A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

The delay‐dependent stability problem of linear continuous/discrete systems with time‐varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay‐dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results. Copyright © 2008 John Wiley & Sons, Ltd.     

Output feedback variable structure control of uncertain linear systems in the presence of actuator dynamics

A new output feedback variable structure control scheme is developed based on a novel passivity idea. This scheme may practically stabilize a class of higher‐relative‐degree uncertain linear systems, and realize output tracking and disturbance attenuation as well. The controller is composed of linear filters and a single relay, without employing real‐time exact differentiators. Under this framework, we also explain how actuator dynamics affect the closed loop behavior. A simulation example shows the simplicity and efficiency of this method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new adaptive backstepping Coulomb friction compensator for servo control systems

A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time‐derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time‐variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Modalities in linear logic weaker than the exponential “of course”: Algebraic and relational semantics

We present a semantic study of a family of modal intuitionistic linear systems, providing various logics with both an algebraic semantics and a relational semantics, to obtain completeness results. We call modality a unary operator on formulas which satisfies only one rale (regularity), and we consider any subsetW of a list of axioms which defines the exponential of course of linear logic. We define an algebraic semantics by interpreting the modality as a unary operation on an IL-algebra. Then we introduce a relational semantics based on pretopologies with an additional binary relationr between information states. The interpretation of is defined in a suitable way, which differs from the traditional one in classical modal logic. We prove that such models provide a complete semantics for our minimal modal system, as well as, by requiring the suitable conditions onr (in the spirit of correspondence theory), for any of its extensions axiomatized by any subsetW as above. We also prove an embedding theorem for modal IL-algebras into complete ones and, after introducing the notion of general frame, we apply it to obtain a duality between general frames and modal IL-algebras.     

Confidence regions of two-stage stochastic linear complementarity problems

Two-stage stochastic linear complementarity problems (TSLCP) model a large class of equilibrium problems subject to data uncertainty, and are closely related to two-stage stochastic optimization problems. The sample average approximation (SAA) method is one of the basic approaches for solving TSLCP and the consistency of the SAA solutions has been well studied. This paper focuses on building confidence regions of the solution to TSLCP when SAA is implemented. We first establish the error-bound condition of TSLCP and then build the asymptotic and nonasymptotic confidence regions of the solutions to TSLCP by error-bound approach, which is to combine the error-bound condition with central limit theory, empirical likelihood theory, and large deviation theory.     

变频器非正弦供电对异步电机的影响

介绍变频器非正弦供电对异步电机的影响,分析谐波电压和电流对电机磁路、定子和转子功率因数、电机损耗与效率、谐波转矩、电应力、轴电流产生的危害和如何防止。     

基于嵌入式系统的电机振动分析仪设计

本文介绍了一种利用触控式面板模块工具在WindowsCE系统上开发LabVIEW程序的方法,并将该方法运用到对电机振动测量与分析上,构成了以嵌入式系统为平台的便携式电机振动分析设备。应用LabVIEW软件的强大数学运算功能对振动信号作频谱分析,作为电机故障的预防和诊断依据,具有重要的意义。     

Absolute Stability of Nonlinear Systems with Two Additive Time-varying Delay Components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.     

Stabilizing switching design for switched linear systems: A state-feedback path-wise switching approach

This paper addresses the problem of switching stabilization for discrete-time switched linear systems. Based on the abstraction-aggregation methodology, we propose a state-feedback path-wise switching law, which is a state-feedback concatenation from a finite set of switching paths each defined over a finite time interval. We prove that the set of state-feedback path-wise switching laws is universal in the sense that any stabilizable switched linear system admits a stabilizing switching law in this set. We further develop a computational procedure to calculate a stabilizing switching law in the set.