Computation of QFT Bounds for Robust Sensitivity and Gain-Phase Margin Specifications

Algorithms are presented for generation of QFT controller bounds to achieve robust sensitivity reduction and gain-phase margin specifications. The proposed algorithms use quadratic constraints and interval plant templates to derive the bounds, and present several improvements over existing QFT bound generation algorithms: (1) The bounds can be generated over interval controller phases, as opposed to discrete controller phases in existing QFT algorithms. This feature essentially solves the safety problems associated with phase discretization process in QFT bound generation; (2) The generated bounds are guaranteed to be safe and reliable, even for very coarse interval templates (of poor accuracy), and despite all kinds of computational errors; (3) Inner as well as outer enclosures of the exact bound values can be obtained using the proposed algorithms. Such enclosures directly provide upper bounds on the error in the generated results for any given interval template; (4) A very significant reduction in computational effort—typically, reduction in flops by 2–3 orders of magnitude is achieved; (5) The vertical line (or rectangle) nature of plant templates exhibited in the low and high frequency ranges can be readily exploited to obtain bounds with very little effort; (6) The number of flops required to generate the bounds for any given template can be estimated closely a priori; (7) The (entire) algorithms can be programmed using vectorized operations, resulting in small execution times. [S0022-0434(00)02403-5]