An off-and-towards-equilibrium strategy for vibrational control of structures

Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.

Study of the control-equilibrium of control systems

Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this theory, a perfect control method should not only guarantee stability of the system, but also ensure the control-equilibrium of the system. To achieve the control-equilibrium, feed-forward control is required.

Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model

The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.

The Analysis of the Dynamic Equilibrium State in Linear Control System

This paper discusses not a point of equilibrium to free system,but a certain family of equilibrium state of dynami- cal system with inputs.This equilibrium state depends on the input,so it is called the dynamic equilibrium state.The expression of the dynamic equilibrium state can be given under some certain condition.With deductions and proofs in linear control system,es- tablish the expression of the dynamic equilibrium state in two cases,where the linear systems are nonsingular or singular.Also pre- sent the concept and the condition of the controllability of the dynamic equilibrium state.The controllability of the dynamic equilib- rium state is different from the controllability of the state to system,but these two are closely related.

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

A Mixed-control Mechanism Model of Proeutectoid Ferrite Growth under Non-equilibrium Interface Condition in Fe-C Alloys

By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

Poloidal Field Control for the HT-7U Super-conducting Tokamak

Controlling the poloidal field (PF) in the HT-7U superconducting tokamak is critical to the realization of the mission of advanced tokamak research. Plasma start-up, plasma position, shape, current control and plasma shape reconstruction have been performed as a part of its design process. The PF coils have been designed to produce a wide range of plasmas. Plasma start-up can be achieved for multiple conditions. Fast controlling coils for plasma position inside the vacuum vessel are used for controlling the plasma vertical position on a short timescale. The PF coils control the plasma current and shape on a slower timescale. VXI (VME bus extensions for Instrumentation) Bus system and DSP (Digital Signal Processor is a basic unit of the feedback control system), the response time of which is about (2-4) ms. The basic unit of this system, the shape-controlling algorithms of a few critical points on plasma boundary and real-time equilibrium fitting (RTEFIT) will be described in this paper.

Seismic structural control using semi-active tuned mass dampers

This paper focuses on how to determine the instantaneous damping of the semi-active tuned mass damper (SATMD) with continuously variable damping.An off-and-towards-equilibrium (OTE) algorithm is employed to examine the control performance of the structure/SATMD system by considering the damping as an assumptive control action.The damping modification of the SATMD is carried out according to the proposed OTE algorithm,which is formulated based on analysis of the structural movement under external excitations,and the measured responses of the structure at every time instant. As examples two numerical simulations of a five-storey and a ten-storey shear structures with a SATMD on the roof are conducted.The effectiveness on vibration reduction of MDOF systems subjected to seismic excitations is discussed.Analysis results show that the behavior of the structure with a SATMD is significantly improved and the feasibility of applying the OTE algorithm to the structural control design of SATMD is also verified.

A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.

Time Optimal Control in Time Series Movement

The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.

航天器多级自由边界模拟系统姿态平衡协调控制

为了消除天地力学环境不一致对航天器在轨运行精度的影响,需要在地面开展航天器在轨微振动环境模拟试验,因此针对航天器的设施部分和平台部分,在航天器上、下两端建立了自由边界模拟系统和自动控制模块,通过力闭环和位移闭环对航天器重力卸载过程的平衡协调控制算法进行了设计和实施;并通过硬件设施搭建和软件程序编写完成现场试验,验证了控制系统的可行性和稳定性,也为未来航天器地面模拟试验中重力卸载过程控制系统的设计提供技术支撑并积累了工程经验。

Coordinating control of multiple rigid bodies based on motion primitives

This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.

Mathematical Model and Non-Pharmaceutical Control of the Coronavirus 2019 Disease in Madagascar

For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic. By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement is unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction number R0 can go down from 3 to 1.7. The pressures on the economic and social situation are rather viable. It is the most suitable for the Malagasy health system. The results proposed are a way to control the spread of the disease and limit its devastation in a country like Madagascar.

转移概率部分未知的离散时间Markov跳变系统Nash微分博弈

考虑到转移概率矩阵元素无法完全获悉,如何在转移概率部分未知的情境下研究离散时间Markov跳变系统Nash微分博弈是有待解决的问题之一,这一问题可以为转移概率部分未知的Markov跳变系统Nash微分博弈理论在管理问题上的应用提供理论支撑。基于此,本文首先研究单人博弈情形,即ε-次优控制问题,借助自由连接权矩阵和配方法,得到了ε-次优控制策略存在的充分性条件,并给出了成本函数上界的显式表达;然后延伸至双人博弈进行分析,得到了ε-次优Nash均衡策略存在的条件等价于求解双线性矩阵不等式和矩阵不等式的优化问题,并通过启发式算法求解优化问题得到ε-次优Nash均衡策略;最后通过数值算例证明了主要结论的有效性。

