Input shaping and variable structure control for simultaneous precision positioning and vibration reduction of flexible spacecraft with saturation compensation

This paper treats the question of simultaneous robust attitude control and vibration suppression of orbiting spacecraft with flexible appendages. The spacecraft consists of a rigid body and two flexible appendages and the finite dimensional representation of the flexible spacecraft is assumed to be of arbitrary order. Robust nonlinear variable structure control (VSC) strategy integrated with input shaping technique is concerned for the pitch angle control and elastic vibration suppression under actuator saturation limit. More specially, the input shaper is implemented outside of the feedback loop, which is designed for the reference model and achieves the exact elimination of residual vibration; while for the feedback loop, the variable structure controller is designed to make the closed-loop system behave like the reference model with the input shaper in the presence of parametric uncertainty, external disturbances and actuator saturation. To prevent the presence of input saturation from destroying the system performance, a saturation compensator is designed as well for the variable structure attitude control system. For the synthesis of the attitude controller, only the pitch angel and its derivative are used. Simulation results are presented which show that in the closed loop, pitch angel control and elastic mode stabilization are accomplished in spite of uncertainty and external disturbance.     

Chaos suppression of uncertain gyros in a given finite time

The gyro is one of the most interesting and everlasting nonlinear dynamical systems,which displays very rich and complex dynamics,such as sub-harmonic and chaotic behaviors.We study the chaos suppression of the chaotic gyros in a given finite time.Considering the effects of model uncertainties,external disturbances,and fully unknown parameters,we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible.Using the finite-time control technique,we give the exact value of the chaos suppression time.A mathematical theorem is presented to prove the finite-time stability of the proposed scheme.The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.     

Booster stage adaptive backstepping tracking control for interceptor

An adaptive backstepping tracking controller in the presence of uncertain parameters and external disturbance is designed for the thrust vector-controlled interceptor during its booster stage. The dynamic equation is formulated into a parametric-strict-feedback form under reasonable assumption. The controller design is decomposed into two loops, which are aerodynamic angle loop and angular rate loop. The whole closed system is proved to converge into a compact set asymptotically by employing feedback control laws and adaptive estimate laws designed in this paper. The controller proposed here has two main advantages. First, it can deal with the disturbances whose bounds have the expression of all system states. Second, there is no chattering in the tracking process by using continuous hyperbolic tangent function in place of sign function. Simulation results demonstrate that the proposed method in this paper not only afford strong capability but also achieve a fast and accurate response of resistance to parameters uncertainty and external disturbances.     

Disturbance rejection control for vibration suppression of piezoelectric laminated thin-walled structures

Thin-walled piezoelectric integrated smart structures are easily excited to vibrate by unknown disturbances. In order to design and simulate a control strategy, firstly, an electro-mechanically coupled dynamic finite element (FE) model of smart structures is developed based on first-order shear deformation (FOSD) hypothesis. Linear piezoelectric constitutive equations and the assumption of constant electric field through the thickness are considered. Based on the dynamic FE model, a disturbance rejection (DR) control with proportional-integral (PI) observer using step functions as the fictitious model of disturbances is developed for vibration suppression of smart structures. In order to achieve a better dynamic behavior of the fictitious model of disturbances, the PI observer is extended to generalized proportional-integral (GPI) observer, in which sine or polynomial functions can be used to represent disturbances resulting in better dynamics. Therefore the disturbances can be estimated either by PI or GPI observer, and then the estimated signals are fed back to the controller. The DR control is validated by various kinds of unknown disturbances, and compared with linear-quadratic regulator (LQR) control. The results illustrate that the vibrations are better suppressed by the proposed DR control.     

RCLSJ约瑟夫森结混沌系统的鲁棒自适应滑模控制

讨论了具有不确定参数和外界扰动的非线性电阻-电容-电流分路结模型(RCLSJ)混沌系统的广义控制问题。基于Lyapunov稳定性理论和滑模变结构控制方法,设计了鲁棒自适应滑模控制器,使得RCLSJ混沌系统能以任意比例因子追踪期望的参考信号。该方法不需要预先知道不确定参数和外界扰动的上下界,在控制器中引入一类简单的自适应律,用以在线估计参数和界值。该控制方法对参数不匹配和外界扰动具有较强的鲁棒性。数值仿真表明了该方法的有效性。     

Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance

A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J_2 perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation(SDRE), a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode(IM) control law is added to eliminate disturbances.These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method.Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.     

