Control of discrete time systems based on recurrent Super-Twisting-like algorithm

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator.     

Filtering in linear discrete systems with unknown perturbations

This paper considers an algorithm for the synthesis of an optimal filter providing a state vector estimator for a discrete linear dynamic system with additive perturbations containing an unknown constant component. The algorithm does not use perturbation estimators. Results of a computation experiment are given.     

Model predictive control of discrete-time hybrid systems with discrete inputs

This paper proposes and discusses a model predictive control approach to hybrid systems with discrete inputs only. The algorithm, which takes into account a model of a hybrid system, described as a mixed logical dynamical system, is based on a performance-driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a "tree of evolution." The nodes of the tree represent the reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. A cost-function value is associated with each node, and based on this value the exploration of the tree is driven. As soon as the exploration of the tree is finished, the corresponding input is applied to the system and the procedure is repeated.     

Optimal selection of parameters of multichannel continuously scanning digital-radiography systems

For continuously scanning digital-radiography systems containing a linear detector array, a problem of optimal selection of the length and width of the aperture of an individual detector in this array, the radiation detection time, and the impulse response of a digital filter was solved. The maximum of the system’s spatial resolution in the “worst case” served as the optimality criterion for a specified testing capacity.     

饱和离散时间系统非保守输出反馈控制器设计

针对输入饱和离散系统由于采用输出反馈而导致的控制器设计存在很强保守性的问题,将凸多面体分析的方法应用于系统吸引域描述中,给出了基于状态的系统可控域的顶点描述和面描述形式,建立了系统输出反馈与基于状态的系统可控域之间的关系;为解决由于不稳定系统输出反馈第一步控制不施加任何控制作用而造成的系统状态可控域大大减小的保守性问题,提出了基于状态观测器的输出反馈非保守控制器设计方法;针对二阶不稳定系统,根据系统输出矩阵及输出初始值的不同情况,给出了输出反馈控制器第一步控制作用的具体形式,并证明了在该控制器作用下,系统的可控域达到最大,从而最大程度减小了控制器的保守性。最后通过Matlab进行了数值仿真实例研究。研究结果验证了所设计控制器的有效性。     

Multi-displacement continuum model for discrete systems

A first-order multi-displacement microstructure continuum model is introduced to represent a discrete diatomic lattice system. This model is developed based on a two-term Taylor series expansion of the local displacement of the lattice. It is found that the multi-displacement continuum model obtained by keeping two terms in the Taylor series yields, in general, a better representation of the lattice system than the effective modulus model. However, this microstructure continuum model cannot characterize the negative group velocity of an optical mode of harmonic wave motion in the diatomic lattice. To capture the negative group velocity, a higher-order multi-displacement continuum model is necessary.     

Optimization the parameters of multichannel continuously scanning digital X-ray radiography systems

Analytical formulas for optimal selection of the values of the main parameters of a multichannel continuously scanning digital X-ray radiography system, which is based on a linear detector array, and the minimum required value of the exposure dose rate from an X-ray source are obtained using the specified values of the system’s spatial resolution in the “worst case” and the testing capacity taking the digital filtering of the radiation detection results into account.     

Numerical integration of discrete mechanical systems with mixed holonomic and control constraints

The present work aims to incorporate control (or servo) constraints into finite-dimensional mechanical systems subject to holonomic constraints. In particular, we focus on underactuated systems, defined as systems in which the number of degrees of freedom exceeds the number of inputs. The corresponding equations of motion can be written in the form of differential-algebraic equations (DAEs) with a mixed set of holonomic and control constraints. Apart from closed-loop multibody systems, the present formulation accommodates the so-called rotationless formulation of multibody dynamics. The rotationless formulation has proven to be especially well-suited for the design of energy and momentum conserving schemes, which typically exhibit superior numerical stability properties (see [4, 7, 10]). Subsequent to the incorporation of the servo constraints, we deal with a reformulation of the underlying DAEs, which is amenable to a direct numerical discretization. To this end, we apply a specific projection method to the DAEs in terms of redundant coordinates. A similar projection approach has been previously developed in the framework of generalized coordinates by Blajer & Kolodziejczyk [12]. A numerical example is presented, which deals with a 3D rotary crane. This paper was presented at the 4th Asian Conference on Multibody Dynamics(ACMD2008), Jeju, Korea, August 20–23, 2008. Peter Betsch received his degree in aerospace engineering from the University of Stuttgart, Germany in 1991, his Ph.D. degree in computational mechanics from the University of Hanover, Germany in 1996, and his venia legendi (Habilitation) in mechanics from the University of Kaiserlautern, Germany in 2002. Since 2003 he has been a Professor of Computational Mechanics with the University of Siegen, Germany. Mahmut Quasem received his BSc in mechanical engineering from Bangladesh University of Engineering and Technology, Dhaka in 2000. He then received his MSc in mechatronics from the University of Siegen, Germany in 2006. He has been working as a research assistant at the chair of computational mechanics at the University of Siegen, Germany since June 2006. Stefan Uhlar received his degree in mechanical engineering from the University of Kaiserslautern, Germany in 2005. He is a Ph.D. candidate at the chair of computational mechanics at the University of Siegen, Germany.     

