Integral of the error squared as a performance index for automatic control systems

IN 1943, Hall proposed the integral-of-squared-error (ISE) criterion as an indirect measure of the speed of response (to a step input) of servomechanism systems.1 This index of performance was proposed as an analytical function of the servomechanism parameters which would be minimized by adjustment of the system parameters, the relationship between the parameters and the ISE being less complex than that between the parameters and the speed of response itself. As a result of Hall's work the ISE was tabulated as a function of system constants for systems whose error function is of tenth order or less.2,3