The Bode integrals and wave front tilt control

Abstract

This paper reviews four of Bode's (1940) integrals and what those integrals tell about feedback design in the frequency domain. The resulting design paradigm is known as the Bode ideal cutoff. The Bode ideal cutoff design can be done with pencil and paper and without requiring that the compensator be of a certain fixed order or even a rational function of frequency. The Bode ideal cutoff is applied to the preliminary feedback design of wave front tilt control by two mirrors on a space based interferometer. The design example illustrates how the Bode ideal cutoff takes into account bandwidth, sensor noise constraints, and uncertainties via stability margins, and then maximizes the feedback (loop gain or disturbance rejection) over a prescribed frequency band.