A complementary quantitative feedback theory solution to the 2 × 2 tracking error problem. (23rd July 2020)

• Record Type: Journal Article
• Authors: Pretorius, Arnold; Boje, Edward
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 16(2020)
• Page Start: 6569
• Page End: 6584
• Publication Date: 2020-07-23
• Subjects: MIMO QFT -- robust control -- tracking error specifications; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5120
• Languages: English
• ISSNs: 1049-8923

Abstract

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.