Constructing Reachable Sets for Control Systems of Second
			Order of Accuracy with Respect to Time Step

A computational fluid dynamics (CFD) solver based on the gradient smoothing method (GSM) with moving mesh enabled is presented in this paper. The GSM uses unstructured meshes which could be generated and remeshed easily. The spatial derivatives of field variables at nodes and midpoints of cell edges are calculated using the gradient smoothing operations. The presented GSM codes use second-order Roes upwind flux difference splitting method and second-order 3-level backward differencing scheme for the compressible Navier–Stokes equations with moving mesh, and the second-order of accuracy for both the spatial and temporal discretization is ensured. The spatial discretization accuracy is verified using the method of manufactured solutions (MMS) on both structured and unstructured triangle meshes, and the results show that the observed order of accuracy achieves 2 even when highly distorted meshes are used. The temporal discretization accuracy is verified using the results with different time step lengths, and second-order accuracy is also obtained. Therefore, it is confirmed that the proposed GSM-CFD solver is a uniform second-order scheme.

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The phenomenon of the second order steady modes in the relay control systems with time delay

1997 European Control Conference (ECC) ◽

10.23919/ecc.1997.7082576 ◽

1997 ◽

Cited By ~ 2

Author(s):

L. M. Fridman ◽

E. M. Fridman ◽

E. I. Shustin

Keyword(s):

Time Delay ◽

Control Systems ◽

Second Order ◽

Relay Control

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A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2020-0009 ◽

2020 ◽

Vol 20 (4) ◽

pp. 769-782

Author(s):

Amiya K. Pani ◽

Vidar Thomée ◽

A. S. Vasudeva Murthy

Keyword(s):

Splitting Method ◽

Diffusion Problem ◽

Euler Method ◽

Second Order ◽

Time Step ◽

Convection Diffusion ◽

First Order ◽

Backward Euler ◽

Strang Splitting ◽

Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

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Controllability of impulsive second order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions

Applied Soft Computing ◽

10.1016/j.asoc.2015.10.006 ◽

2016 ◽

Vol 39 ◽

pp. 251-265 ◽

Cited By ~ 3

Author(s):

Mohit Kumar ◽

Sandeep Kumar

Keyword(s):

Control Systems ◽

Initial Conditions ◽

Second Order ◽

Nonlocal Initial Conditions

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Analysis of Reset Control Systems Consisting of a FORE and Second-Order Loop1

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1367335 ◽

2001 ◽

Vol 123 (2) ◽

pp. 279-283 ◽

Cited By ~ 36

Author(s):

Qian Chen ◽

Yossi Chait ◽

C. V. Hollot

Keyword(s):

Control Systems ◽

Closed Loop ◽

Second Order ◽

Step Response ◽

Steady State Response ◽

First Order ◽

State Response ◽

Loop Transfer Function ◽

Performance Specifications ◽

Reset Control

Reset controllers consist of two parts—a linear compensator and a reset element. The linear compensator is designed, in the usual ways, to meet all closed-loop performance specifications while relaxing the overshoot constraint. Then, the reset element is chosen to meet this remaining step-response specification. In this paper, we consider the case when such linear compensation results in a second-order (loop) transfer function and where a first-order reset element (FORE) is employed. We analyze the closed-loop reset control system addressing performance issues such as stability, steady-state response, and transient performance.

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