模糊离散事件系统的自适应监督控制

针对基于模糊自动机的模糊离散事件系统模型在实际工程应用中的不足,从产生式规则出发,建立了该类系统的模糊规则化模型.通过定义结构化的模糊因子并以其构成模糊规则,实现了对模糊状态转移函数的描述.提出了一种包含模糊监控器和模糊控制器的系统闭环监控结构,并针对模糊推理环节给出了具体的实现方法.通过定义一种可动态调整的模糊规则允许发生度,实现了系统的自适应监控机制.借助电动汽车电池均衡管理系统对方法进行了验证.结果表明,系统的运行过程符合预定的目标.     

A mathematical model of multichannel continuously scanning systems for digital X-ray analysis

A mathematical model of continuously scanning systems for digital X-ray analysis is developed. The systems contain a linear array of detectors that can be used not only in systems of radiation sources with an anisotropic angular distribution and a nonuniform distribution of the quantum yield over the focal spot but also in systems of detectors with nonuniform spatial sensitivity to incident radiation. The systems also make it possible to normalize the records of the radiation image of a tested object and perform digital filtering of the results.     

Lyapunov functions for nabla discrete fractional order systems

This paper focuses on the fractional difference of Lyapunov functions related to Riemann–Liouville, Caputo and Grünwald–Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results.     

Decentralized supervisory control of continuous timed discrete event systems

<正>In this paper,we presented the decentralized supervisory control problem of discrete event system with continuous-time variable.By presenting the definition of coobservability for the timed specification,a necessary and sufficient condition for the existence of decentralized supervisors is obtained.Finally,a numerical example is given.     

Modeling dynamic behavior of MDOF systems with multiple bilinear springs

A computational scheme is presented in this paper to simulate dynamical behavior of multiple degrees of freedom (MDOF) systems with multiple bilinear springs. In the proposed scheme, a bilinear spring is modeled using by two parallel springs - a primary spring and a secondary spring. The primary spring is an ordinary linear spring having identical stiffness in tension and compression, and is active for tension and compression. The secondary spring, whose stiffness characterizes the bilinearity, is active only during compression. It is employed in connection with the Newmark integration method and the linear complementarity problem (LCP) formulation to obtain time-domain responses of dynamical systems with bilinear springs due to initial disturbances and harmonic excitations. The scheme described in this paper is effective in dealing with the sudden transition from tension to compression and vice versa simultaneously for all bilinear springs. Numerical results for bilinear oscillators with finite bilinearity ratios and impact oscillators with an infinite bilinearity ratio show that the proposed bilinear spring model is accurate, generic and valid for bilinearity ratios ranging from zero to infinity. Orderly and chaotic behavior of viscously damped 3-DOF system under harmonic excitation is studied for a wide range of excitation frequencies and bilinear ratios to demonstrate the effectiveness and applicability of the proposed model for MDOF bilinear systems.     

具有控制器增益变化的离散系统时滞记忆鲁棒可靠控制

研究具有控制器增益变化的不确定时滞系统的鲁棒可靠控制.针对同时具有状态时滞和输入时滞的不确定离散系统,通过引入有增益变化的状态反馈控制器,给出了含有记忆和无记忆状态反馈鲁棒可靠控制器的存在条件.在H∞性能指标约束下,又给出了有外界扰动输入时含有记忆和无记忆状态反馈鲁棒H∞可靠控制器的设计方法.仿真结果表明了该方法的可行性.     

Stability and coefficients properites of polynomials of linear discrete systems

In this paper, by examining the coefficients of a given polynomial, we derive sufficient conditions for the zeros of the polynomial to be either inside the unit disk in the complex plane or at least one zero not inside the unit disk. The results are easily verifiable and provide handy ways of checking. Most results are proved using either Rouché's Theorem or fundamental mathematical ideas. Some of the results are extensions of known coefficient properties found in the literature.     

Influence of temperature at multiple discrete contacts on the frictional properties of slipping pairs with lubricant

The stochastic temperature field corresponding to temperature processes at the contact areas of rough surfaces in friction with lubricant is described in mathematical form. A relation is established between the stochastic temperature field and the frictional properties of the surfaces (the frictional coefficient). Practical recommendations are made for specific frictional pairs.     

Determination and adaptive correction of calibration intervals of measuring instruments and systems

Methods of analytic determination of calibration intervals for off-line measuring facilities and means of determining the calibration intervals by simulation for redundant measuring systems are discussed.     

A new hybrid approach to discrete multiple facility location problem

Locating certain facilities in predetermined sites is named the multiple facility location problems (MFLP). The objective of these kinds of problems is locating facilities to serve a given set of customers so that candidate sites and requirements are known. When the new facility sites have to be selected from a given set of candidate sites, the mentioned location problem becomes a discrete multiple facility location problem (DMFLP). In this paper, a special approach of DMFLP is considered where different multiple facilities have to be placed (location decision) and also customers have to be assigned to these facilities (allocation or assignment). The mathematical model of the proposed problem is developed, and with respect to the complexity of solving the mathematical model, especially in large scale, a new hybrid approach is proposed based on tabu search algorithm to solve the problem at each scale. Computational results on several randomly generated problems in comparison with a new proposed lower bound obtained from Lagrangian relaxation indicate that the proposed hybrid approach is both accurate and efficient.     

A geometrical interpretation of damping for discrete classically damped systems

A geometrical interpretation of complex eigenvalues for discrete classically damped systems is demonstrated. Systems with symmetric mass, stiffness, and damping matrices are considered. Graphical results are presented for mass-proportional, stiffness-proportional and for Rayleigh damping. The basic consequences of proportional damping are underlined.