AbstractAn adaptive process control scheme—which uses a differential equation model, requires no differentiations in the adaptive circuitry, and no identification of the varying process parameter—was analyzed mathematically and studied on an analog computer. The adaptive loop is operative only during a transient and corrects only in the direction of mismatch between the process and model. Linear analysis of the system differential equations when the correction signal is not introduced into the controller provides a means of designing the adaptive circuitry and approximating the effect when the signal is introduced. The effects on system stability with a pure delay, measurement lag, or an additional pole in the process are presented. Computer results show that when large differences exist between the actual process time constant and the original controller setting, the adaptive feature reduces the overshoot to essentially zero.