Control Of Space Structures Research Articles

Active Damping, Vibration Isolation, and Shape Control of Space Structures: A Tutorial

This tutorial reviews the author’s contributions to the active control of precision space structures over the past 35 years. It is based on the Santini lecture presented at the IAC-2022 Astronautical Congress in Paris in September 2022. The first part is devoted to the active damping of space trusses with an emphasis on robustness. Guaranteed stability is achieved by using decentralized collocated actuator–sensor pairs. The so-called integral force feedback (IFF) is simple, robust, and effective, and the performances can be predicted easily with simple formulae based on modal analyses. These predictions have been confirmed by numerous experiments. The damping strategy for trusses has been extended to cable structures, and also confirmed experimentally. The second part addresses the problem of vibration isolation: isolating a sensitive payload from the vibration induced by the spacecraft (i.e., the unbalanced mass of attitude control reaction wheels and gyros). A six-axis isolator based on a Gough–Stewart platform is discussed; once again, the approach emphasizes robustness. Two different solutions are presented: The first one (active isolation) uses a decentralized controller with collocated pairs of the actuator and force sensor, with IFF control. It is demonstrated that this special implementation of the skyhook, unlike the classical one, has guaranteed stability, even if the two substructures it connects are flexible (typical of large space structures). A second approach (passive) discusses an electromagnetic implementation of the relaxation isolator where the classical dash-pot of the linear damper is substituted by a Maxwell unit, leading to an asymptotic decay rate of −40 dB/decade, similar to the skyhook (although much simpler in terms of electronics). The third part of the lecture summarizes more recent work done on the control of flexible mirrors: (i) flat mirrors for adaptive optics (AO) controlled by an array of piezoelectric ceramic (PZT) actuators and (ii) spherical thin shell polymer reflectors controlled by an array of piezoelectric polymer actuators (PVDF-TrFE) aimed at being deployed in space.

Multi-Scenario Simulation of Land Use and Landscape Ecological Risk Response Based on Planning Control.

This study applied territorial spatial planning control to a land use multi-scenario simulation in Changde, China, and measured the landscape ecological risk response. It embedded five planning control schemes, respectively, involving inertial development, urban expansion size quantity control, ecological spatial structure control, land use zoning control, and comprehensive control. Findings show that: (1) Woodland and arable land in Changde occupy 31.10% and 43.35% of land use, respectively, and constitute the main functional space of the research area. The scale of construction land in Changde has enlarged continuously, with ecological space represented by woodland and water constantly squeezed and occupied. (2) Comprehensive control has the most remarkable restraining effect on the disordered spread of construction land, while ecological space structure control is the most effective way to control ecological land shrinkage. (3) The overall landscape ecological risk index expanded over 2009-2018, presenting an S-type time evolution curve of "sharp increase-mitigation". Landscape ecological risk presents a single-core, double-layer circle structure with the north and east regions as the core, attenuating to the periphery. (4) Landscape ecological risk under land use zoning control increased significantly more than in other scenarios. Comprehensive control best prevented landscape ecological risk and restrained the disorderly expansion of construction land.

Generalized invexity and duality in multiobjective variational problems involving non-singular fractional derivative

AbstractIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo–Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.

Long-range piezoelectric actuator with large load capacity using inchworm and stick-slip driving principles

Conventional long-range piezoelectric actuators (LRPAs) can produce large travel motions based on stepping driving actions. However, their load capacity is limited due to the difficulty in lifting the clamping force that acts against the external load when considering light wear on the clamping interface and fine displacement resolution. This study proposes a hybrid driving method that combines the inchworm and stick-slip driving principles, such that it can significantly improve the load capacity of LRPAs. By introducing a ball-screw-based clamping mechanism driven by the stick-slip rotary driving principle, a ball-screw-based inchworm piezoelectric actuator is designed, which achieves a driving force of 546 N, whereas the clamping force required to balance the external load is significantly reduced, leading to light wear on the clamping interface. Meanwhile, bidirectional motion with a resolution of less than 80 nm is achieved by relying only on a simple driving voltage sequence. The proposed hybrid driving method is instructional for the design of actuators used for the shape control of space structures, such as antennas and trusses, wherein a large driving stroke with fine resolution and a high load capacity with high reliability are important considerations.

