Modal control of large flexible space structures using collocatedactuators and sensors

The authors consider the problem of assigning the eigenvalues associated with critical modes of a large flexible space structure into a specified region in the left-half plane via direct velocity feedback control (DVFC) using collocated actuators and sensors. Conditions for the existence of a DVFC using collocated actuators and sensors that can achieve the eigenvalue assignment are derived. When there exist nonunique feasible DVFCs, the one with least Frobenius norm feedback gain is determined. An experimental four-bay truss is used to illustrate the results     

Sliding mode control of a large flexible space structure

This paper presents an experimental study on active vibration control of a flexible structure. The control uses constant force air-jet thrusters as actuators, and the switching logic is designed using the theory of sliding mode control. The design of the sliding surface for the system is based on a quadratic criterion involving the first six natural modes of the structure. It allows the system response to be shaped and the relative importance of the control of each mode to be defined with respect to the control power available. Experimental results were found to be very satisfactory when compared with those obtained in previous studies on the same structure. To face the same disturbance, the control time is shorter and the residual speed smaller.     

On the design of large flexible space structures (LFSS)

For a general finite-element model of an LFSS, a strictly passive compensator results in an exponentially stable feedback system when actuators and sensors are colocated. In the general case (no colocation) we state necessary and sufficient conditions on the parameterQfor stabilizing a certain number of modes. We give conditions for robust stability and show that feedback does not destabilize the unmodeled modes under certain conditions.     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

大型挠性空间机械臂振动抑制的一种关节控制策略

大型空间机械臂在操作过程中,一个突出的问题是超低频挠性,不仅存在机械臂的弯曲振动,而且还存在关节的扭转变形振动;另外一个不能忽视的问题就是减速器的扭矩传递特性,以及机械臂关节运动与基座扰动（空间站）之问的耦合特性,这就要求根据关节结构和传感器配置实现关节位置控制,同时稳定和衰减机械臂及其关节的低频挠性振动．本文运用集中参数法对空间机械臂的挠性动力学进行建模,设计了工程可实现的单个关节控制策略及其控制律,分析和数值仿真了其稳定性,对未来空间站的大型挠性空间机械臂设计、动力学与控制的研究具有一定的参考价值．     

The decentralized Markov parameters and the selection of control structures

The properties of the decentralized pole placement map under constant output feedback are investigated and they are linked to known invariants of the decentralized pole assignment problem. A new expression of the differential of this map allows the derivation of relationships between the decentralized Plucker matrix invariant and the Markov parameters and leads to the definition of the Decentralized Markov Parameters (DMP). The matrix associated with the DMPs provides a new simple test for selection of decentralization schemes using as criteria the avoidance of formation of fixed modes and the preconditioning of the decentralized problem to be linearly assignable which excludes also almost fixed modes and it is a necessary condition for solution of the decentralized control problem. The natural link of this test to the Markov parameters and state space parameters of the models provides the means for affecting the shaping of properties of Plucker matrices by design, redesign of the input, and output structure of the system model. The results which are originally presented for the decentralized constant output feedback are subsequently extended to the case of decentralized PI feedback.     

Optimal root loci of flexible space structures

It is shown that simple generic properties can be proved for the optimal root loci of flexible space structures (FSS). It is proved that the angles and rates at which closed-loop poles depart from the open-loop poles can be found by inspection for any FSS with sufficiently widely space natural frequencies. Similar results also apply to the angles at which certain loci approach the transmission zeros of any FSS with compatible (physically colocated and coaxial) sensors and actuators, as a consequence of the special properties of the zeros of such systems. Finally, determining the number and orders of the Butterworth configurations of such as FSS is much more straightforward than for a general state-space system: it amounts only to checking whether structural displacements or their rates are the measured outputs. These results depend on the fundamental second-order nature of such systems, and five considerably more insight than is possible a priori for general linear multivariable systems     

The optimal decentralized control of a large power system: Load and frequency control

The load and frequency control of a multi-area interconnected power system is studied. In this problem, the system is assumed to be subject to unknown constant disturbances, and it is desired to obtain, if possible, robust decentralized controllers so that the frequency and tieline/net-area power flow of the power system are regulated. The problem is solved by using some structural results recently obtained in decentralized control, in conjunction with a parameter optimization method which minimizes the dominant eigenvalue of the closed-loop system. A class of minimum order robust decentralized controllers which solves this general multi-area load and frequency control problem is obtained. Application of these results is then made to solve the load and frequency control problem for a power system consisting of nine synchronous machines (described by a 119th-order system). It is shown that the load and frequency controller obtained in this case is not likely to be significantly improved by using more complex controllers; in particular, it is shown that the conventional controller, used in regulating the net-area power flow of a system, is not likely to be significantly improved upon by using more complex controllers.     

