抄録
Using a control action which consists of constant infusing and exhausting speeds and a neutral zone to maintain liquid level within a give range, a gamma-ray source, a detector and two relays at the upper and lower limits of the counting rate are provided. The optimum condition in this case is discussed and ensured experimentally.
Since a counting rate meter has a time constant and its output is subject to statistical fluctuation, the liquid level may overrun to the opposite limit or move again after settling within the range. Formulas are derived providing the conditions such that these phenomena will not occur more frequently than a given probability. These give the relations between the counting rates of the upper and lower limits, the time constant of the rate meter, a factor of the standard deviation of the counting rate, the infusing and exhausting speeds, and the hysteresis widths of the limiting relays. Since it is derived that the first two of the five terms be smaller and the next two greater, the optimum condition can be decided from the formulas. When the infusing and exhausting speeds are the same and the hysteresis widths are equal, the formulas show the optimum is a case where the ratio of the counting rates at the two limits, which is taken smaller than unity, is small, and where each hysteresis width is equal to 0.34 times the difference between the two counting rates, almost regardless of the value of the ratio.
Similar relations can be also derived in a batch process control composed of a single infusion or exhaust to the desired level.
The above-mentioned deductions were examined in a system constructed with a backscattered gamma-ray type level gauge and a controller for infusion and exhaust of water.Its results almost agreed with those of the deductions when the factor of the standard deviation is substituted for by 2.
