An improved non‐sequential multi‐input multi‐output quantitative feedback theory design methodology

Abstract

SUMMARYThis paper presents an improved non-sequential multi-input multi-output (MIMO) Quantitative Feedback Theory (QFT) design methodology for uncertain systems. A non-sequential MIMO QFT stability theorem is derived that serves as the basis for an improvement of the design methodology, whereby it can be successfully applied to non-minimum phase systems, albeit with a degree of conservatism partially inherent in independent and decentralized design methodologies. The results reduce the conservatism in a nonsequential MIMO QFT design and provide insight into the plant cases for which the methodology can be successfully applied.

Non‐sequential MIMO QFT control of the X‐29 aircraft using a generalized formulation

“…While the stability of the designed control system was questioned in [49], recently [24] confirmed the robust stability properties of a successful design when applied to a MP plant family and hence confirmed the stability properties of the design methodology as presented in [15]. More recently [50,51] extended the result of [24] such that it is broadly applicable to MP/NMP and stable/unstable plant families. This was achieved by exploiting the freedom offered by not stabilizing each MISO loop in the decomposed multivariable control problem, which has important implications on design conservatism [50,51].…”

“…More recently [50,51] extended the result of [24] such that it is broadly applicable to MP/NMP and stable/unstable plant families. This was achieved by exploiting the freedom offered by not stabilizing each MISO loop in the decomposed multivariable control problem, which has important implications on design conservatism [50,51].…”

“…In related work, Horwitz et al [55] considered performance limitations associated with NMP transmission zeros and Yaniv [59] presented sufficient conditions for the achievement of arbitrary small sensitivity in MIMO uncertain systems using the sequential MIMO design methodology. In [24,51] existence conditions for a non-sequential MIMO QFT design were presented, where in [51] it was reasoned that the methodology cannot simultaneously stabilize a connected plant family with differing numbers of RHP transmission zeros. The limitations due to NMP transmission zeros were also considered in [60], where loop transmission cross-over frequency limitations were presented on specific SISO loops in a multivariable design.…”

“…The improved non-sequential MIMO QFT design methodology [50,51] employs the standard two degree of freedom (DOF) feedback configuration in Figure 2. The design approach follows the original non-sequential MIMO QFT methodology, with all the loops designed independently and the cross-coupling bounded by the closed-loop performance specifications.…”

Advanced Attitude and Position MIMO Robust Control Strategies for Telescope-Type Spacecraft with Large Flexible Appendages

“…The new methodology was also applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Regarding the field of non-sequential MIMO QFT techniques, it is to be remarked the approach by Kerr, Jayasuriya and co-workers in (Kerr, 2004;Kerr et al, 2005b;Kerr & Jayasuriya, 2006;Kerr et al, 2007;Lan et al, 2004). Stability conditions have also been established within this framework (Kerr & Jayasuriya, 2003;Kerr et al, 2005a).…”