H_∞ SYNCHRONIZATION CONTROL OF LINEAR SYSTEMS AND ITS APPLICATION TO WAFER-RETICAL STAGE

For the outputs of two nth-order linear control systems to work insynchronization and meanwhile to track their commands, a H_(infinity) synchronization control schemeis presented. In terms of two uncoupled single variable linear systems, a multivariable coupledsystem is established by choosing one output and the difference of the two outputs as a new outputvector, so that both command tracking and synchronization properties can be demonstrated by aH_(infinity) performance index. To improve the synchronization and trailing performance and toguarantee the system robust stability, the mixed sensitivity H_(infinity), design methodology isadopted. The presented synchronization scheme is then extended to the case where one of the twosystems include two input variables, and then applied to the position synchronization control of awafer-retical stage. The wafer-reticle stage consists of a wafer stage, a reticle coarse stage, anda reticle fine stage. The reticle coarse stage picks up the reticle fine stage. The three stagesought to tack their commands, but synchronization between the wafer stage and the reticle fine stagemust be stressed in the tracking process. In the application, by appropriately determining theweighting matrices for the sensitivity function and the complementary sensitivity function, asatisfactory KL synchronization controller is obtained to realize highly accurate positionsynchronization, and to guarantee tracking performance. The above results are verified by simulationexperiments.

N-PD cross-coupling synchronization control based on adjacent coupling error analysis

In order to improve the trajectory tracking precision and reduce the synchronization error of a 6-DOF lightweight robot, nonlinear proportion-deviation （N-PD） cross-coupling synchronization control strategy based on adjacent coupling error analysis is presented. The mathematical models of the robot, including kinematic model, dynamic model and spline trajectory planing, are established and verified. Since it is difficult to describe the real-time contour error of the robot for complex trajectory, the adjacent coupling error is analyzed to solve the problem. Combined with nonlinear control and coupling performance of the robot, N-PD cross-coupling synchronization controller is designed and validated by simulation analysis. A servo control experimental system which mainly consists of laser tracking system, the robot mechanical system and EtherCAT based servo control system is constructed. The synchronization error is significantly decreased and the maximum trajectory error is reduced from 0.33 mm to 0.1 mm. The effectiveness of the control algorithm is validated by the experimental results, thus the control strategy can improve the robot＇s trajectory tracking precision significantly.

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.

Synchronization control for electro-hydraulic dual-cylinder system based on force/position switching

If the rigidity of a mechanism is stiff enough, the position synchronous error of the two cylinders driving one degree-of-freedom （DOF） of the mechanism may be less than the resolution of position sensors. To handle this synchronization problem this paper proposes a force/position switching scheme, which partitions the two cylinders into a master cylinder and a slave cylinder. The master cylinder is always position tracking controlled by a second-order sliding mode controller and the slave cylinder is integrated with a force tracking controller which is a first order sliding mode controller. When the position tracking error is less than a given value, the slave cylinder switches to be force controlled. Two synchronization control methods are presented based on the switching scheme： the master - master ＋ force/position switching control and the master - slave ＋ force/position switching control. Simulations show that the formance compared with two given proposed synchronization control position-based control methods. methods can get a better per-

Synchronization Control of Planar 2-DOF Robot with Redundant Actuation

Considering the special characteristics of the redundant parallel manipulator, with emphasis on the variable of structure, the relatively small workspace and the strong coupling relationship among arms, a synchronization control strategy is presented in this paper. Since in the feedforward, the inertial and the coriolis matrix are designed constant according to the relatively small workspace, position measurement of the endeffector in plane is ignored. Synchronization error and coupling error are introduced to reject the model errors of inertial and coriolis matrix as stated above. Using the method, the errors of driving arms can be reduced, and the synchronization performance among axes can be improved. The stability of the controllers was proved by Lyapunov method. Finally, experimental results show the feasibility of the method.

