Stability enhancement of flexible structures by nonlinear boundary-feedback control

In this study, the absolute stability problem for the axially moving Kirchhoff string with nonlinear boundary feedback control has been investigated. Based on the generalized Hamilton’s variational principle, the nonlinear governing equations of the motion and boundary conditions have been deduced. The proposed boundary control, which satisfies a sector constraint condition, is a negative feedback of the transversal velocity at the right end of the string. Applying the integral-type multiplier method, the absolute stability of the axially moving Kirchhoff system is established. To validate the proposed theoretical results, numerical simulations are expressed by the finite element method.

Controlling vibration of structures is essential for both space structures as well as terrestrial structures. Due to the ambient acceleration levels anticipated for the International Space Station, active vibration isolation is required to provide a quiescent acceleration environment for many science experiments. An overview is given of systems developed and flight tested in orbit for microgravity vibration isolation. Technology developed for vibration control of flexible space structures may also be applied to control of terrestrial structures such as buildings and bridges subject to wind loading or earthquake excitation. Recent developments in modern robust control for flexible space structures are shown to provide good structural vibration control while maintaining robustness to model uncertainties. Results of a mixed H-2/H-infinity control design are provided for a benchmark problem in structural control for earthquake resistant buildings.

: The goals of these research projects were to examine the nonlinear dynamics and control of flexible structures, some of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers. A major part of the research was on trusses/frames structures. Five different truss structures from three to ten meters in size were constructed, two with active controls. However, nonlinear dynamics of continuous beam type structures were also investigated. One of the principal themes was to explore what types of nonlinearities would result in chaotic and unpredictable vibrations. Loose joints in truss structures, friction, buckling and geometric nonlinearities were all found to lead to chaotic motions under certain periodic forcing conditions. Actuators and sensors for space truss active vibration suppression was investigated. New methods were developed for structural control using techniques for simulated annealing for actuator placement, nonlinear random vibrations of pin-jointed trusses, vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally, a major numerical effort resulted in new codes to predict large motions of structures under active control using parallel processing algorithms.

A special output feedback control design technique for flexible large space structures is proposed in this paper to achieve: (a) increase in both the damping and frequency of selected modes for more effective control, (b) integrated control of elastic and rigid-body modes, and, in particular, (c) closed-loop system stability and its robustness to modal truncation and to parameter variation. This technique represents an improvement over previous work concerning large space structures output feedback control.

Flexible space structures generally have very low levels of inherent damping, which makes the problem of controlling such systems quite challenging. For instance, unmodeled modes can easily be made unstable by spillover effects. One way to avoid these difficulties is to use a low-authority control loop to simply increase structural damping, typically to 5-10% of critical, and then use a more sophisticated high-authority control loop to achieve the desired control objectives. A very important design question that then arises is: what are the best choices of locations for the dampers used to implement the low-authority controller? This question is studied here, and it is shown that it is more important to increase the damping of the zeros of the damping-augmented structure than that of the poles. A simple algorithm is then derived for determining the damper locations that make the zeros as heavily damped as possible. Finally, the operation of this algorithm is illustrated by application to a simple cantilever beam example. In this approach, a LAC loop, acting through dampers placed on the structure, is used to augment the inherent damping of the vehicle, typically raising it to 5-10% of critical. The intention is to make it easier for the main HAC loop, acting through its own actuators, to give good closed-loop system performance as measured at the HAC sensor stations. The increase in damping provided by the LAC loop also helps to prevent any unmodeled modes being destabilized by spillover from the main control loop. The high-authority controller is usually chosen to be an optimal regulator, as many FSS control prob- lems are readily expressible in an optimization form; an exam- ple is the problem of minimizing the rms surface deflection of a flexible antenna without using excessive amounts of propel- lant. The LAC design problem considered in this paper is as follows: Given an optimal regulator HAC loop with specified sensor and actuator locations and a fixed number of dampers of given strengths, where should these dampers be placed on the structure to give the best overall system performance? Central to this analysis are the results recently derived in Ref. 11 concerning the optimal root loci8 of FSS, which in turn are closely related to the generic properties19 of the transmission zeros6 of these systems. In particular, if the HAC loop is permitted to use fairly high gains (as is necessary if reasonably good performance is to be obtained), then the finite poles of the closed-loop system (FSS + LAC + HAC) will approach the zeros of (FSS + LAC). Typical LAC analyses in the past1-22 have concentrated on positioning dampers so as to maximize the damping of the poles of (FSS + LAC), with no attention being paid to the zeros of this damping-augmented system. It can therefore be seen that placing dampers in this traditional way will not necessarily improve the performance of the overall closed-loop system (FSS + LAC + HAC) signif- icantly. This question will be studied in the paper and a simple algorithm given, based on orthogonality to the HAC modal influence matrix, for determining damper locations that pro- duce as much zeros damping as possible. The poles will always also be damped by this scheme. The converse, however, would not be true: a method designed to maximize the damping of the poles may leave the zeros totally undamped. Numerical results for a simple cantilever beam will be used to illustrate these results.

