Minimizing effects of disturbing signals through a minimum square-error criterion

One of the reasons for using feedback is the improvement in the rejection of disturbing signals. This improvement can be obtained through an analytical design utilizing as a performance index the integral square-error criterion. In the usual technique the sum of the command signal plus the disturbing signal transferred to the input of the system is used as the input signal. When this is done, one of the two compensating transfer functions (for the particular case of a system with two degrees of freedom) has to be fixed arbitrarily. Then the optimum over-all transfer function, which minimizes the integral of the square of the error between the desired output and the actual one, is calculated and thus the remaining compensator can be obtained. As the technique does not provide a method for determining one of the compensators, and the transferred disturbing signal is a function of this compensator, a required rejection of the disturbing signal may not be satisfied. The purpose of the present paper is to suggest an analytical technique for determining both of the two compensators which have the minimum bandwidth necessary to satisfy a desired over-all transfer function and a required rejection of a disturbing signal. In addition, the technique provides physically realizable compensating transmissions.