Statistical Optimization of Regulators Employing a Binary Error Criterion

Abstract

The problem is considered of minimizing total costs of a regulator subject to both a steady reference input and a statistical load disturbance. A binary error criterion is used which directly relates the error magnitude to the economic penalty entailed by the error. In contrast it is not easy to relate the mean-square error to economic penalty. Experimental work shows that the amplitude probability density distributions in saturating loops are altered sufficiently from the Gaussian that the statistical linearization technique does not predict results with satisfactory accuracy in many cases of interest. The use of modified distributions alleviates this problem, but analog computer experiments provide the most satisfactory attack for complicated situations and are easily instrumented.