Survey of decentralized control methods for large scale systems

This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.     

Some questions of control of the robotized in-orbit assembly of large space structures

Presented was an analytical review of the foreign and domestic scientific literature published over more than two decades on the dynamics and theory of motion control of large space structures and free-flying space robots meant for assisting the astronauts or replacing them at execution of diverse maintenance operations in open space. Although many results on the design of control systems for each of the aforementioned kinds of objects are very significant taken separately, nevertheless the most important problem of using the flying robots for in-orbit assembly of the large space structures remains still unsolved. Formulated was the concept of complex approach to the problem of robot-assisted in-orbit assembly of space structures which lies in combining the algorithms of all subsystems involved in the assembly of the objects with regard for the requirements on safe interaction of the participants, high resultant precision and reliability of operation, and minimal use of the consumable fuel.     

基于LMI的分散式深空飞行器编队控制

针对深空探测任务中飞行器编队的控制问题,提出了一种基于线性矩阵不等式(LMI)的分散式控制方案.该方案考虑了深守编队与传统的近地编队之间的差异,把该方案转化为一类LMI问题;对比传统的基于"黎卡提方程一线性二次调节器"(Riccati-LQR)的编队方法,本方法更精确地实现了控制目标,并减轻了通讯压力,降低了燃耗.对该方案的仿真实例,展示出在燃耗最小及编队质心位置不变的条件下,队形机动的实现过程;并对结果作出了分析.     

Modeling and control of flexible space stations

In this article, a preliminary formulation of large space structures and their stabilization is considered. The system consists of a (rigid) massive body and flexible configurations that consist of several beams, forming the space structure. The rigid body is located at the center of the space structure and may play the role of experimental modules. A complete dynamics of the system has been developed using Hamilton's principle. The equations that govern the motion of the complete system consist of six ordinary differential equations and several partial differential equations together with appropriate boundary conditions. The partial differential equations govern the vibration of flexible components. The ordinary differential equations describe the rotational and translational motion of the central body.The dynamics indicate very strong interaction among rigid-body translation, rigid-body rotation, and vibrations of flexible members through nonlinear couplings. Hence, any rotation of the rigid body induces vibration in the beams and vice versa. Also, any disturbance in the orbit induces vibration in the beams and wobbles in the body rotation and vice versa. This makes the system performance unsatisfactory for many practical applications. In this article, stabilization of the above-mentioned system subject to external disturbances is considered. The asymptotic stability of the perturbed system by application of velocity feedback controls is proved using Lyapunov's method.Numerical simulations are carried out in order to illustrate the impact of dynamic coupling or interaction among several members of the system and the effectiveness of the suggested feedback controls for stabilization. This study is expected to provide some insight into the complexity of modeling, analysis, and stabilization of actual space stations.     

Placement optimization of actuator and sensor and decentralized adaptive fuzzy vibration control for large space intelligent truss structure

Large space truss structure is widely used in spacecrafts.The vibration of this kind of structure will cause some serious problems.For instance,it will disturb the work of the payloads which are supported on the truss,even worse,it will deactivate the spacecrafts.Therefore,it is highly in need of executing vibration control for large space truss structure.Large space intelligent truss system(LSITS) is not a normal truss structure but a complex truss system consisting of common rods and active rods,and there...     

Active vibration control of large space flexible slewing truss using cable actuator with input saturation

This paper proposes a composite approach to implementing attitude tracking and active vibration control of a large space flexible truss system. The system dynamic model is based on Hamilton's principle and discretized using the finite difference method. A nonlinear attitude controller for position tracking is developed based on the input‐output linearization of the discretized system, which can effectively improve system performance compared with a traditional proportional‐differential feedback controller. A taut cable actuator scheme is presented to suppress tip vibration because the mechanical model is a large large‐span spatial structure; furthermore, because the cable has the feature of unilateral input saturation constraint, which can provide only a pulling force, a nonlinear quadratic regulator controller is developed by introducing a piecewise nonquadratic cost function to suppress the vibration of the flexible structure. To investigate the factors that influence the damping effects of the cable, the parametrically excited instability of a cable under 2 supports is analyzed. Simulation results illustrate that the proposed attitude controller can implement the task of position tracking, and the vibration suppression control law is shown to be optimal for functional performance with input saturation.     

