PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.      

Global practical stabilization of planar linear systems in the presence of actuator saturation and input additive disturbance

In this note, we revisit the problem of global practical stabilization for planar linear systems subject to actuator saturation and input additive disturbances. A parameterized linear state feedback law is designed such that, by tuning the value of the parameter, all trajectories of the closed-loop system converge to an arbitrarily small neighborhood of the origin in a finite time and remain in there.     

A further result on global stabilization of oscillators with bounded delayed input

This note revisits the problem of globally stabilizing an oscillator with a bounded delayed input. It establishes that an oscillator with input saturation can be globally asymptotically stabilized by a linear state feedback even in the presence of an arbitrarily large delay in the input. This result strengthens a recent result in the literature, which shows that such an oscillator can be globally asymptotically stabilized with a sufficiently small control input and the magnitude of the control input goes to zero as the delay increases to infinity. The controller constructed in this note thus improves the efficiency of the closed-loop system by fully utilizing the actuator capacity.     

非线性物理学中的多体描述

讨论了系统在参量改变中的非线性突变行为，企图采用统一的方法，阐明性质相异多种多样的非性问题应当遵守的规律．     

拉西瓦高拱坝岩体力学、工程地质研究成果综述

拉西瓦水电站高拱坝建基岩体工程地质、岩体力学研究是中国水电顾问集团2004年度专题科研成果之一“高混凝土拱坝建基岩体工程地质、岩体力学综合研究”的主要成果,其重点内容为岩体风化、卸荷、岩体质量级别的定量划分、河谷应力场分带、建基岩体主要岩体力学参数研究,坝肩抗滑稳定、开挖后综合检测验证等;在理论探讨、方法实践、预测验证和创新尝试等方面取得了一定成果,具有一定的社会、经济效益。     

On the backstepping design procedure for multiple input nonlinear systems

In a recent paper, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. In this paper, we exploit the structural properties of such a decomposition in the application of the backstepping design technique on multiple input nonlinear systems. In particular, this decomposition simplifies the conventional backstepping design and motivates new backstepping design procedures that are able to stabilize systems on which the conventional backstepping procedure is not applicable. Copyright © 2011 John Wiley & Sons, Ltd.     

恒定水头岩体混凝土裂纹水入浸过程分析

针对自然营造力作用下岩体或混凝土裂纹的水力劈裂特点,基于裂纹水流运动的立方定律建立了恒定水头作用下裂纹内水流入浸过程计算模型与迭代步骤.通过对不同裂纹张开宽度、裂纹表面起伏差、裂纹形状等因素变化,分别计算了水流入浸过程.计算结果表明,裂纹内水流入浸过程是先快后慢,随着时间的推移,裂纹内水压会发展为全水头.当裂纹张开宽度大于0.02 mm,水流入浸过程及其短暂,裂纹内水流很快就达到裂尖,而且水压基本就是全水头.当裂纹的张开宽度特别小,达到微米级,水流就很难进入,即产生不透水的现象.裂纹表面的起伏差对于裂纹张开宽度较小的裂纹影响程度要大于宽度较大的裂纹.     

乌东德水电站建设岩石力学工程问题科技创新的思考

乌东德工程因所处河谷复杂严峻的自然环境条件及区域地质地震背景,面临枢纽工程布置、高陡边坡治理、大坝建基岩体选择与建基面确定、复杂地下洞室群安全施工、远程泥石流灾害预警、近坝大型滑坡体及水库岸坡安全稳定等工程地质和岩石力学关键问题的挑战。建设单位、设计单位、科研单位与技术咨询单位的众多工程师和科学家协同攻关,艰辛探索,攻克了工程建设过程中一系列的岩石力学关键技术问题,创新了遵循岩石力学规律特性的工程管理方法,促进了乌东德工程安全优质建设。本文结合工程建设进展,总结了乌东德工程岩石力学关键技术的科技创新,展望了绿色水电开发、建设、运行科技创新的方向。     

Semi‐global output consensus of a group of linear systems in the presence of external disturbances and actuator saturation: An output regulation approach

This paper studies the problem of semi‐global leader‐following output consensus of a multi‐agent system. The output of each follower agent in the system, described by a same general linear system subject to external disturbances and actuator saturation, is to track the output of the leader, described by a linear system, which also generates disturbances as the exosystem does in the classical output regulation problem. Conditions on the agent dynamics are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the output consensus is achieved when the communication topology among the agents is a digraph containing no loop, and the leader is reachable from any follower agent. We also extend the results to the non‐identical disturbance case. In this case, conditions based on both the agent dynamics and the communication topology are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the leader‐following output consensus is achieved when the communication topology among the follower agents is a strongly connected and detailed balanced digraph, and the leader is a neighbor of at least one follower. In addition, under some further conditions on the agent dynamics, the control algorithm is adapted so as to achieve semi‐global leader‐following output consensus for a jointly connected undirected graph and the leader reachable from at least one follower. Copyright © 2015 John Wiley & Sons, Ltd.     

An analysis of the exponential stability of linear stochastic neutral delay systems

This paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches h_max, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.