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In response to the issues of vibrations affecting the construction safety, speed, and accuracy of suspended structures due to dynamic disturbances during lifting, environmental disturbances, and improper operator actions, this paper investigates the application of the Active Rotary Inertia Driver (ARID) system for double-rope suspended structures, namely analyzes, and applies control to the vibration response of double-rope suspended structures under external excitations. Taking the double-rope suspended structure as an example, a dynamic analytical model of the double-rope suspended structure is established based on D’Alembert’s principle. Through shake table tests, the dynamic response characteristics and vibration control effects of the double-rope suspended structure under various external excitations are studied, and the influence of the twisting radius of the suspended structure on the control effect is analyzed. The experimental results show that the ARID control system achieves significant control effects on the swing and torsional vibrations of the suspended structure, which validates the accuracy of the theoretical model for the ARID control system and demonstrates its feasibility for practical applications.

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

This paper aims at studying the basic properties and chaotic synchronization of complex Lorenz system:

Numerically we show that this system is a chaotic system and exhibits chaotic attractors. The necessary conditions for system (⋆) to generate chaos are obtained. Analytical and numerical calculations are presented to achieve synchronization. Active control technique is used to synchronize chaotic attractors of equations (⋆).

Considering the time lag produced by the transmission in chaos-communication, we present self-time-delay synchronization (STDS) of complex chaotic systems. STDS implies that the synchronization between the time-delay system (the receiver) and the original system (the transmitter) while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. It is more suitable to simulate real communication situation. Aimed to time-delay coupled complex chaotic systems, the control law is derived by active control technique. Based on STDS, a novel communication scheme is further designed according to chaotic masking. In simulation, we take time-delay coupled complex Lorenz system transmitting actual speech signal (analog signal) and binary signal as examples. The speech signal contains two components, which are transmitted by the real part and imaginary part of one complex state variable. Two sequences of binary bits are converted into analog signals by 2^M-ary and zero-order holder, then added into the real part and imaginary part of one complex state variable. Therefore, the STDS controller is realized by one critical state variable. It is simple in principle and easy to implement in engineering. Moreover, the communication system is robust to noise. It is possible to adopt cheap circuits with time-delay, which is economical and practical for communication.

This paper presents an active control method for controlling general uncertain chaotic systems with parameters perturbation. And a sufficient condition is drawn for the stability of the controlled chaotic systems and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.

This paper analyzes anti-synchronization of three-dimensional autonomous chaotic systems and achieves the anti-synchronization of a class of three-dimensional autonomous chaotic systems, i.e., Lorenz system, Chen system, and Lü system with one another via active control. Numerical simulations are demonstrated to verify the effectiveness of the proposed method.

oActive sliding mode control is one of the effective methods to synchronize chaotic systems in the presence of uncertainties. Use of the method, however, requires decision making on how to choose the control parameters for a specific performance. In this paper we propose an algorithm to determine the best control parameters for which the minimum control efforts are required to synchronize two identical or non-identical chaotic systems. We have also determined the maximum range of the uncertainties on which the selected control parameters to work properly. The effectiveness of the proposed method has been verified through numerical simulations.

This paper analyzes the synchronizations for autonomous chaotic systems with disturbance of parameter, achieves the self-synchronization of Lü system, a modified coupled dynamos system and a four-dimensional hyperchaotic system by the methods of active control and adaptive parameter. In addition, the synchronization of Lorenz system and Chen system is presented. Numerical simulations are provided for illustration and verification of the proposed method.

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

This study deals with the active control of T-S (Tollmien-Schlichting) wave in a two-dimensional boundary layer over a flat plate using a neural network and a flapping actuator. The flapping actuator consists of a thin aluminum plate and a piezoelectric element bonded together. Microphones were used as sensors to measure the pressure fluctuation in the boundary layer. A neural network was used to control the piezoelectric actuator based on the pressure signals from the sensors. The experimental results shows that the T-S wave in the boundary layer can be successfully suppressed even when its phase, amplitude and frequency change with time.

In this study, active and passive control techniques are applied for the synchronization of two identical Vilnius chaotic oscillators. The differential equations of Vilnius oscillator are described according to its circuit model. Based on Lyapunov function, the active and passive controllers are used to realize the synchronization of Vilnius chaotic systems. Numerical simulations are presented to verify and compare the effectiveness of proposed control techniques.

This paper addresses the synchronization problem of two modified Chen systems in the presence of unknown system parameters. One-way coupling and active control laws are applied to achieve the state synchronization of two identical modified Chen systems. Based on Lyapunov stability theory, active control laws are derived such that the two modified Chen systems are to be synchronized. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

This paper deals with the dynamics and active control of a driven multi-limit-cycle Van der Pol oscillator. The amplitude of the oscillatory states both in the autonomous and nonautonomous case are derived. The interaction between the amplitudes of the external excitation and the limit-cycles are also analyzed. The domain of the admissible values on the amplitude for the external excitation is found. The effects of the control parameter on the behavior of a driven multi-limit-cycle Van der Pol model are analyzed and it appears that with the appropriate selection of the coupling parameter, the quenching of chaotic vibrations takes place.