A modal disturbance estimator for vibration suppression in nonlinear flexible structures

This paper presents a control strategy for the suppression of vibration due to unknown disturbance forces in large, nonlinear flexible structures. The control action proposed, based on the modal approach, consists of two contributions. The first is the well-known Independent Modal-Space Control, which increases system damping and improves its behavior close to the resonance frequencies. The second is a disturbance estimator, which calculates the modal components of the external forces acting on the system and compensates for them using actuator forces. The system modal coordinates, required by both logics, are estimated through a modal state observer.The proposed control logic is tested on a flexible boom. The paper reports the numerical and experimental results both for the linear and nonlinear (large motion) boom configuration.     

Active vibration control in Duffing mechanical systems using dynamic vibration absorbers

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass–spring–damper dynamic vibration absorbers. An active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform reference position trajectory tracking tasks planned for the nonlinear primary system. A differential flatness-based disturbance estimation scheme is also described to estimate the unknown multiple time-varying frequency disturbance signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. Some numerical simulation results are provided to show the efficient performance of the proposed active vibration absorption scheme and the fast estimation of the vibration disturbance signal.     

Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber

In this paper, a tunable vibration absorber set (TVAs) is designed to suppress regenerative chatter in milling process (as a semi-active controller). An extended dynamic model of the peripheral milling with closed form expressions for the nonlinear cutting forces is presented. The extension part of the cutting tool is modeled as an Euler–Bernoulli beam with in plane lateral vibrations (x–y directions). Tunable vibration absorbers in x–y directions are composed of mass, spring and dashpot elements. In the presence of regenerative chatter, coupled dynamics of the system (including the beam and x–y absorbers) is described through nonlinear delay differential equations. Using an optimal algorithm, optimum values of the absorbers' position and their springs' stiffness in both x–y directions are determined such that the cutting tool vibration is minimized. Results are compared for both linear and nonlinear models. According to the results obtained, absorber set acts effectively in chatter suppression over a wide range of chatter frequencies. Stability limits are obtained and compared with two different approaches: a trial and error based algorithm and semi-discretization method. It is shown that in the case of self-excited vibrations, the optimum absorber improves the process stability. Therefore, larger values of depth of cut and consequently more material removal rate (MRR) can be achieved without moving to unstable conditions.     

Anti-optimisation for modelling the vibration of locally nonlinear structures: An exploratory study

Modelling the vibration of complex structures with uncertain nonlinearities is a significant challenge. However, nonlinearities are often spatially localised: this enables efficient linear methods to describe the behaviour of the majority of the structure and reduces the size of the nonlinear problem. This paper explores anti-optimisation as an approach to modelling uncertain nonlinearities for this class of system. The ‘worst-case’ output metric is sought by considering nonlinear forces as an external input subject to constraints that capture what is known about the nonlinearity. A systematic sequence of tests is carried out using a mass on spring system within a pair of end-stops: the results show how the anti-optimised solutions become less conservative as the constraints are increasingly restrictive. The method is applied to bending vibration of a beam within a pair of local end-stops. Anti-optimised solutions are found as a function of frequency and are compared with a Monte Carlo set of benchmark simulations. Almost all anti-optimised solutions over-predict the simulations and the overall trend of the simulations is also clearly captured. The method shows significant potential and motivates further research.     

Nonlinear analysis,design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

This paper combines cubic nonlinearity and time delay to improve the performance of vibration isolation. Nonlinear dynamics properties, design methodology and isolation performance are studied for a piecewise bilinear vibration isolation system with the time-delayed cubic velocity feedback control. By the multi-scale perturbation method, the equivalent stiffness and damping are first defined to interpret the effect of feedback control loop on dynamics behaviours, such as frequency island phenomenon. Then, a design criterion is proposed to suppress the jump phenomenon induced by the saddle-node bifurcation. With the purpose of obtaining the desirable vibration isolation performance, stability conditions are obtained to find appropriate feedback parameters including gain and time delay. Last, the influence of the feedback parameters on vibration transmissibility is assessed. Results show that the strategy developed in this paper is practicable and feedback parameters are significant factors to alter dynamics behaviours, and more importantly, to improve the isolation effectiveness for the bilinear isolation system.     

Optimizing parametric oscillators with tunable boundary conditions

Parametric excitation or pumping is an effective method to create large oscillations by periodically altering a physical parameter of the governing dynamics. Precisely tuned pumping frequencies can lead to exponentially growing oscillations limited only by nonlinear effects like axial stretching of transversely vibrating string. It is demonstrated that a tuned passive dynamical system amplifies the otherwise limited transverse vibrations amplitudes of a nonlinear string considerably and thus increasing the selectivity of the system. This effect becomes more noticeable for shorter wavelengths where nonlinear stretching limits the obtainable vibration amplitudes severely. The present work analyses a passive dynamical system connected to one end of a taught string which parametrically couples its axial motion to transverse vibration. Analysis shows that a specific selection of parameters can reduce the limiting effect of nonlinear stretching thus allowing one to excite high-order modes with small external forces. The result can possibly affect other disciplines where effective parametric amplification is necessary.     

Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics

We describe experimental studies of the dynamical behavior of a recently proposed electro-optic discrete time nonlinear delay oscillator. With appropriate choice of the oscillator loop parameters and external forcing of the dynamics using a pulsed laser source, the system allows for the physical realization of a high dimensional mathematical nonlinear mapping. The dynamical features observed with this new class of discrete time delay oscillator differ significantly from those observed with similar continuous time nonlinear delay feedback oscillators and reveal the intrinsic discrete time nature of the dynamics. We also discuss specific applications to chaos communications using regularly clocked binary data.     

Dynamics of arrays of cylinders with internal and external axial flow

Various aspects of the dynamics and stability of clusters of tubular cylinders containing internally flowing fluid and surrounded by a bounded external axial flow are examined. The general character of free motions is established by obtaining the eigenfrequencies of the system and studying their evolution with increasing flow, internal or external. Stability diagrams have been obtained for the critical flow velocities, beyond which the system would lose stability by buckling (divergence), under the combined effect of internal and external flow. Free vibration, following an initial disturbance of one of the cylinders, is studied, in order further to examine the effect of hydrodynamic coupling. It is found that beating phenomena may arise, implying energy transfer between cylinders and the possibility of transient amplitudes much larger than the initial disturbances. Also, the vibration of the system (in still fluid) when one cylinder is constrained to oscillate in a prescribed manner is examined, establishing that transmission of vibration from cylinder to cylinder can be very rapid; indeed, such constrained motion of one cylinder at certain frequencies may induce large amplified motions of others.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems

A system’s response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann’s equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.     

基于DSP的直线感应电机模糊矢量控制系统研究

针对直线感应电机强耦合、多变量、非线性、时变的控制特点,将模糊控制策略应用到转差频率直线感应电机矢量控制系统中。建立了计及端部效应的直线感应电机等效数学模型,设计了基于DSP的直线感应电机模糊控制系统的软硬件,采用磁链开环、速度和电流闭环的矢量控制系统,对速度模糊控制器进行了设计。对直线感应电机在起动和负载情况下的动态特性进行了仿真实验,结果表明：采用模糊控制实现的直线感应电机转差频率矢量控制系统比具有基本数学模型的传统PI控制系统具有更强的鲁棒性。     

Automatic alignment of a rigid spacer cavity

A bench-top auto-alignment system employing an invariant Gouy phase telescope is described in this paper. Our system uses external galvanometer-actuated mirrors for the tilt and offset control of a laser beam onto a rigid spacer cavity. Wavefront sensing diagnostics which accurately decouple tilt and offset er-rors are employed, and corresponding orthogonal corrections are enabled with the aid of electronic nulling. The closed loop system achieves an alignment fluctua-tion suppression of 50.4 dB for angular tilt and 58.3 dB for lateral offset at 1 Hz, with a unity gain bandwidth in excess of 115 Hz.     

Dynamic effects of delayed feedback control on nonlinear vibration isolation floating raft systems

Vibration suppression and chaotification are the key issues in the study of the concealment capability of underwater vehicles. Time delay control is superior in chaotification, but the involved dynamics are sensitive and complex. This paper presents an analysis to obtain an analytical solution of the nonlinear delay differential equations and determine the effect of delay control on the vibration amplitude. Besides, by checking the stability of the analytical solution, dependence of chaotification upon the time delay control parameters is examined. Based on the theoretical derivation, the effects of different configurations of system parameters and delay control parameters on vibration amplitude are demonstrated in numerical simulation. What?s more, the outcome of our results shows the significant role the time delay control plays in vibration suppression and chaotification. According to the analytical solution and stability analysis, not only can the appropriate delay be found to reduce the vibration amplitude, but also the suitable delay control setting can be selected for chaotification.     

DYNAMIC ANALYSIS OF DELAYED DAMPER SYSTEM IN ENGINEERING STRUCTURES

The delayed damper (DD) is a new active vibration absorption technique that uses time-delayed partial state feedback to generate ideal resonance on a passive vibration absorber. It has many attractive features such as real-time adjustability, ease of implementation, and total suppression of vibration for tonal frequency disturbances. In this paper, a major advantage of engineering structures analysis is the reduction of characteristic roots from infinite to finite numbers and the consequent simplicity in the dynamic analysis of the controller. The dynamic model principle is employed to design controllers for the structure. The system is examined by simulation. It is shown that engineering structures control application for DD yields better vibration suppression considering the sampled control structure in implementations.