scholarly journals Coupling Effect of Nonlinear Stiffness of Tape Spring Hinges and Flexible Deformation of Panels during Orbit Maneuvers

Aerospace ◽  
2022 ◽  
Vol 9 (1) ◽  
pp. 30
Author(s):  
Wenyan Gu ◽  
Jinsheng Zhang ◽  
Longye Pan ◽  
Yegao Qu ◽  
Jin-Hwan Choi ◽  
...  
Keyword(s):  
Coupling Effect ◽  
Thin Sheet ◽  
Order Reduction ◽  
Local Deformation ◽  
Dynamic Responses ◽  
Solar Panels ◽  
Precise Control ◽  
Nonlinear Properties ◽  
Flexible Deformation ◽  
Order Reduction Method

Many solar panels for spacecrafts are deployed by Tape Spring Hinges (TSHs) which have changeable stiffness. The stiffness of TSH is small when panels are folded, and it becomes large quickly in its deployed status. Since the solar panel is a thin sheet, flexible deformation is easily generated by orbit maneuvers. The coupling effect between the nonlinear TSHs and the flexible panels generates obvious vibration which affects the operational stability of the satellite. To investigate this coupling effect, non-deformable, linear deformable and nonlinear deformable panels were modelled by rigid body, modal order reduction method (MORM) and finite element method (FEM), respectively. The driving torque of TSH was described as a function of the rotation angle and angular velocity. The nonlinear properties of the TSH were reflected by one angle-stiffness spline multiplied by one stiffness coefficient. Dynamic responses of a satellite in deployment and orbit steering were analyzed by numerical simulations. Analysis results indicate the local deformation of panels keeps the stiffness of the TSH within a large range which accelerates the orbit maneuvers. However, much vibration is generated by the coupling effect if the luck-up status is broken up. The coupling effect affects the sequence of deployment, overshoot phenomenon and acceleration magnitude of the panels. Although the MORM is more efficient than FEM in computation, we propose FEM is better suited in the design of TSH and in studying the precise control of spacecraft with flexible solar panels and TSHs.

scholarly journals Approximate inertial manifold-based order reduction of rigid-flexible coupling manipulator

2021 ◽  
Vol 260 ◽  
pp. 03014
Author(s):  
Lisha Xu ◽  
Xiaoshan Qian ◽  
Chong Lin
Keyword(s):  
Controller Design ◽  
Order Reduction ◽  
Order System ◽  
Response Analysis ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold ◽  
Deformation Response ◽  
Flexible Deformation ◽  
Order Reduction Method ◽  
Manifold Theory

An order reduction method for the flexible deformation response analysis of rigid flexible manipulators is proposed based on the approximate inertial manifold theory. This method allows a lower dimensional simplified model to be constructed from a subspace smaller than the entire state space. In this paper, truncated three-order modes are used to construct a first-order system of AIM. Compared with the traditional Galerkin method, the results show that the proposed method can reduce the degree of freedom of the system and improve the computational efficiency without obviously losing the precision of the solution, which is convenient for the subsequent vibration analysis and controller design of the system.

scholarly journals The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart
Keyword(s):  
Predictive Control ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Double Precision ◽  
Model Order ◽  
Numerical Errors ◽  
Multiple Input ◽  
Multidimensional Objects ◽  
Order Reduction Method

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.

The Application of Neural Operator in subsurface process simulation 

2021 ◽  
Author(s):  
Zhouji Liang ◽  
Denise Degen ◽  
Florian Wellmann
Keyword(s):  
Initial Conditions ◽  
Order Reduction ◽  
Input Function ◽  
Reduced Basis ◽  
Distribution Boundary ◽  
Process Simulations ◽  
Imperfect Knowledge ◽  
Computationally Intensive ◽  
Geothermal Reservoir Simulation ◽  
Order Reduction Method

<p>Numerical simulations of subsurface processes are essential to the success of many geoengineering projects. These simulations often contain significant uncertainties due to imperfect knowledge of material properties and their spatial distribution, boundary conditions, and initial conditions. However, efficient implementations for the quantification of uncertainties for such simulations are big challenges in Computational Geoscience, mainly due to the curse of dimensionality. Process simulations often involve solving high-dimensional Partial Differential Equations (PDE) by using discretization methods such as Finite Difference (FD) or Finite Elements (FE) methods. Although such methods often give good approximations, they are computationally intensive and expensive and therefore infeasible in the applications such as MCMC where thousands of evaluations of the forward simulation are required. Previous work by Degen et.al. (2020) has addressed this problem by using a model order reduction method, the so-called reduced basis (RB) method. However, the method has limitations when considering complex (i.e., hyperbolic and non-linear) PDEs. In this work, we aim to employ the recently developed Fourier Neural Operator (FNO) (Li, 2020) as a tool to implement efficient approximation of PDEs in the application of Geothermal reservoir simulation. FNO involves a Fast Fourier transform to directly learn the mapping from the input function to the output function. FNO has the advantage of being independent of the resolution and complexity of the governing PDE. Our preliminary results show that FNO can provide good approximation results in solving four-dimensional PDEs and thus can be used as a tool for further probability studies of the parameters of interest.</p>

Order Reduction of Controller Based on LMIs Improving Error Bounds

1997 ◽  
Author(s):  
Roberd Saragih ◽  
Yoshida Kazuo
Keyword(s):  
Projection Method ◽  
Order Reduction ◽  
Feasibility Problem ◽  
Closed Loop System ◽  
Reduced Order ◽  
Bounded Real Lemma ◽  
Convex Feasibility ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Order Reduction Method

Abstract In this paper, we propose an order reduction method of controller based on combination of the alternating projection method and the balanced truncation. In this method both the errors of controller and the closed-loop system caused by the reduced-order controller can be improved simultaneously. By using a generalized Bounded Real Lemma, a feasible reduced-order controller can be derived. The sufficient condition for the existence of a reduced-order controller leads to a non-convex feasibility problem. To solve the problem, we can use an improved computational scheme based on the alternating projection method. But it is needed so much time to solve the problem if compared by the other methods. To validate the proposed method, some numerical calculations and simulations are carried out.

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