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From user Saeid Bina, Dr. :
"Hello everyone,
The controller is ON if it was previously OFF and Th (Input 1) minus Tl (Input 2) is greater than the upper dead band. Otherwise the controller is OFF."
The first value, or upper value of the differential controller (Th), is indeed disconnected in this example, and therefore always equal to its initial value (0). The second value, or lower value of the differential controller (Tl), is connected to the tank level indicator, which as you stated may vary from -1 (tank is empty) to 1 (tank is full). This means the difference "Th (input 1) minus Tl (input 2)" may vary from (0 - (-1) = 1) when the tank is fully empty, to (0 - (1) = -1) when the tank is completely full. So, if the controller is OFF, the tank is running close to empty, and Tl <= -0.9, then the difference (Th-Tl) will be >=0.9, the control signal that was previously OFF will turn ON, and the fill pump will fill the tank. If the controller is ON, the tank is running close to full, and Tl >= 0.9, then the difference (Th-Tl) will be <=-0.9, the control signal that was previously ON will turn OFF, and the fill pump will stop running.
The controller output is connected to the control function input (Input 4) to provide hysteresis - this is how the controller knows what its control state was on its prior iteration. I agree, it is a confusing convention 🙂 The Type can be replaced with Type 165, if you like, which has all the same functionality but handles storing its prior control state internally, and thus doesn't require the external control state connection. There are some applications where you may want to leave the prior control state (Input 4) disconnected, or cascade the control signal from another controller to Input 4, but I think those are less common, and I've never personally used the controller in that way.
