Nondiagonal MIMO QFT Controller Design for Darwin-Type Spacecraft With Large Flimsy Appendages

Abstract

This paper deals with the design of robust control strategies to govern the position and attitude of a Darwin-type spacecraft with large flexible appendages. The satellite is one of the flyers of a multiple spacecraft constellation for a future ESA mission. It presents a 6×6 high order multiple-input–multiple-output (MIMO) model with large uncertainty and loop interactions introduced by the flexible modes of the low-stiffness appendages. The scientific objectives of the satellite require very demanding control specifications for position and attitude accuracy, high disturbance rejection, loop-coupling attenuation, and low controller order. The paper demonstrates the feasibility of a sequential nondiagonal MIMO quantitative feedback theory (QFT) strategy controlling the Darwin spacecraft and compares the results with H-infinity and sequential diagonal MIMO QFT designs.

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

“…This Section shows some illustrative results achieved when applying the non-diagonal MIMO QFT control methodology introduced in Section 3 to one of the telescope-type spacecraft (a 6-inputs/6-outputs MIMO system) of a multiple formation flying constellation of a European Space Agency (ESA) cornerstone mission: the Darwin mission (Garcia-Sanz et al, 2008). It consists of one master satellite (central hub) and three to six telescopes arranged in a symmetric configuration flying in formation (Fig.…”

“…Controller complexity and order: minimum. To achieve these goals, the astronomical, engineering and control specifications are translated into frequency domain requirements (see some examples at D'Azzo, Houpis, & Sheldon, 2003), defined as shown in Table I, where (p ii *e ) -1 is the inverse of the equivalent plant, which corresponds to p ii (s) in the SISO case (Garcia-Sanz et al, 2008 2,3,4,5,6 () …”

“…Additionally, De Bedout and Franchek established sufficient stability conditions for non-diagonal sequential procedures (De Bedout & Franchek, 2002). Another important sequential technique to be considered is the one presented by GarciaSanz and collaborators (Garcia-Sanz & Egana, 2002;Garcia-Sanz & Eguinoa, 2005;Garcia-Sanz & Hadaegh, 2007;Garcia-Sanz et al, 2008;Houpis, Rasmussen & Garcia-Sanz, 2006). Following Horowitz's ideas, they extended Horowitz's sequential methodology (Horowitz, 1982) to the design of fully populated MIMO controllers.…”

Non‐diagonal MIMO QFT controller design reformulation

“…GARCIA-SANZ, I. EGUINOA AND S. BENNANI the significant values of the RGA matrix (see [24] for more details):…”

“…GARCIA-SANZ, I. EGUINOA AND S. BENNANI For tracking or disturbance rejection at plant output, the expression of the previous non-diagonal MIMO QFT methodology described in [5,[20][21][22][23][24] for 2×2 MIMO plants was…”