A modified finite element-transfer matrix for control design of space structures

Tan, Tein-Min; Yousuff, A.; Bahar, Leon Y.; Konstantinidis, M.

doi:10.1016/0045-7949(90)90173-y

Cited by 12 publications

(14 citation statements)

References 10 publications

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“…By following the model reduction process presented in Section 3 for each control input, we obtain two reduced-order models as shown in (37), and their mathematical descriptions would depend on where the control inputs are applied. For comparisons, we consider only four pairs of mass locations: (8,9), (7,10), (3,15), and (5,13). Table II shows the comparisons of the total system energy for the four pairs of input locations while subjected to similar levels of control input energy.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Extended discrete-time transfer matrix approach to modeling and decentralized control of lattice-based structures

Cramer

Swei

Cheung

et al. 2016

Struct. Control Health Monit.

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SUMMARYThis paper presents the modeling and control of an aircraft wing structure constructed by lattice-based cellular materials/components. A novel model reduction process is proposed that utilizes the extended discrete-time transfer matrix method (E-DT-TMM). Through recursive application of the E-DT-TMM, an effective reduced-order model can be obtained in which a decentralized discrete-time linear quadratic regulator (LQR) controller can be designed. To demonstrate the efficiency of the proposed concept, a prototype wing structure is studied. The analysis and simulation results show that the performance of the proposed E-DT-TMM based decentralized LQR controller is comparable with that of the full-state continuous LQR controller.

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Section: Numerical Simulationsmentioning

confidence: 99%

Extended discrete-time transfer matrix approach to modeling and decentralized control of lattice-based structures

Cramer

Swei

Cheung

et al. 2016

Struct. Control Health Monit.

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“…We now have the capability of adding in external forces and quantifying some of contributions of a state to its self, to continue the left to right propagation the next set of states to the left must be related to the node. Equation 12 shows the means of propagating the previous states contributions to the left vector.…”

Section: Left To Rightmentioning

confidence: 99%

“…The damping incorporates extremely low internal damping of the carbon fiber and the friction due to the reversible attachment of the parts. The basic concept behind this approach was inspired by the work of Tan et al [12], where the notion of modified transfer matrix method (M-TMM) approach was developed by utilizing the dynamic stiffness matrix of finite element. The primary goal there was to reduce the computational efforts involved in structural analysis.…”

Section: Introductionmentioning

confidence: 99%

Discrete Time Finite Element Transfer Matrix Method Development for Modeling and Decentralized Control

Cramer

Swei

Cheung

et al. 2015

Volume 8: 27th Conference on Mechanical Vibration and Noise

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The current emphasis on increasing aeronautical efficiency is leading the way to a new class of lighter more flexible airplane materials and structures, which unfortunately can result in aeroelastic instabilities.To effectively control the wings deformation and shape, appropriate modeling is necessary. Wings are often modeled as cantilever beams using finite element analysis. The drawback of this approach is that large aeroelastic models cannot be used for embedded controllers. Therefore, to effectively control wings shape, a simple, stable and fast equivalent predictive model that can capture the physical problem and could be used for in-flight control is required.The current paper proposes a Discrete Time Finite Element Transfer Matrix (DT-FETMM) model beam deformation and use it to design a regulator. The advantage of the proposed approach over existing methods is that the proposed controller could be designed to suppress a larger number of vibration modes within the fidelity of the selected time step. We will extend the discrete * Address all correspondence to this author time transfer matrix method to finite element models and present the decentralized models and controllers for structural control. NomenclatureA n = Acceleration integration scaling value for the n th node B n = Acceleration integration constant for the n th node C i j = Galerkin finite element damping matrix sub-block D n = Velocity integration constant for the n th node E n = Velocity integration scaling value for the n th node f n = Control input force at n th node F n = Forward propagation matrix of the right force for the n th node H n = Reverse propagation matrix of the left force for the n th node J n = Reverse propagation matrix for the n th node K i j = Galerkin finite element elastic matrix sub-block M i j = Galerkin finite element mass matrix sub-block P n = Forward propagation matrix for the n th node Q n = Transfer matrix from left boundary condition to n th node T n = Transfer matrix from right boundary condition to n th node v n = Propagation vector 1Copyright c 2015 by ASME x n = n th node position stateṡ x n = n th node velocity states x n = n th node acceleration states τ n = Internal forces at the n th node for either left or right side 7

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“…The FE-TM approach was then applied for chain-like structure analysis [9] and closed-loop kinematic chain of flexible structures like the four-bar mechanism [10]. A modified version of FE-TM allowed researchers to extend the method to Space structures for control purposes: Tan et al [11] proposed the collocated control of a beam by Linear Quadratic Regulator (LQR) theory. Rui et al [12] provided the dynamic model of a multiple launch rocket system.…”

Section: Introductionmentioning

confidence: 99%

“…There are mainly two limitations in FE-TM formulation: the first one comes from the derivation of the transfer-matrix which requires the inversion of the sub-matrices associated with each element [11], that is possible if and only if these sub-matrices are non-singular and square; the second one consists in the difficulty to model non tree-like multibody structures with both multiple input and multi output ends [15]. The latter limitation is an important issue in the Space field, where complex and different flexible appendages such as solar arrays, antennas or robotic arms are attached to the spacecraft's central body.…”

Section: Introductionmentioning

confidence: 99%

Finite element based N-Port model for preliminary design of multibody systems

Sanfedino

Alazard

Pommier-Budinger

et al. 2018

Journal of Sound and Vibration

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Keywords: Multibody dynamics Mechanical preliminary design Bending plate Model reduction a b s t r a c tThis article presents and validates a general framework to build a linear dynamic Finite Element-based model of large flexible structures for integrated Control/Structure design. An extension of the Two-Input Two-Output Port (TITOP) approach is here developed. The authors had already proposed such framework for simple beam-like structures: each beam was considered as a TITOP sub-system that could be interconnected to another beam thanks to the ports. The present work studies bodies with multiple attaching points by allowing complex interconnections among several sub-structures in tree-like assembly. The TITOP approach is extended to generate NINOP (N-Input N-Output Port) models. A Matlab toolbox is developed integrating beam and bending plate elements. In particular a NINOP formulation of bending plates is proposed to solve analytic two-dimensional problems. The computation of NINOP models using the outputs of a MSC/Nastran modal analysis is also investigated in order to directly use the results provided by a commercial finite element software. The main advantage of this tool is to provide a model of a multibody system under the form of a block diagram with a minimal number of states. This model is easy to operate for preliminary design and control. An illustrative example highlights the potential of the proposed approach: the synthesis of the dynamical model of a spacecraft with two deployable and flexible solar arrays.

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A modified finite element-transfer matrix for control design of space structures

Cited by 12 publications

References 10 publications

Extended discrete-time transfer matrix approach to modeling and decentralized control of lattice-based structures

Extended discrete-time transfer matrix approach to modeling and decentralized control of lattice-based structures

Discrete Time Finite Element Transfer Matrix Method Development for Modeling and Decentralized Control

Finite element based N-Port model for preliminary design of multibody systems

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