Quaternion versus Rotation Matrix Feedback for Spacecraft Attitude Stabilization Using Magnetorquers

The purpose of this paper is to compare performances between stabilization algorithms of quaternion plus attitude rate feedback and rotation matrix plus attitude rate feedback for an Earth-pointing spacecraft with magnetorquers as the only torque actuators. From a mathematical point of view, an important difference between the two stabilizing laws is that only quaternion feedback can exhibit an undesired behavior known as the unwinding phenomenon. A numerical case study is considered, and two Monte Carlo campaigns are carried out: one in nominal conditions and one in perturbed conditions. It turns out that quaternion feedback compares more favorably in terms of the speed of convergence in both campaigns, and it requires less energy in perturbed conditions.

q-Rung Orthopair Fuzzy Rough Einstein Aggregation Information-Based EDAS Method: Applications in Robotic Agrifarming

The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers’ unknown weights as well as attributes’ weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information.

Coupled Time and Passage Spectral Method for an Efficient Resolution of Turbomachinery Far Upstream Wakes

The paper proposes a novel numerical method called coupled time and passage spectral method for an efficient resolution of far upstream wakes in an unsteady analysis of flow field within generic multiple blade rows. The proposed method is a very simple and natural extension of the time spectral form harmonic balance method. By including inter-blade phase angle and passage index in a truncated Fourier series, the proposed method is capable of circumventing the limitations of the harmonic balance method in dealing with zero frequency harmonics and time harmonics with the same frequency but different inter blade phase angles. Different from the harmonic balance method, which seeks solutions at different time instants of the same passage, the coupled spectral method seeks solutions at different passages and time instants. Same as the harmonic balance method, all these solutions are connected via a spectral operator. Coupled time and passage sampling is performed using the modified Gram Schmidt process to choose the time and passage pairs which give the most orthogonal rows of an inverse Fourier transform matrix. The coupled time and passage spectral method requires minimum change to an existing harmonic balance solver. A numerical case study has been provided in the paper to demonstrate the expected capability against the harmonic balance method.

Coupled Time and Passage Spectral Method for an Efficient Resolution of Turbomachinery Far Upstream Wakes

The paper proposes a novel numerical method called coupled time and passage spectral method for an efficient resolution of far upstream wakes in an unsteady analysis of flow field within generic multiple blade rows. The proposed method is a very simple and natural extension of the time spectral form harmonic balance method. By including inter blade phase angle and passage index in a truncated Fourier series, the proposed method is capable of circumventing the limitations of the harmonic balance method in dealing with zero frequency harmonics and time harmonics with same frequency but different inter blade phase angles. Different from the harmonic balance method, which seeks solution at different time instants of the same passage, the coupled spectral method seeks solutions at different passages and time instants. Same as the harmonic balance method, all these solutions are connected via a spectral operator. Coupled time and passage sampling is performed using the modified Gram Schmidt process to choose the time and passage pairs which give the most orthogonal rows of an inverse Fourier transform matrix. The coupled time and passage spectral method requires minimum change to an existing harmonic balance solver. A numerical case study has been provided in the paper to demonstrate the expected capability against the harmonic balance method.