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This article presents a new refinement design routine aimed at solving the robust multivariable tracking error problem with reduced conservatism. The prevailing multivariable quantitative feedback theory (QFT) approach is to implicitly overbound the model‐error tracking set frequency response in magnitude using the triangle inequality, with the intention of arriving at a set of univariate design constraints that independently describe the feedback controller solution space. While this method is effective in the low‐frequency range (where the loop gain tends to be large), the mid‐ to high‐frequency design regions (where diagonal dominance is not possible in general) suffers from arbitrarily large design conservatism. This inhibits minimum gain‐phase solutions and necessitates undesirable over‐design in the frequency band that can contribute to large, expensive control action. The proposed method follows a refinement approach that makes use of information from an a priori feedback control design. In this way, the tracking error problem is reposed as a differential design, and gain‐phase information from the previous iteration can be captured to reduce the conservatism imposed when applying the triangle inequality. Additionally, a constrained optimization routine is used to select a prototype feedforward filter that can relax the constraint set, thereby increasing the accessible solution space of the diagonal feedback controller. Finally, a nondiagonal, multivariable feedforward filter bound generation routine is defined that relies on existence conditions and is free of induced design conservatism. The viability of this design methodology is demonstrated on two benchmark problems of varying complexity, in order to demonstrate the widespread efficacy. [ABSTRACT FROM AUTHOR]

Summary: This article presents a solution to the 2 × 2 multivariable tracking error problem. Current quantitative feedback theory methods commonly employ plant‐inverting splittings in order to arrive at an approximately decoupled design on the feedback control elements. This results in suitable design regions in the high‐gain, low‐frequency range, but can result in conservative design at and above the gain‐crossover frequency, resulting in overdesigned feedback controllers. Our method aims to reduce this conservatism by supplementing a plant‐inverting design with a non‐plant‐inverting design, which tends to perform well at higher frequencies. Decoupling the design of the controller elements is facilitated by making use of appropriate existence conditions. The union of the two resulting design regions then describes a larger solution space, and by enlarging the admissible design regions for the feedback controller, lower gain feedback controller design at all design frequencies of interest may be possible. A benchmarking example is presented, showing the viability of the proposed method. [ABSTRACT FROM AUTHOR]