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The basis of the work described in this paper is the use of the moments of the error signal resulting from a unit step input to a feedback system for the detection of changes in the characteristics of the plant. Expressions for the moments of the error in terms of moments of the input-error transfer function of the system are developed first. Then, from the relationship of the moments of the input-error transfer function to the parameters in the transfer functions of the various components of the system, a solution is obtained for those values of the adjustable parameters of an adaptive compensator that will reduce the first several moments of the error function to zero. An example is presented next, to illustrate the procedure for designing an adaptive system by the proposed method, and experimental results obtained from a system so designed are introduced to demonstrate the effectiveness of the adaptation obtainable by the use of this approach. Finally, it is concluded that the method proposed loses somewhat in effectiveness if the impulse response of the plant becomes highly oscillatory but that it has the advantage that the degree of the differential equation describing the plant need not be known.