Flexible Truss Structure Research Articles

Finite element dynamic modeling and attitude control for a slender flexible spacecraft

This paper aims to study the dynamic modeling and attitude control of a kind of slender flexible spacecraft. The basic structure of this kind of spacecraft is different from the traditional structure of a center rigid body with flexible appendages, but rigid bodies at both ends, which are connected by a flexible truss structure. Firstly, the finite element modeling method is adopted to establish the dynamic model of this kind of spacecraft, and the vibration frequency and damping of the flexible structure are obtained. The unconstrained modes of the flexible spacecraft are obtained through mathematical analysis, finite element analysis and frequency domain analysis. In addition, a nonlinear sliding surface with angular velocity constraint is designed. On this basis, an adaptive sliding mode (ASM) controller is proposed, stability of the close-loop system under the controller is proved, and the dynamic model is verified through mathematical simulation.

3D-printed, electrically conductive structures for magnetic attitude control

The use of embedded current loops for the attitude control of large, flexible spacecraft is investigated. Length-scaling laws are derived by determining what fraction of a planar spacecraft’s mass would need to be allocated to the conductive current loops in order to produce a torque at least as large as the gravity gradient torque. Simulations are then performed of a flexible truss structure, modelled as a spring–mass system, for a range of structural flexibilities and a variety of current loop geometries. Simulations demonstrate rotation of the structure via the electromagnetic force on the current carrying elements, and are also used to characterise the structural deformations caused by the various current loop geometries. An attitude control simulation is performed, demonstrating a 90∘ slew manoeuvre of a 250 × 250 m flexible structure through the use of three orthogonal sets of current loops embedded within the spacecraft.

Fuzzy PD hybrid control of low frequency vibration of annular antenna

The annular antenna is a typical large flexible space truss structure featured by small damping and low modal frequencies. The external disturbances, e.g. impulse load resulting from satellite attitude adjusting, may induce the low frequency large amplitude vibrations of annular antenna for a long time and thus reduce working precision and cause even its damage. The active control of vibration of annular antenna under impulse excitation is investigated in the paper. The voice coil actuator instead of piezoelectric stack actuator is used in order to meet the demand of large output displacement. The governing equation of active vibration control system is established by use of finite element method. The proportional differential (PD) control and fuzzy control algorithms are firstly studied in the active control. The results show that the fuzzy control exhibits worse control performance than PD control due to weak control function near structural equilibrium position. To circumvent the drawback of fuzzy control, a fuzzy PD hybrid control strategy is proposed which can combine the merits of both control methods. The simulated and experimental results show that the fuzzy PD hybrid control can yield the best control effect under impulse excitation comparing with the PD control and ordinary fuzzy control. The work provides a promising control way for active control of low frequency and large displacement vibration of annular antenna in satellite engineering.

Design and performance assessment of a distributed vibration suppression system of a large flexible antenna during attitude manoeuvres

One of the major needs of future Earth Observation satellites is to fulfil high demanding pointing requirements when using instrumentations supported by or mounted at the end of very large flexible truss structures. Those spacecraft often call for the capacity of performing fast and precise manoeuvres without exceeding deformation requirements related to their flexible parts. On-board mechanical disturbances can be generated by an attitude control equipment and pointing mechanisms. In this perspective, a network of smart actuators/sensors can be mounted on a passive structure to counteract undesired elastic vibrations. In this paper, the problem of micro-vibration control for a spacecraft equipped with a very large flexible antenna is addressed. The instrument is sustained by an active frame hosting an optimally distributed network of actuators and sensors dedicated to vibrations suppression. The fully coupled 3-D equations for a flexible spacecraft subjected to forces of the orbital environment are derived taking the presence of the smart materials into account. The 3-D flexible structure model is developed and validated via FEM formulation by using commercial codes. The model is then reduced to obtain a system to be easily handled by control systems algorithms. A placement strategy to identify the best location for vibration control devices is carried out by using Gramian-based techniques. Typical profiles of attitude manoeuvres are then simulated by applying a control torque while simultaneously suppressing unwanted vibrations. To achieve a high performance, feedback methods are implemented to coordinate the actuators and ensure that maximum tip displacement requirements are satisfied during operations.

Dynamic analysis of suspension cable based on vector form intrinsic finite element method

A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.

The Analysis of Stiffness and Stability of Luffing Jib Cranes Based on Theory of Second Order

Luffing jib cranes are large flexible complex truss structure, and their mechanical property is nonlinearity. So the Precise analysis method for the stiffness and stability problem has been paid attention to by the researchers. To solve this problem, the equivalent mechanical model of luffing jib crane was established by taking the lifting load, counter weight and dead weight into consideration. The stiffness and stability of luffing jib crane was analyzed by using the differential equation of deflection based on second-order effect. The calculating formulas of lateral deflection, amplification factor of deflection and stability was derived. Taking a luffing jib tower crane for example, the lateral stiffness was calculated respectively by the formula given by this paper, the traditional linear method and the finite element method, and show that the result calculated by the formula given by this paper is identical to that by finite element software ANSYS, the error is 1.8%. and the error of traditional method is 7.6%, It is clear that calculation expression of lateral deflection, deflection amplification factor and the stability in this paper are accuracy. This method can be applied to the analysis of calculation of luffing jib tower crane stiffness and stability.

Optimum placement of actuators in structural and control design using Stackelberg games

Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.