Adaptive Performance-Constrained Synchronization Control for Hypersonic Flight Vehicle Swarms: A Novel Finite-Time Convergence Protocol Methodology

This paper proposes a novel neural adaptive performance-constrained synchronization tracking control algorithm for multiple hypersonic flight vehicles(HFVs),which are subject to actuator faults and full-state constraints.The proposed method is based on advanced Lyapunov finite-time stability theory and a sophisticated backstepping design scheme.The longitudinal model of HFV is converted into velocity and altitude subsystems through functional decomposition.Our method presents three significant contributions over the existing state-of-the-art approaches:(a)ensuring finite-time convergence of HFVs systems by guaranteeing that the setting time is lower bounded by a positive constant that is related to the initial states;(b)utilizing a tan-type Barrier Lyapunov function(BLF)to ensure that the synchronization tracking errors of velocity,altitude,flight path angle,angle of attack,and pitch angle rate are maintained within certain performance bounds;and(c)designing a neural adaptive control algorithm and adaptive parameter laws by combining the backstepping design technique and radial basisfunction neural networks(RBFNNs)to handle unknown actuator faults and modeling uncer-tainties.Finally,comparative simulations are conducted to validate the efficacy of the proposed scheme.

Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology

The synchronous conditions of two kinds of the small-world （SW） network are studied. The small world topology can affect on dynamical behaviors of the beam transport network （BTN） largely, if the BTN is constructed with the SW topology, the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology, respectively. This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems, and may have potential use in prospective applications for halo-chaos secure communication.

Optimal synchronization control formulti-agent systems with input saturation:a nonzero-sum game

This paper presents a novel optimal synchronization control method for multi-agent systems with input saturation.The multi-agent game theory is introduced to transform the optimal synchronization control problem into a multi-agent nonzero-sum game.Then,the Nash equilibrium can be achieved by solving the coupled Hamilton–Jacobi–Bellman(HJB)equations with nonquadratic input energy terms.A novel off-policy reinforcement learning method is presented to obtain the Nash equilibrium solution without the system models,and the critic neural networks(NNs)and actor NNs are introduced to implement the presented method.Theoretical analysis is provided,which shows that the iterative control laws converge to the Nash equilibrium.Simulation results show the good performance of the presented method.

Multi-agent differential game based cooperative synchronization control using a data-drivenmethod

This paper studies the multi-agent differential game based problem and its application to cooperative synchronization control.A systematized formulation and analysis method for the multi-agent differential game is proposed and a data-driven methodology based on the reinforcement learning(RL)technique is given.First,it is pointed out that typical distributed controllers may not necessarily lead to global Nash equilibrium of the differential game in general cases because of the coupling of networked interactions.Second,to this end,an alternative local Nash solution is derived by defining the best response concept,while the problem is decomposed into local differential games.An off-policy RL algorithm using neighboring interactive data is constructed to update the controller without requiring a system model,while the stability and robustness properties are proved.Third,to further tackle the dilemma,another differential game configuration is investigated based on modified coupling index functions.The distributed solution can achieve global Nash equilibrium in contrast to the previous case while guaranteeing the stability.An equivalent parallel RL method is constructed corresponding to this Nash solution.Finally,the effectiveness of the learning process and the stability of synchronization control are illustrated in simulation results.

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality（LMI） technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.

Research on adaptive control Lorenz chaotic system synchronization

With the help of adaptive control theory to chaos synchronization, this paper provides a kind of controlling strategy that is adaptive control by which we can synchronize the Lorenz chaotic dynamical system. The theoretical analysis and simulation show using this controlling strategy, we can synchronize chaotic systems with the unknown parameters and the different initial conditions.

Review on grid-forming converter control methods in high-proportion renewable energy power systems

Grid-forming(GFM)converters can provide inertia support for power grids through control technology,stabilize voltage and frequency,and improve system stability,unlike traditional grid-following(GFL)converters.Therefore,in future“double high”power systems,research on the control technology of GFM converters will become an urgent demand.In this paper,we first introduce the basic principle of GFM control and then present five currently used control strategies for GFM converters:droop control,power synchronization control(PSC),virtual synchronous machine control(VSM),direct power control(DPC),and virtual oscillator control(VOC).These five strategies can independently establish voltage phasors to provide inertia to the system.Among these,droop control is the most widely used strategy.PSC and VSM are strategies that simulate the mechanical characteristics of synchronous generators;thus,they are more accurate than droop control.DPC regulates the active power and reactive power directly,with no inner current controller,and VOC is a novel method under study using an oscillator circuit to realize synchronization.Finally,we highlight key technologies and research directions to be addressed in the future.

Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory

An adaptive synchronization control method is proposed for chaotic permanent magnet synchronous motors based on the property of a passive system. We prove that the controller makes the synchronization error system between the driving and the response systems not only passive but also asymptotically stable. The simulation results show that the proposed method is effective and robust against uncertainties in the systemic parameters.

HIGH-ACCURACY SYNCHRONIZA-TION CONTROL WITH HYBRID NEURAL NETWORKS

A novel nonlinear control algorithm based on hybrid neural networks ispresented to cope with the high-accuracy synchronization control problem for a dual-actuatorelectrohydraulic drive system which plays an important role for the development of elastomericlaunchers. A new objective function for better synchronization performance is introduced and alearning algorithm to adjust the weights of the neural network, based on the gradient descentalgorithm, is also derived. The hybrid neural network control algorithm guarantees high-accuracysynchronization performance of two motion cylinders and fast dynamic response as well as goodstability of the control system. Prototype test results on the dual-actuator electrohydraulic drivesystem verifys the effectiveness of the proposed approach.

Multi-goal Control of Chaotic Connected Complex Networks

Beam transport network(BTN)with small world(SW)(so-called BTN-SW)and Lorenz chaotic connectednetwork with scale-free(SF)are taken as two typical examples,we proposed a global linear coupling and combined withlocal error feedback methods in sub-networks to realize multi-goal control method of halo and chaos in two networksabove.The simulation results show that the methods above is effective for any chaotic connected networks and has apotential of applications in based-halo-chaos secure communication.

Disturbance observer based finite-time coordinated attitude tracking control for spacecraft on SO(3)

To solve the problem of attitude synchronization control for spacecraft formation flying(SFF)suffering from external disturbances under a directed communication topology,a sliding mode disturbance observer(SMDO)based on the finite-time control strategy is developed to observe the time-varying external disturbance via estimating the upper bound of its first derivative.Meanwhile,the rotation matrix is employed to describe the attitude of SFF for the purpose of the avoidance of singularity and unwinding phenomenon.As for the attitude synchronization and the tracking control architecture,a sliding mode surface(SMS)is given such that the control objective can be achieved.The effectiveness and the validity of the proposed method are elaborated via theoretical analysis and numerical simulations.

The Velocity Synchronizing Control on the Electro-Hydraulic Load Simulator

This paper builds up an accurate nonlinear mathematical model of anelectro-hydraulic force/ torque servo control system, and provides a thorough theoretical analysison the feedforward compensation for extraneous force/torque, whose limitation is analyzed andrevealed. The nonlinear factors and the servo valve dynamics have much influence on the systemcharacteristics. Subsequently a velocity syn-chronizing-compensation method by using the controlsignal of the control actuator is proposed, which can reduce the lagging effects for the betterperformance. For the reason of similarity between the model of control actuator and that of the loadsimulator, the proposed method performs well against the influence of nonlinear factors. Thesimulations and the experiments confirm that this control scheme results in a quick response,robustness, and excellent ability against disturbance.

Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.

Control Strategy of a Two-Lap Connection Converter

Two-lap sequential control converters are usually adopted to supply and improve the power factor of input side. The line harmonic damage generated by a sequential control thyristor converter can be serious. To solve this prob-lem and seek an optimum control strategy,we derived the changeable regular of the line-input-current,the fundamen-tal-frequency-current,the harmonic-current-content and the harmonic total distortion ratio of the converter at different firing angles. We obtained relevant data from experiments with a sequential control system of a DC 2.2kW/220V motor. With the example of the operating condition of a DC mine elevator,the harmonic current is two times approximately in sequential control compared to synchronous control when the firing angle of the two converters differs in 30°. At dif-ferent operating states of a two-lap connection converter,the ideal strategy is an exchange between sequential control and synchronous control,by which we can achieve the complementary goal of improving the power factor and har-monic effect. All analytical conclusions are supported by simulation and experimental results.

The Paralleling of High Power High Frequency Amplifier Based on Synchronous and Asynchronous Control

The vertical position of plasma in the HT-7U Tokamak is inherently unstable. In order to realize active stabilization, the response rate of the high-power high-frequency amplifier feeding the active control coils must be fast enough. This paper analyzes the paralleling scheme of the power amplifier through two kinds of control mode. One is the synchronous control; the other is the asynchronous control. Via the comparison of the two kinds of control mode, both of their characteristics are given in the text. At last, the analyzed result is verified by a small power experiment.