Abstract: An apparatus is provided for controlling a system to achieve a specified response. In one embodiment, the apparatus is a proportional, integrative, and derivative (PID) controller having a proportional element, an integrative element, and a derivative element coupled together. The elements respond to a reference signal and generate a control signal that causes a plant to generate a plant output. The proportional element has a gain element where the gain is a function of the ultimate gain of the plant (Ku) and the ultimate period of the plant (Tu). The controllers may also be embodied in non-PID controllers that share common elements, such as the use of: (a) Astrom-Hagglund controller output as an input for a subsequent controller; (b) internal feedback; and (c) a subsequent controller that performs a subtraction operation to generate the difference between the output of the Astrom-Hagglund controller and the output of the subsequent controller.