The acidity of water draining from a coal mine is often controlled by adding lime to the water. A valve controls the lime addition and a sensor is downstream. For the model of the system shown in Figure AP9.6, determine K and the distance D to maintain stability. We require D > 2 meters in order to allow full mixing before sensing.

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FIGURE AP9.6 Mine water acidity control. R(s) = 0 Desired acidity Motor and valve K (s² + 10s + 100) Delay e SD/4 Y(s) Actual acidity