Nonlinear vibration control effects of membrane structures with in-plane PVDF actuators: A parametric study

In recent years, with the increasing use of membrane structures in space applications, the problems of large-amplitude (compared to the thickness) vibrations arise; leading to the degradation of their working performance. It is challenging to control the large-amplitude vibrations of membranes due to the high flexibility, low damping, and strong geometrical nonlinearity. In this study, polyvinylidene fluoride (PVDF) actuators are considered to develop the active vibration control of a pre-tensioned Kapton membrane. The governing equations are established based on the geometrically nonlinear theory of plates, taking into account the modal control force induced by the actuators. To analyze the nonlinear dynamic characteristics of the membrane, the theoretical and approximate solutions of nonlinear frequencies of the membrane are obtained, and the discrepancies between the two solutions under different vibration amplitudes are discussed. Control performance for both free vibration and harmonic forced vibration of the membrane is numerically studied. A comprehensive parametric study is carried out to investigate the influences of different system parameters, including the pretension and the size of the membrane, and the position and number of the actuators, on the control performance. Analytical results indicate that the vibration of the membrane can be effectively suppressed with the appropriately laminated PVDF actuators. The results of this research can be extended to the active control of different gossamer space structures.

Observer based active vibration control of flexible space structures with prescribed performance

This paper proposes an active vibration control approach to solve the vibration suppression problem of flexible space structures in the presence of external disturbances and parameter uncertainties. Based on the independent modal space control method, each mode can be decoupled and controlled separately. To meet the case that the velocity sensors are not available on the flexible structures, a neural network based state observer is designed for the estimation of the modal velocity. The neural network approximation is introduced into the observer design which can effectively deal with the disturbances and uncertainties in order to obtain more accurate observation results. Further, the controller and the adaptive law are derived by using the backstepping technique and prescribed performance control method with the stability of the whole closed-loop system analyzed via Lyapunov theory. Simulation results illustrate the effectiveness and vibration control performance of the proposed method.

Integrated system identification and modal state estimation for control of flexible space structures

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

Design and evaluation of a shunted flexible piezoelectric damper for vibration control of cable structures

In this work a shunted flexible piezoelectric damping system is designed and numerically evaluated for the purpose of vibration attenuation of large deployable space cable structures. We propose a design of a tube-shaped flexible piezoelectric energy absorber consisting of multilayered PVDF sectors, which could be shunted with two types of passive electric circuits, i.e. the series resistance-inductance (LR) shunt and the series resistance-negative capacitance (NC-R) shunt. The compatible stiffness of the PVDF tube ensures an effective transformation of deformation from the vibrating cable to the energy absorber. For best performance we carried out optimization on the geometric parameters of the PVDF tube. By analysis we found that the optimal thickness of the PVDF tube is roughly 0.4 times of the inner tube radius. We optimized the shunt circuits and selected the appropriate distribution position of the damper in the flexible cable structures. The performance of the design was numerically evaluated based on three problems, namely the longitudinal vibration of a single-cable structure, the transverse vibration of a single-cable structure and the vibration of a cross-cable structure. Based on the results, we confirm the remarkable performance of the design. Being highly frequency dependent, the design with the LR shunt only works for one deformation mode at a time, e.g. bending or stretching. In contrast, the design with the NC-R shunt works for both modes as it has a much wider frequency band. The design with the LR shunt has better performance than the NC-R shunt when dealing with the stretching deformation mode only. For vibration with combined stretching and bending, however, the performance of both designs is equally good. This is because the NC-R shunt can work for both deformation modes simultaneously, and hence it shows great adaptability and application potential in vibration control of complex flexible space structures.

Special topic: Dynamics and control of deployable space structures

Special topic: Dynamics and control of deployable space structures

Critically stable damping in flexible structure control

The concept of critically stable damping and its application to flexible structure control are presented. Critically stable damping was originally noted from the viewpoint of control-structure integration. It was recognized that a slight augmentation of structural damping would result in substantially more robust control without decreased performance and could guarantee the stability margin for any structural frequency increase. This paper illustrates the wide occurrence of critically stable damping phenomenon, establishes its basic relationship for the insight of the general design procedure, and applies the concept into the practical design of a satellite with a large deployable antenna. It is noted that the critically stable damping concept could provide a feasible approach to overcome the difficulty in ultra-large space structure design and control, and enhance the performance of a variety of excellent control design methodologies for flexible structure control. This critically stable damping provides new insight into the integrated design of control and structure.

