Controllable set analysis for planetary landing under model uncertainties

ABSTRACT Motivated by the recently discovered kinematic ‘Hubble sequence’ shown by the stellar orbit-circularity distribution of 260 CALIFA galaxies, we make use of a comparable galaxy sample at z = 0 with a stellar mass range of $M_{*}/\mathrm{M}_{\odot }\in [10^{9.7},\, 10^{11.4}]$ selected from the IllustrisTNG simulation and study their stellar orbit compositions in relation to a number of other fundamental galaxy properties. We find that the TNG100 simulation broadly reproduces the observed fractions of different orbital components and their stellar mass dependences. In particular, the mean mass dependences of the luminosity fractions for the kinematically warm and hot orbits are well reproduced within model uncertainties of the observed galaxies. The simulation also largely reproduces the observed peak and trough features at $M_{*}\approx 1\rm {-}2\times 10^{10}\, \mathrm{M}_{\odot }$ in the mean distributions of the cold- and hot-orbit fractions, respectively, indicating fewer cooler orbits and more hotter orbits in both more- and less-massive galaxies beyond such a mass range. Several marginal disagreements are seen between the simulation and observations: the average cold-orbit (counter-rotating) fractions of the simulated galaxies below (above) $M_{*}\approx 6\times 10^{10}\, \mathrm{M}_{\odot }$ are systematically higher than the observational data by $\lesssim 10{{\ \rm per\ cent}}$ (absolute orbital fraction); the simulation also seems to produce more scatter for the cold-orbit fraction and less so for the non-cold orbits at any given galaxy mass. Possible causes that stem from the adopted heating mechanisms are discussed.

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Robust Position Control of an Over-actuated Underwater Vehicle under Model Uncertainties and Ocean Current Effects Using Dynamic Sliding Mode Surface and Optimal Allocation Control

Sensors ◽

10.3390/s21030747 ◽

2021 ◽

Vol 21 (3) ◽

pp. 747

Author(s):

Mai The Vu ◽

Tat-Hien Le ◽

Ha Le Nhu Ngoc Thanh ◽

Tuan-Tu Huynh ◽

Mien Van ◽

...

Keyword(s):

Control System ◽

Motion Control ◽

Optimal Allocation ◽

Position Control ◽

Sliding Mode ◽

Underwater Vehicle ◽

Ocean Current ◽

Model Uncertainties ◽

Control Module ◽

Dynamic Sliding Mode

Underwater vehicles (UVs) are subjected to various environmental disturbances due to ocean currents, propulsion systems, and un-modeled disturbances. In practice, it is very challenging to design a control system to maintain UVs stayed at the desired static position permanently under these conditions. Therefore, in this study, a nonlinear dynamics and robust positioning control of the over-actuated autonomous underwater vehicle (AUV) under the effects of ocean current and model uncertainties are presented. First, a motion equation of the over-actuated AUV under the effects of ocean current disturbances is established, and a trajectory generation of the over-actuated AUV heading angle is constructed based on the line of sight (LOS) algorithm. Second, a dynamic positioning (DP) control system based on motion control and an allocation control is proposed. For this, motion control of the over-actuated AUV based on the dynamic sliding mode control (DSMC) theory is adopted to improve the system robustness under the effects of the ocean current and model uncertainties. In addition, the stability of the system is proved based on Lyapunov criteria. Then, using the generalized forces generated from the motion control module, two different methods for optimal allocation control module: the least square (LS) method and quadratic programming (QP) method are developed to distribute a proper thrust to each thruster of the over-actuated AUV. Simulation studies are conducted to examine the effectiveness and robustness of the proposed DP controller. The results show that the proposed DP controller using the QP algorithm provides higher stability with smaller steady-state error and stronger robustness.

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