Frequency Response Specifications and Sensitivity Functions in Quantitative Feedback Theory

Within the scope of control of uncertain systems, the problem of performance robustness, especially in the face of parametric uncertainty, has been increasingly recognized as a predominant issue of engineering significance in many design applications. Quantitative Feedback Theory (QFT), a frequency response-based method introduced by Horowitz, has been shown advantageous in many cases where performance specifications for such systems, in terms of hard constraints on closed loop response, are to be met. In this paper, these traditional QFT design criteria are contrasted with a relaxed, sensitivity-based formulation for single input single output (SISO) feedback systems. The advantage of the latter is a greater degree of mathematical commonality with alternative frequency domain methods, thus laying the groundwork for future benchmark studies in control design. The methodology is demonstrated by application to a lateral autopilot design problem for the C-135 aircraft, both to the traditional QFT design specifications as well as to the relaxed sensitivity based criterion.