Active control of bright electron beams with RF optics for femtosecond microscopy.

A frontier challenge in implementing femtosecond electron microscopy is to gain precise optical control of intense beams to mitigate collective space charge effects for significantly improving the throughput. Here, we explore the flexible uses of an RF cavity as a longitudinal lens in a high-intensity beam column for condensing the electron beams both temporally and spectrally, relevant to the design of ultrafast electron microscopy. Through the introduction of a novel atomic grating approach for characterization of electron bunch phase space and control optics, we elucidate the principles for predicting and controlling the phase space dynamics to reach optimal compressions at various electron densities and generating conditions. We provide strategies to identify high-brightness modes, achieving ∼100 fs and ∼1 eV resolutions with 106 electrons per bunch, and establish the scaling of performance for different bunch charges. These results benchmark the sensitivity and resolution from the fundamental beam brightness perspective and also validate the adaptive optics concept to enable delicate control of the density-dependent phase space structures to optimize the performance, including delivering ultrashort, monochromatic, high-dose, or coherent electron bunches.

Two-Dimensional Continuous Wavelet Transform Method for Multidamage Detection of Space Structures

AbstractAlthough many studies have been carried out to optimize the performance of space structures, no research has been undertaken into nondestructive evaluation and health control of space structures. Multiplicities of structural elements and joints are the main challenges in damage detection of space structure. In this research, a new two-dimensional (2D) continuous wavelet transform method (CWT) based on signal processing is applied by exploiting the concept of simulating the mode shape of space structure to a 2D spatially distributed signal. The proposed method is a response-based damage detection technique that requires only the mode shapes of the damaged and intact space structure. The method is among a few limited studies that explore the application of 2D wavelets in damage detection and can be used as a a fast and effective technique for damage localization of space structure without being concerned with the size and shape of structure. Several numerical examples are performed on three types of...

A piezo-driven micro-inclination stage for calibration of a micro-acceleration transducer: structure and control strategy

In some space applications, such as space navigation and vibration control of the large space structures, micro-acceleration transducers are required and have to be calibrated accurately. Unfortunately, providing extremely small static and quasi-static stimuli (accelerations) for the calibration of the micro-acceleration transducer has been a challenging task. This paper proposes a novel piezo-driven micro-inclination stage (PMIS) that can produce both discrete and continuous tumbles in a gravity field so that extremely small static and quasi-static stimuli (accelerations) can be obtained from a tiny component of the gravity constant. The proposed PMIS, which is driven by the lead zirconate titanate (PZT) stack, employs a rhombic mechanism to provide the PZT stack with a proper preload for the purpose of outputting a bidirectional force. To produce accurate static and quasi-static stimuli, the hysteresis non-linearity inherent in PZT stack is compensated by employing the strain feedback based adaptive control where the hysteresis property is identified online using the controlled auto-regressive moving average model. Furthermore, to improve the resolution of strain feedback, the strain sensitivity is maximized through structure optimization of the rhombic mechanism. The experimental results demonstrated that the proposed PMIS can produce minimal micro-inclination of (corresponding to the induced micro-acceleration of ) with the frequency ranging from 0 (DC) to 2 Hz.

Tethered actuator for vibration control of space structures

Effectiveness of a micro-tension actuator for vibration control of such flexible space structures as the tethered space solar power satellites is experimentally studied on the ground. A flexible leverage is employed as the micro-tension actuator in order to control the microtension of tether. The flexible leverage is connected through a tether to the flexible beam as an experimental model of the flexible solar panel with the low first modal frequency of order 1Hz. The nonlinearity of the flexible tether is taken into account for the vibration control since the tether becomes ineffective when it slacks, i.e., when it is tension-free. The feedback controller is designed by means of the Mission Function control algorithm. Flexural rigidity of the flexible leverage plays an important role in the vibration suppression and is studied experimentally to shed light on the effectiveness of the leverages with five different kinds of rigidity. The experimental results show not only the effect of the flexural rigidity of the flexible leverage on the control performance of the vibration suppression but also the importance of selection of the rigidity to control the vibration of tethered flexible space structures through the microtension of tethers in space.