基于塔内位移观测器和均衡空间低维控制器的高塔结构振动主动控制系统

高塔结构振动适合也需要主动控制技术,但需要满足位移直接观测和单点控制下的低维高效控制。本文应用现代摄像观测技术,建立了一套从塔内实时连续观测振动位移的方法,为高塔结构振动主动控制提供了最直接的位移观测器,避免了以往只能建立加速度观测器,经滤波后再与假定的外荷载结合计算输出位移的冗长过程。基于均衡系统空间变换和平衡截断法,对顶端设置主动质量块的高塔结构进行降维,可以有效保留结构的主要动力特性。以某施工状态的700 m高塔为例,进行了风振和地震的主动控制仿真分析。结果表明:以少数位移状态作为反馈信号的降维控制器的控制效果和基于全状态反馈的全维控制器基本一致,可以作为高塔结构振动的主动控制策略。

自主平衡恢复过程中姿势调控反应时与运动时的增龄性变化研究

目的:观察人体在失稳后的自主平衡恢复过程中姿势调控反应时间与运动时间的增龄趋势与年龄敏感性变化区。方法:使用DE-A体感平衡检测系统对20—79岁的健康成年受试者97例进行姿势调控时间测试,包括在静态平衡与动态平衡状态下的支撑面前倾、后倾、左倾和右倾失稳应激时的姿势调控反应时与运动时测试,并记录所有测试的各姿势调控时间指标。按照10岁为一年龄分段将受试者依次分为6个年龄组,其中组1(20—29岁)为16例、组2(30—39岁)为10例、组3(40—49岁)为17例、组4(50—59岁)为18例、组5(60—69岁)为31例、组6(70—79岁)为5例,观察姿势调控反应时与运动时的增龄变化,并分析其年龄敏感变化区。结果:姿势调控反应时和运动时随年龄增长呈现延长趋势。静态平衡状态下,组6的各反应时和运动时均较组1—5长,与组1—4比较均具有显著性差异(P<0.05),与组5比较均无显著性差异(P>0.05);组5的各反应时和运动时均较组1—4长,且均具有显著性差异(P<0.05);组4的各反应时和运动时均较组1—3长,支撑面右倾时的反应时与组1比较具有显著性差异(P<0.05),其余指标组间比较均无显著性差异(P>0.05);组3的各反应时和运动时均较组1—2长,支撑面左倾时的运动时与组1比较具有显著性差异(P<0.05),其余指标组间比较均无显著性差异(P>0.05);组2的各反应时和运动时与组1比较均无显著性差异(P>0.05)。动态平衡状态下,组6的各反应时和运动时均较组1—5长,与组1—4比较均具有显著性差异(P<0.05),与组5比较均无显著性差异(P>0.05);组5的各反应时和运动时均较组1—4长,且均具有显著性差异(P<0.05);组4的各反应时和运动时均较组1—3长,支撑面左倾时的反应时与组1比较无显著性差异(P>0.05),其余指标组间比较均具有显著性差异(P<0.05),而支撑面后倾和左倾的运动时与组2比较具有显著性差异(P<0.05),其余指标组间比较均无显著性差异(P>0.05);组3的各反应时和运动时均较组1—2长,各运动时与组1比较均具有显著性差异(P<0.05),而各反应时与组1比较无显著性差异(P>0.05);组2的各反应时和运动时与组1比较均无显著性差异(P>0.05)。结论:人体在失稳后的自主平衡恢复过程中姿势调控反应时和运动时随年龄增长而逐渐延长。静态平衡恢复的姿势调控反应时和运动时可能在60岁左右开始出现明显恶化,而动态平衡恢复的姿势调控反应时与运动时可能分别在50岁左右和40岁左右便开始出现明显恶化。

基于多Agent的锂电池主动均衡策略控制仿真研究

【目的】针对锂电池的荷电状态均衡管理问题,提出一种基于多智能体的电池组荷电状态一致性均衡方案。【方法】首先,将多智能体控制策略引入电池管理的下垂控制中,实现了主动均衡电路拓扑下的自主均衡;其次,建立领航跟随者模型,利用参数已知的虚拟智能体使各个荷电状态不一致的电池的状态向其靠近,实现充放电模式下的荷电状态均衡;最后,对二阶多智能体荷电状态均衡控制策略进行仿真验证。【结果】实验结果表明,相比一阶均衡控制策略,自主均衡时间减少了43.02%,充电模式中均衡时间减少了16.13%,放电模式中均衡时间降低了32.90%。【结论】多智能体系统在电池的均衡管理中能够实现荷电状态的均衡,有效地降低了锂电池荷电状态到达一致性的收敛时间。

航天器姿态控制群体博弈分布式分配方法

针对由多个细胞星构成的组合卫星的姿态控制问题,提出了一种包含控制力矩计算层与冗余力矩分配层的双层姿态控制方法。将细胞星间的冗余力矩分配问题转化为群体博弈的策略选择问题,综合考虑能量消耗、飞轮输出力矩裕度和飞轮角动量裕度设计收益函数,以力矩分配系数作为群体质量,以细胞星作为策略建立群体博弈模型。考虑群体演化中模仿和比较形成的不同演化策略,分别采用Smith动力学以及复制器动力学修订协议求解博弈的Nash均衡解,并利用有限制策略的群体博弈理论形成分布式冗余力矩分配方式,得到各个细胞星的控制策略。最后通过仿真实验验证了此分配方式的有效性。