Optimal scanning control of flexible structures in two-dimensional space

The main transmission system of a scraper conveyor direct-driven by the high-power permanent magnet synchronous motor (PMSM) is taken as a study object. With the effect of the nonlinear friction torque caused by the nonuniformity of the transported coal quality in the operation process considered, the torsional vibration bifurcation mechanism and the corresponding control measures for the main transmission system of the scraper conveyor are investigated. Firstly, based on the Lagrange–Maxwell principle, the global electromechanical-coupling dynamic models for the main transmission system of the scraper conveyor are constructed. Secondly, by the Routh–Hurwitz stability criterion, the Hopf bifurcation characteristics of the main transmission system are analyzed to reveal the influence of supercritical bifurcation and subcritical bifurcation on the torsional oscillation of the transmission shafting. Thirdly, in order to suppress the system unstable oscillation caused by the Hopf bifurcation, the motor speed is fed back to construct the nonlinear state feedback controller for the quadrature axis current of the PMSM by the $$I_{d}=0$$ vector control strategy. Similarly, on the basis of the Routh–Hurwitz criterion, the influence of the linear feedback coefficient in the nonlinear state feedback controller on the system bifurcation position is discussed. Meanwhile, by the central manifold theory and canonical form theory, the effect of the square and cubic nonlinear feedback coefficients on the Hopf bifurcation type of the torsional vibration and the amplitude of the stable limit cycle are investigated. Finally, the numerical simulation results show the effectiveness of the designed controller.

Outline of Flexible Structures in Space

As the stability of stochastic ordinary differential equations has become highly developed over the past three decades, there has also been research directed towards the question of the stability of stochastic partial differential equations. Recently, there has been an increased interest in this topic motivated by the problems of dynamics of flexible structures in space. In this paper we shall present a brief discussion of some of the directions these studies have taken in recent years.

An area of current interest in the decentralized control of large flexible structures is the development of adaptive strategies that will allow for acceptable vibration suppression and tracking in the presence of uncertainties. One such strategy is the Gavel-Siljak approach, which is based upon direct control using adaptive gains. The approach treats the interconnections effects between subsystems as uncertain quantities. The current study is aimed at examining the appropriateness of such an algorithm for the control of multibody flexible structures. A two body simulation model is developed. The application of the adaptive control algorithm to this structure is discussed in the context of the simulation model. Results using this model are presented and discussed.

An Overview of Modeling and Control of Large Flexible Space Structures

Sliding mode control of a large flexible space structure

Implementation and Evaluation of Non-linear Optimal Feedback Control for Ship’s Automatic Berthing by Recurrent Neural Network

Synchronization analysis of nabla fractional-order fuzzy neural networks with time delays via nonlinear feedback control

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.