A novel approach toward actuator placement for cylindrical shells undergoing axisymmetric buckling

Buckling control of space structures using piezoelectric actuators is an emerging area of research. In particular, cylindrical shells present several challenges as they exhibit multiple buckling modes. This work focuses on placement of ring actuators on cylindrical shells exhibiting axisymmetric buckling. A new method based on the characteristic wavelength of the cylindrical shell is proposed for actuator placement. It is shown by means of numerical studies that passive control of these shells shows a distinct advantage over the conventional actuator placement. It is possible to obtain a stiffer load– axial shortening response as well as a peak load enhancement of the shell using the present approach. The results obtained give important insights into the actuator placement problem for cylindrical shells undergoing axisymmetric buckling.

Semi-active friction tendons for vibration control of space structures

Semi-active vibration control systems are becoming popular because they offer both the reliability of passive systems and the versatility of active control without high power demands. In this work, a new semi-active control system is proposed and studied numerically. The system consists of variable-friction dampers linked to the structure through cables. Auxiliary soft springs in parallel with these friction dampers allow them to return to their initial pre-tensioned state. Using cables makes the system suitable for deployable, flexible and lightweight structures, such as space structures (spacecraft). A control system with three control laws applied to a single-degree-of-freedom structure is studied. Two of these laws are derived by using Lyapunov theory, whereas the third one is developed heuristically. In order to assess the performance of the control system, a parametric study is carried out through numerical simulations. An application of the proposed method to multi-degree-of-freedom structures is also presented and demonstrated through a numerical example. The system in semi-active mode is more effective than in passive mode and its effectiveness is less sensitive to loss of pre-tension.

2A15 Decentralized Robust Optimal Control of Large Flexible Space Structures by Local Proper Controllers Using Displacement Output(The 12th International Conference on Motion and Vibration Control)

2A15 Decentralized Robust Optimal Control of Large Flexible Space Structures by Local Proper Controllers Using Displacement Output(The 12th International Conference on Motion and Vibration Control)

Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes

The space industry in China is eager to have the advanced technology of large space structures composed of trusses cables and meshes. Such a large space structure, deployed on orbit, may serve as the large antenna for different space missions. The important scientific basis of the technology is the nonlinear dynamics modeling, analysis and control of these space structures during their deployment and service. This review article surveys the advances in relevant researches and proposes three open problems as follows. The first is the flexible multibody dynamics for the deployment of such a space structure, especially the nonlinear dynamics modeling and analysis for the contacts and wraps of mesh under microgravity, the internal impacts in clearance joints, and the coupling between structure deployment and spacecraft attitude. The second is the dynamics analysis of the space structures after deployment and during service, especially the complicated nonlinear vibrations of the flexible structure with numerous backlash joints under periodic thermal impacts. The third is the dynamic control of the space structures after deployment and during service, especially the under-actuated and lower-powered control for structure vibrations and waves.

Robust Optimal Control of Flexible Space Structures by a Proper Controller Using Displacement Output

This paper considers robust optimal control of flexible space structures with collocated sensors and actuators. First, we introduce a third order low-pass filter of which relative degree is 1, at each input channel. Then, we feed back output of the filter and displacement and velocity output of the space structure to input of the filter, so that we obtain a third order proper controller using only displacement output. By choosing parameters of the proper controller as the controller becomes a phase lead compensator, a closed-loop system becomes robustly stable against uncertainty of characteristic parameters of the structures such as mass, damping, and stiffness. The purpose of this paper is to show the closed-loop system becomes not only robustly stable but also optimal for a quadratic cost function by making two feedback gains contained in the proper controller sufficiently large.

Stability and periodic oscillations in the Moon–Rand systems

The Moon–Rand systems, developed to model control of flexible space structures, are systems of differential equations on R3 with polynomial or rational right hand sides that have an isolated singularity at the origin at which the linear part has one negative and one pair of purely imaginary eigenvalues for all choices of the parameters. We give a complete stability analysis of the flow restricted to a neighborhood of the origin in any center manifold of the Moon–Rand systems, solve the center problem on the center manifold, and find sharp bounds on the number of limit cycles that can be made to bifurcate from the singularity when it is a focus. We generalize the Moon–Rand systems in a natural way, solve the center problem in several cases, and provide sufficient conditions for the existence of a center, which we conjecture to be necessary.