Nonlinear self-defined truss element based on the plane truss structure with flexible connector

A finite-element method based on the self-defined truss element is developed to model the plane truss structure with the flexible connector, and the dynamic characteristic of the corresponding model is analyzed in this paper. Firstly, a new type truss structure with flexible connectors included clearance, friction and axial constraint is analyzed. A self-defined truss element is defined based on the mechanical analysis of the new type truss structure, and a finite-element model is introduced based on this element. The nonlinear elastic-damper model and the Coulomb friction model are adopted to analyze the nonlinear nodal forces from the impact and friction in the clearance field. Secondly, a modified numerical solution method is developed based on the Newmark implicit integrate method together with Newton–Raphson iterated method, and then is applied to solve the nonlinear dynamic model. Finally, an example is simulated by the above numerical method, and the effects of several key parameters (such as the linkage stiffness, contact stiffness, and clearance) on the dynamic characteristic are analyzed. The results validate the numerical method, and show the effectiveness of the nonlinear finite-element model. The dynamic analysis about the key parameters offers some helpful guidelines for designing flexible truss structure.

Sliding Mode Output Feedback Control of Vibration in a Flexible Structure

This paper presents a new approach for the robust control of vibration in a flexible structure in the presence of uncertain parameters and residual modes. The technique is based on the sliding mode control algorithm using direct output feedback and assumes that actuators and sensors are not collocated. The uncertainty matrix need not satisfy the invariance or matching conditions. The small gain theorem/μ analysis is applied to analyze the asymptotic behavior of the closed-loop system with parametric uncertainties inside boundary layers. The model of a flexible tetrahedral truss structure is used to conduct numerical verification of the theoretical analysis.

Design & Modeling of a Segmented Reflector Test-bed

Because of the weight and volume constraints of space-borne astronomical instruments, segmented reflectors have become the only practical choice for future astrophysical missions. While a monolithic reflector depends on the mechanical properties of its material to provide the dimensional stability required for good optical performance, a segmented reflector requires an active segment-alignment control system in order to make the reflecting surface have the optical performance of a monolithic unit. This paper describes an experimental test-bed that is being developed at the Control and Structures Research Laboratory (CSRL) at California State University, Los Angeles (CSULA). The CSRL test-bed is a 2.4 m focal length Cassegrain optical configuration consisting of a 2.66 m actively controlled segmented primary and an active secondary. The primary consists of six hexagonal panels surrounding a fixed central panel and supported by a light-weight flexible truss structure. The project has been funded by NASA to study the complex dynamic behavior of large segmented optical systems.

Solving the damper placement problem via local search heuristics

The damper placement problem for large flexible space truss structures is to determine thep truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and columns indexed on the truss members we seek to find a set ofp columns such that the smallest row sum, over thep columns, is maximized. An extension of this model is formulated for the passive damper case. This formulation includes the frequency of maximum displacement as a decision variable for each passive damper. Each formulation can be written as a mixed 0/1 integer linear program. We compare the performance of tabu search and simulated annealing for the damper placement problem on a laboratory test article, the NASA Langley Controls-Structures Interaction Phase I Evolutionary Model (10 modes and 1507 truss members). Tabu search, coupled with the starting solution generated by rounding the solution to a linear programming relaxation, is shown to provide the highest quality solutions in the shortest amount of computing time.

Control of a class of nonlinear uncertain systems via compensated inverse dynamics approach

The tracking control problem of a class of nonlinear systems via inverse dynamics method is addressed. The motivation for the study stems from the need to control practical systems arising from aerospace and mechanical engineering. Because modeling uncertainties and external disturbances are always present in these systems, inverse dynamics technique is not applicable directly. A compensated inverse dynamics approach is proposed to account for the effect of uncertainties. The compensation is achieved by adaptive and robust schemes. Application of the proposed strategy to the vibration suppression of a two-bay flexible truss structure is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification and Adaptive Control of Flexible Truss Structures

This paper describes investigations on adaptive vibration control and shape adjustment of truss structures making use of the active member actuator. The actua tor was manufactured in an attempt to achieve these functions by linear actuating. Funda mental characteristics were examined statically and dynamically. Numerical simulations of planar truss model with the configuration of one pair of collocated actuator and sensor shows that a state observer can estimate truncated modes well and the excited vibration can be controlled rapidly.

Robust control of a flexible space structure in the presence of parameter variations and unmodelled dynamics

The control of a flexible truss structure is discussed with respect to robustness against parameter uncertainty and high frequency unmodelled dynamics. Emphasis is placed upon providing vibration suppression and improving system damping in the presence of these uncertainties. A robust control design is achieved by simultaneously constraining both the linear quadratic Gaussian (LQG) performance index and the H∞ norm of a specific disturbance transfer matrix. Closed loop simulation is then performed to determine the effectiveness of the control design.

Model reduction in limited time and frequency intervals

The controllability and observability gramians in limited time and frequency intervals are studied, and used for model reduction. In balanced and modal coordinates, a near – optimal reduction procedure is used, vielding the reduction error (norm of the different between the output of the orginal system and the reduced model) almost minimal. Several examples are given to illustrate the concept of model reduction in limited time or/and frequency intervals, for continuous- and discrete-time systems, as well as stable and unstable systems. In modal coordinates, the reduced model obtained from a stable system is always stable. In balanced coordinates it is not necessarily true, and stability conditions for the balanced reduced model are presented. Finally, model reduction is applied to advanced supersonic transport and a flexible truss structure.

Control technology test bed for large segmented reflectors

A description is given of an experimental test apparatus for active control of a seven-segment primary reflector (mirror). Segmented reflectors require an active segment-alignment control system to give the reflecting surface the optical performance of a single-piece reflector. The apparatus, called the Advanced Structures/Controls Integrated Experiment, consists of a Cassegrain optical configuration with a 2-m, seven-segment, actively controlled primary mirror supported by a light, flexible truss structure. The testbed is a response to the need for experiments that can simulate the complex dynamic behavior of a large structure and address the myriad problems associated with precision control of optical surfaces. The testbed is described, details of the control and optical measurement systems are presented, and preliminary performance results are reported. >