added to the original formula is:

(K_C x E) + M_X = M_O

The bias is also called offset because it provides the function of adding offset value to the output device. E.g., previously when the PV temperature in the laboratory furnace was 75°F and the SP was changed to 100°F, the gain factor in the formula could only get the process temperature to about 85-90°F. At this temperature, the controller reached a steady-state point where the output stabilized at approximately 35-40%. From trial runs in manual mode, the technician has determined that the furnace required approximately 48% output for the PV temperature to reach 100°F. The technician can begin adding bias to the controller which would add value to the output percentage and make it increase.

If a value of 10 was added as bias, the output would rise from 35% to 45% and the process temperature would rise to approximately 96°F. Since the PV temperature is closer to the SP, the value from the (K_C X E) part of the formula will be reduced because the error is smaller. In fact when the PV temperature is exactly at the SP, the value from the (K_C X E) part of the formula will be zero because the error is zero. At this point, the value that the controller sends the output must all come from the bias term. When the engineer is originally setting up the controller for the furnace, bias could be continually added until the temperature is exactly 100°F. After the bias term has been determined, it can be written down to be used again. If the furnace was brought from room temperature to 100°F each time, the bias value could be left in the controller and the temperature would reach the SP each time the furnace was turned on.

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