Reference governors and maximal output admissible sets for linear periodic systems

ABSTRACT

In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we introduce the periodic-invariant maximal output admissible sets for LP systems. We extend the earlier results in the literature to Lyapunov stable LP systems with output constraints, which arise in RG applications. We show that, while the invariant sets for these systems may not be finitely determined, a finitely-determined inner approximation, which is periodically invariant, can be obtained by constraint tightening. We then analyze the geometric and algebraic relationship between these sets and show that these sets are related via simple transformations, implying that it suffices to compute only one of them for real-time applications. This greatly reduces the memory burden of RG (or other similar constraint management strategies), at the expense of an increase in processing requirements. We present a thorough analysis of this trade-off. In the second part of this paper, we present two RG formulations, and discuss their properties and algorithms for their computation. Numerical simulations demonstrate the efficacy of the approach.     

The periodic system and the idea of a chemical element: From Mendeleev to superheavy elements

Like other scientific concepts, the idea of a chemical element has changed considerably over time, since it was first established in the Enlightenment era. In Dmitri Mendeleev's construction of the periodic system, he distinguished between simple substances and elements as defined by their atomic weights. The foundation of the periodic system on the latter concept led to several challenges. For example, the system seemed unable to accommodate the radioactive substances eventually recognised as isotopes. Around 1920, elements were consequently redefined in terms of their atomic numbers, a nuclear property that could be determined by X‐ray spectroscopy. Although this understanding of an element has stood the test of time, new questions turned up relating to the concept of an element following the syntheses of transuranic elements since the early 1940s. These syntheses of very heavy elements have additionally led chemists and physicists to reconsider the criteria for the discovery of a new element. Recently, elements have been officially recognised on the sole ground that a small number of very heavy atomic nuclei were identified. The paper discusses how the notion of an element was modified during different periods of time, the reasons for the modifications, and the values ascribed to them in the communities of chemists and physicists.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Drying kinetics of poplar lumber during periodic hot-press drying

The drying kinetics of poplar lumber was experimentally investigated as a function of drying temperature (115, 135, 160, 185 and 205°C) during a periodic hot-press-drying process. Poplar lumber was dried under contact (compression ratio of 10%) and high-press states (compression ratio of 44%). Compared with the contact-state, the high-press-state showed higher drying rate and higher efficiency of removing free water than bound water in wood. Eight mathematical models from the literature were established to analyze the drying behavior. The Weibull model, with an average determination coefficient R² of 0.9958, fitted well for all applied drying conditions. The scale parameter decreased with increasing drying temperature and was lower for high-press-state drying compared with that for contact-state drying. Moisture diffusivity and activation energy were calculated according to the Weibull model. Diffusivity increased with increasing drying temperature, with the average value of 1.734?×?10^?6 and 3.313?×?10^?6?m²/s and activation energy of 34.79 and 32.85?kJ/mol for contact-state drying and high-press-state drying, respectively. Hot-press drying created an M-shaped curve of density distribution, with high density at the two surface regions gradually decreasing toward the core region. The contact state-dried wood showed increased density near the wood surface. Both average density and peak density improved in the case of high-press-state-dried wood. Furthermore, the hydrophilic index of wood for high-press-state drying was lower than that of the contact-state drying, and the opposite was true regarding crystallinity index. The hygroscopicity of high-press-dried poplar decreased with lower equilibrium moisture content and higher moisture excluding efficiency, compared with contact-state-dried poplar. The rapid, high-quality drying of poplar lumber through periodic hot-press was more potentially achieved by the high-press-state compared with contact-state drying.     

薄煤层坚硬顶板的薄板理论分析及来压预报

在用薄板理论分析白腊坪煤矿K13煤层顶板的应力分布规律的基础上，根据最大拉应力强度理论建立顶板初次及周期来压步距的计算式，利用该计算式在现场实施顶板来压预报结果表明，用薄板理论研究薄煤层坚硬顶板的应力分布规律是合理的。     

基于库存ABC分类法的矿山企业物料管理

针对矿山企业库存管理中存在的典型问题,采用库存ABC分类法将物料进行分类,从而分清物料的主次关系。对不同物料采用定量、定期储备等方法,实行ABC物料管理法。并结合矿山企业供应市场复杂度和物料价值将库存ABC方法进行改进,进一步合理划分物料。从而降低了库存管理成本。     

地音监测技术及其在矿压监测中的应用研究

在总结我们的研究成果基础上，较全面地介绍了我国地音监测技术的研究现状及其在冲击地压预测预报、顶板动态监测方面的应用实践。研究与实践的结果表明，经过１０多年的研究和应用，我国地音监测技术获得了很大发展，地音监测技术在矿压中的应用已达到了实用阶段。     

Growth and control of filamentous microbes in activated sludge: an integrated hypothesis

Since its initial development and application, the activated sludge process has undergone a continual evolution aimed at maximizing process efficiency and controlling population selection. Organic loading rate, dissolved oxygen concentration and reactor configuration have been implicated as key process variables affecting sludge settleability, their combined effects determining which microbe or microbes are best able to grow and survive in a given system. Using available pure and mixed culture observations, a conceptual hypothesis centered around three model organisms has been developed to explain the growth and control of filamentous organisms in activated sludge. Organism selection in continuously fed systems has been hypothesized to be dominated by filamentous organisms with high sustainable growth rates at low reactor substrate concentrations/organic loading rates and filaments best able to compete for dissolved oxygen at elevated reactor substrate concentrations/organic loading rates. Intermittently fed systems, on the other hand, enrich for nonfilamentous organisms which both rapidly extract substrate from solution and maintain peak activity during extended periods of endogeneous metabolism. While both types of reactor induced feeding patterns can control filamentous organism growth, intermittently fed systems are capable of operation over a wider range of operating conditions by accentuating differences in organism physiology. Additional selection pressures such as substrate composition, non-ideal reactor hydraulics and time-variable influent waste streams were also discussed in relation to their impact on idealized systems.     

概周期过程周期初态的虚拟寻优法

概周期过程最优控制的核心是周期初态的寻优。本文提出一种虚拟寻优法,再配之以周期之间适当的状态连接,既大大减少了计算量和存贮量,又收到了较好的优化效果。水厂最优控制的仿真验证了本文方法的有效性。