Chaos synchronization is a very important nonlinear phenomenon, which has been studied to date extensively on dynamical systems described by real variables. There also exist, however, interesting cases of dynamical systems, where the main variables participating in the dynamics are complex, for example, when amplitudes of electromagnetic fields are involved. Another example is when chaos synchronization is used for communications, where doubling the number of variables may be used to increase the content and security of the transmitted information. It is also well-known that similar generalization of the Lorenz system to one with complex ODEs has been introduced to describe and simulate the physics of a detuned laser and thermal convection of liquid flows. In this paper, we study chaos synchronization by applying active control and Lyapunov function analysis to two such systems introduced by Chen and Lü. First we show that, written in terms of complex variables, these systems can have chaotic dynamics and exhibit strange attractors. We calculate numerically the values of the parameters at which these attractors exist. Active control and global synchronization techniques are then applied to study the phenomenon of chaos synchronization. Analytical criteria concerning the stability of these techniques are implemented and excellent agreement is found upon comparison with numerical experiments. In particular, studying the time evolution of "errors" (or differences between drive and control dynamics), we show that both techniques are very effective for controlling the behavior of these systems, even in regimes of very strong chaos.

In this work, we introduce and investigate the modified projective lag synchronization (MPLS) of two nonidentical hyperchaotic complex nonlinear systems. The idea of an active control technique based on complex Lyapunov function with lag in time is used for an approach to investigate MPLS of hyperchaotic attractors of these systems. For illustration, this approach is applied to hyperchaotic complex Chen and Lü systems. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve MPLS.

This article has been retracted due to partial plagiarism. A notice of retraction is published in Vol 28 No.12

Time-delayed fractional-order systems are crucial in modeling and analyzing various physical systems, ranging from mechanical and electrical systems to biological and environmental ones. While estimators play an inevitable role in achieving high accuracy in controlling nonlinear systems, control techniques intended for time-delayed fractional-order systems struggle to estimate uncertainties within finite time. To address this issue, this study proposes a novel control technique that utilizes a finite-time disturbance observer and an active controller for time-delayed fractional-order systems. The stability of this method and the finite-time convergence of the estimator are guaranteed using the Lyapunov stability theorem and active control concepts. Then, the study investigates a fractional-order neural network and exhibits its chaotic behavior. Finally, the synchronization results of the fractional-order time-delayed neural network using the proposed control scheme in the presence of external disturbances are presented, verifying the effectiveness and robustness of the proposed control technique.

A Caputo fractional-order derivative is used in a Quadrotor Unmanned Aerial Vehicle (QUAV) chaotic system to transform it into fractional ordered QUAV (FoQUAV) chaotic system for the first time. Therefore, this study explores three control (adaptive, active, and passive) strategies applied on the FoQUAV system. Further, utilizing Lyapunov theory, we established global stability around the equilibrium point and conducted numerical simulations for validation and comparison. In this work, adaptive control technique is used by considering $a_f$, $a_g$, and $a_h$ as unknown parameters and are derived using updated law. Similarly, active control technique is derived using two sub-controllers including ${\widehat{\mu }}_i=A_i+N_i$ with $A_i$; linear and $N_i$; nonlinear controllers, respectively. Finally, a feedback linearization-based, passive controller is used, which has predefined control input and converges to a stable equilibria. Moreover, this work also revealed, during performing numerical simulations, that the open loop system stabilizes at times $t\approx 4$ s, $t\approx 60$ s, and $t\approx 90$ s, respectively, for adaptive, active, and passive controllers. Finally, the passive controller face several challenges during stabilizing the yaw of a considered system and overall is proved that adaptive controller perform best with respect to time consumption and quick performance in comparison.

A numerical study on the active control of a machine suspension system supported on a cylindrical shell aiming to reduce the sound radiation is presented in this paper. In this system, a rigid-body machine is supported on a simply-supported elastic cylindrical shell through four active isolators. A theoretical model is employed and four types of active control strategies including kinetic energy minimization strategy, power flow minimization strategy, squared acceleration minimization strategy and acoustic power minimization strategy are considered, with corresponding active control force obtained by linear quadratic optimal method. Numerical simulations are conducted and detailed results were presented. Active control performance under these four control strategies is compared and analyzed in terms of radiated sound power, and the effect of the number of active actuators is discussed by numerical analysis. The results show that acoustic power minimization strategy has the best performance to reduce the sound power radiated from supporting shell in general. Through numerical simulations, some comprehensive design principles of active control system are discussed at the end.

Linear buckling of plates and columns is a critical design parameter in many engineering systems. Active stabilization of buckling constrained structures promises positive tradeoffs in terms of mass and performance. An optimal design method for actively stabilizing structural instability, while guaranteeing the performance and stability of the closed loop system, is presented. This method accounts for major design criteria such as active critical load, and sensor and actuator placement. Practical tradeoffs and limitations of this approach are presented for delineating the design space and evaluating potential design applications. These methods are shown to describe the feasible region and tradeoffs for active buckling control to highlight those application areas where active stabilization has greatest promise for expanding design spaces and creating novel structural systems.