Robustness of active modal damping of large flexible structures

The control of large flexible systems is an area of growing concern for control engineers. In particular, the robustness of any control design for a flexible structure is of great interest because of the inexact knowledge of the structure, the necessity of model truncation in the control design or the variability of the structure itself. Numerous techniques have been offered as solutions for one or more of the above problems, but few applications have been produced. This present paper reviews the method of AMD and presents as a design example the pinhole/occulter facility (P/OF). This system is a large space system comprised of a flexible beam (30 m long by 0·3 m wide), a gimbal-pointing system and an optical alignment system mounted in the shuttle cargo bay and excited by typical shuttle disturbances. The flexible modes are assumed known, but only to within about 10%. A controller was designed for the nominal case and the effects of variations of the modal frequencies and modal damping factors on the system performance studied. A series compensator was designed that also resulted in a stable system. The performance effects for the same modal variations are presented for this system as a comparison. The ADM system out-performs the series-compensated system for all cases except the design case.     

Dynamic features of flexible spacecraft control in process of its transformation into a large space structure

Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( $ \tilde f Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( ≤ 0.05 Hz) oscillations which represent one of the attributes of the class of large space structures. The existing quantitative definition of the large space structure was specified. It was demonstrated that as the frequencies of structure’s elastic oscillations approach those of the control of object “rigid” motion, a new kind of interrelations between the motions of both types, the so-called “capture” of the controller frequency by that of the elastic oscillations, arises which impairs control efficiency to the point of losing system stability. Analytical (for the linear control systems) and computer-aided (for the discrete systems) methods for determination of the boundaries separating the two qualitatively different forms of existence of the transformed elastic object were proposed. Some results of computer simulation of the orientation control of variable objects such as flexible spacecraft and large space structure were presented. Original Russian Text ? I.N. Krutova, V.M. Sukhanov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 5, pp. 41–56. This work was supported by the Russian Foundation for Basic Research, project no. 05-08-18175.     

Computing the transmission zeros of large space structures

The transmission zeros of a large space structure are frequently computed by means of the general-purpose algorithm of A. Emami-Naeini and P. Van Dooren (1982). It is shown that careful exploitation of the special form of the equations of motion of structural dynamics leads to an algorithm that is at least 60 times as fast as this when applied to an undamped structure, and 15 times as fast for a lightly damped one     

Robust stabilization of large space structures via displacementfeedback

It has been known that static velocity and displacement feedback with collocated sensors and actuators can stabilize large space structures robustly against "any" uncertainty in mass, damping, and stiffness, independently of the number of flexible modes. The authors present dynamic displacement feedback which can achieve such robust stabilization. The proposed control law can be implemented in a decentralized scheme straightforwardly     

Study of delay-independent decentralized guaranteed cost control for large scale systems

This study introduces delay independent decentralized guaranteed cost control design method based on two controller structures for nonlinear uncertain interconnected large scale systems with time delays. First, a set of equivalent Takagi-Sugeno (T-S) fuzzy models are extended to represent the systems. Then a decentralized state-feedback guaranteed cost performance controller is proposed for the fuzzy systems. Based on delay independent Lyapunov functional approach, some sufficient conditions for the existence of the controller can be cast into the feasible problem of LMIs irrespective of the sizes of the time delays so that the system can be asymptotically stabilized for all considered uncertainties whose sizes are not larger than their bounds. Finally, the minimizing approach is proposed to search the suboptimal upper bound value of guaranteed cost function. Moreover, the corresponding conditions are extended into the generalized dynamic output-feedback close-loop system. Finally, the better control performances of the proposed methods are shown by the simulation examples.     

Input shaping and time-optimal control of flexible structures

We consider the problem of minimum time input shaping and its relation to the classical time-optimal control problem. We demonstrate that some typical minimum time input shapers are equivalent to the time-optimal control of different, although related, systems. The analytical proofs are based on the optimality criteria stipulated by the Karush-Kuhn-Tucker conditions.