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Dynamic Anti-windup Design for Anticipatory Activation:Enlargement of the domain of attraction

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Dynamic Anti-windup Design for Anticipatory Activation:Enlar...

Estimate of the domain of attraction for polynomial systems using bisectional sum-of-squares optimization

第三十一届中国控制会议

作者： Xiongjun Wu~(1 2) Zongli Lin~(3 1) 1.Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing Ministry of Education of China Shanghai 200240 China. 2.The 802 Institute of Shanghai Academy of Space Flight Technology The Eighth Academy of China Aerospace Science and Technology Corporation Shanghai 200090 China. 3.Charles L.Brown Department of Electrical and Computer Engineering University of Virginia P.O.Box 400743 Charlottesville VA 22904-4743 USA.

＜正＞Traditional anti-windup compensators are designed for activation immediately at the occurrence of actuator saturation. Recently,anti-windup compensators designed for actuation either after the saturation has reached a certain level or in anticipation of its *** the case of static anti-windup compensators,it has been shown that an anti-windup compensator designed for activation in anticipation of actuator saturation would lead to better performance than those designed for immediate or delayed activation could,both in terms of transient performance and the size of the domain of *** recently,it has been shown that a dynamic anti-windup compensator designed for anticipatory activation would also result in better transient performance than those designed for immediate or delayed activation *** this paper,we design dynamic anti-windup compensators for the enlargement of the domain of *** compensators are designed respectively for immediate,delayed and anticipatory *** will show by simulation that a dynamic anti-windup compensator designed for anticipatory activation would result in a larger domain of attraction than a dynamic anti-windup compensator designed for immediate or delayed activation could.

关键词： Actuator saturation anti-windup anticipatory activation domain of attraction dynamic compensator

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Estimate of the domain of attraction for polynomial systems ...

Estimating Critical Clearing Time of Grid Faults Using DA of State-Reduction Model of Power Systems

第37届中国控制会议

作者： Linhong Lu Pingfang Zhu Jianping Zeng Department of Automation Xiamen University

This paper proposes a new approach to estimate the domain of attraction（DA） of equilibrium points for polynomial autonomous *** largest estimate of the DA（LEDA） for a given Lyapunov function（LF） is computed via finding the largest sublevel set of the LF,which leads to the nonlinear optimization problem and possibly becomes non-convex when the LF is allowed to *** simplified the complete square metrical representation（CSMR） based LMI conditions to much more simple sum-of-squares（SOS） conditions,and avoided the set containment relationship between the LF and its *** a result,simpler bilinear SOS conditions are formulated to compute the LEDAs for given LFs and search for better LFs which may provide larger LEDAs than a quadratic *** bisectional SOS programming（Bi SOSP） algorithms are given for solving those bilinear SOS *** method is applied to the well known Van der pol system and the computational cost is also discussed.

关键词： Polynomial system domain of attraction Sum-of-squares optimization Bisection method

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CSEE Journal of Power and Energy Systems 2024年第2期10卷 807-820页

作者： Yang Liu Zhongyang Chen Huanjin Yao Lin Yi Q.H.Wu School of Electric Power Engineering South China University of TechnologyGuangzhou 510640China China Southern Power Grid Research Institute Guangzhou 510663China

This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of the Jacobian matrix and the structure of the boundary of the DA, it is found the DA of the state-reduction model and that of the full model of a power system are topological isomorphism. There are one-to-one correspondence relationships between the number of equilibrium points, the type of equilibrium points, and solutions of the two system models. Based on these findings, an expanding interior algorithm is proposed with SOS programming to estimate the DA of the state-reduction model. State trajectories of the full model can be transformed to those of the state-reduction model by orthogonal or equiradius projection. In this way, CCT of a grid fault is estimated with the DA of the state-reduction model. The calculational burden of SOS programming in the DA estimation using the state-reduction model is rather small compared with using the full model. Simulation results show the proposed expanding interior algorithm is able to provide a tight estimation of DA of power systems with higher accuracy and lower time costs.

关键词： Critical clearing time domain of attraction expanding interior algorithm state-reduction model SOS programming

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

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控制理论与应用（英文版） 2012年第2期10卷 195-200页

作者： Airong Wei Yuzhen Wang School of Control Science and Engineering Shandong University Jinan Shandong 250061 China

This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities （LMIs） optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.

关键词： PCH system Actuator saturation domain of attraction Set invariance

CHOVER'S LAW OF THE ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED SEQUENCES

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Journal of Systems Science & Complexity 2010年第2期23卷 293-302页

作者： Qunying WU Yuanying JIANG College of Science Guilin University of Technology Guilin University of Technology Guilin 541004 China.

Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated *** results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.

关键词： domain of attraction law of the iterated logarithm negatively associated.

A LIL and Limit Distributions for Trimmed Sums of Random Vectors Attracted to Operator Semi-stable Laws

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1555-1565页

作者： Wen Sheng WANG Department of Mathematics Hangzhou Normal University

Let θ∈^d be a unit vector and let X, X1, X2,…… be a sequence of i.i.d. Xd-valued random vectors attracted to operator semi-stable laws. For each integer n ≥1, let X1,≤……≤ Xn,n denote the order statistics of X1, X2,..., Xn according to priority of index, namely ｜（X1,nθ）｜≥…≥ [（Xn,n,θ）1, where （., .） is an inner product on Rd. For all integers r ≥ 0, define by （r）Sn =∑n-r i=1Xi,n the trimmed sum. In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums （r）Sn. Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded. A stochastically compactness of （r）Sn is obtained.

关键词： Operator semi-stable law domain of attraction law of the iterated logarithm stochastically compactness affine normalized partial sum trimmed sum

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

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IEEE/CAA Journal of Automatica Sinica 2022年第1期9卷 90-98页

作者： Xujun Lyu Zongli Lin College of Engineering Huazhong Agricultural UniversityWuhan 430070China Charles L.Brown Department of Electrical and Computer Engineering University of VirginiaP.O.Box 400743CharlottesvilleVA 22904-4743 USA

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator *** on the bounds on the growth rates of the nonlinear uncertain function in the system model,the system is placed in a linear differential *** vertex system of the linear differential inclusion is a linear system subject to actuator *** 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 *** equilibrium point corresponds to the desired set point for the system ***,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 *** 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.

关键词： Actuator saturation domain of attraction nonlinear systems PID control uncertainties

Laws of the Iterated Logarithm for-mixing Random Variables with Normal Distribution

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 385-394页

作者： Qun-ying WU College of Science Guilin University of Technology

Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng （1996） from the i.i.d, case to ρ-mixing sequences.

关键词： ρ-mixing sequence of random variables law of the iterated logarithm domain of attraction

Stability Analysis and Anti-windup Design of Switched Systems with Actuator Saturation

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International Journal of Automation and computing 2017年第5期14卷 615-625页

作者： Xin-Quan Zhang Xiao-Yin Li Jun Zhao School of Information and Control Engineering Liaoning Shihua UniversityFushun 113001China School of Foreign Languages Liaoning Shihua UniversityFushun 113001China State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110819China

The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality （LMI） constraints. Two numerical examples are given to show the effectiveness of the proposed method.

关键词： Anti-windup switched systems saturating actuators single Lyapunov function domain of attraction linear matrixinequality (LMI).