In this paper, the composite lining total safety factor design method based on load structure model was established, and the influence of different section shapes on safety was studied. The conclusions are as follows. (1) The representative value of surrounding rock pressure based on the elastoplastic theory is used as the design load, which is suitable for safety and economy. (2) The load structure models established in this paper can calculate the safety factors of shotcrete layer, bolt-surrounding rock bearing arch, anchor bolt and secondary lining, and can obtain the total safety factors of tunnel construction and operation period. (3) The height-span ratio can significantly affect the safety factor. (4) The influence of tunnel depth on surrounding rock pressure and safety factor is relatively large. It is suggested that the corresponding supporting parameters should be adopted according to different burial depths, so as to improve the economy.
Abstract Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.
The paper studies the behavior of multi-mode systems of the Moore-Greitzer model. Its main result is the existence of a parameterized nonlinear state feedback controller which stabilizes the system to the right of the peak of the compressor characteristic. In this process, a rotating stall envelope surface is discovered, and it is shown that the controller design achieves the tasks of preventing the closed-loop system from entering either rotating stall or surge, and making the closed-loop pressure rise coefficient be able to approach its maximum. Numerical simulations of the open-loop and closed-loop models are presented to illustrate the analysis and the results. [S0022-0434(00)00803-0]
In this paper, we introduce a new concept, [Formula: see text]-mean Li–Yorke chaotic operator, which includes the standard mean Li–Yorke chaotic operators as special cases. We show that when [Formula: see text] or [Formula: see text], [Formula: see text]-mean Li–Yorke chaotic dynamics is strictly stronger than the ones that appeared in mean Li–Yorke chaos. When [Formula: see text] or [Formula: see text], it has completely different characteristics from the mean Li–Yorke chaos. We prove that no finite-dimensional Banach space can support [Formula: see text]-mean Li–Yorke chaotic operators. Moreover, we show that an operator is [Formula: see text]-mean Li–Yorke chaos if and only if there exists an [Formula: see text]-mean semi-irregular vector for the underlying operator, and if and only if there exists an [Formula: see text]-mean irregular vector when [Formula: see text], which generalizes the recent results by Bernardes et al. given in 2018. When [Formula: see text], we construct a counterexample in which it is an [Formula: see text]-mean Li–Yorke chaotic operator but does not admit an [Formula: see text]-mean irregular vector. In addition, we show that an operator with dense generalized kernel is [Formula: see text]-mean Li–Yorke chaotic if and only if there exists a residual set of [Formula: see text]-mean irregular vectors, and if and only if there exists an [Formula: see text]-mean unbounded orbit.
We extend our recent results (2001, 2002) to the design of reduced-order observers for nonlinear systems. The approach method is to use the change of coordinates, which is based on the solution of a system of first-order nonlinear PDEs. The sufficient condition for the solution of the PDEs is provided under very general conditions. The approach is also applicable when the system is only detectable. The method proposed in this paper is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics.
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