A Remark on “A New Partial Differential Equation for the Stability Analysis of Time Invariant Control Systems”

1963 ◽  
Vol 1 (3) ◽  
pp. 369-376
Author(s):  
G. P. Szegö ◽  
G. R. Geiss
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stability Analysis ◽  
Control Systems ◽  
Partial Differential ◽  
The Stability ◽  
Invariant Control ◽  
Time Invariant

scholarly journals An active electromagnetic stabilization of the Leipholz column

2012 ◽  
Vol 22 (2) ◽  
pp. 161-174 ◽  
Author(s):  
Tomasz Szmidt ◽  
Piotr Przybyłowicz
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Control System ◽  
Control Systems ◽  
Transverse Displacement ◽  
Safe Operation ◽  
Electromagnetic Actuators ◽  
Active Stabilization ◽  
The Stability ◽  
Galerkin's Procedure

An active electromagnetic stabilization of the Leipholz column We study the application of electromagnetic actuators for the active stabilization of the Leipholz column. The cases of the compressive and tensional load of the column placed in air and in water are considered. The partial differential equation of the column is discretized by Galerkin's procedure, and the stability of the obtained control system is evaluated by the eigenvalues of its linearization. Four different methods of active stabilization are investigated. They incorporate control systems based on feedback proportional to the transverse displacement of the column, its velocity and the current in the electromagnets. Conditions in which these strategies are effective in securing safe operation of the column are discussed in detail.

scholarly journals Numerical methods for the multiplicative partial differential equations

2017 ◽  
Vol 15 (1) ◽  
pp. 1344-1350
Author(s):  
Muhammet Yazıcı ◽  
Harun Selvitopi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Error Estimation ◽  
Truncation Error ◽  
Numerical Solutions ◽  
Partial Differential ◽  
The Matrix ◽  
The Stability ◽  
Truncation Error Estimation

Abstract We propose the multiplicative explicit Euler, multiplicative implicit Euler, and multiplicative Crank-Nicolson algorithms for the numerical solutions of the multiplicative partial differential equation. We also consider the truncation error estimation for the numerical methods. The stability of the algorithms is analyzed by using the matrix form. The result reveals that the proposed numerical methods are effective and convenient.

PID Control System for a Distributed Parameter Process

2014 ◽  
Vol 555 ◽  
pp. 222-231 ◽  
Author(s):  
Mihaela Ligia Ungureşan ◽  
Vlad Mureşan
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Control System ◽  
Control Systems ◽  
Pid Control ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Pid Algorithm

This paper presents the numerical simulation of a control system, with PID algorithm, for a process modeled through a partial differential equation of second order (PDE II.2), with respect to time (t) and to a spatial variable (p). Because these types of control systems are less usual, this paper develops a case study, with a program run on the computer. The details of using the PID control are pointed out, for an example of a system which contains a process with PDE II.2 structure.

scholarly journals Analytical Solution and Application for One-Dimensional Consolidation of Tailings Dam

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hai-ming Liu ◽  
Gan Nan ◽  
Wei Guo ◽  
Chun-he Yang ◽  
Chao Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Great Influence ◽  
Tailings Dam ◽  
Partial Differential ◽  
One Dimensional ◽  
The Stability

The pore water pressure of tailings dam has a very great influence on the stability of tailings dam. Based on the assumption of one-dimensional consolidation and small strain, the partial differential equation of pore water pressure is deduced. The obtained differential equation can be simplified based on the parameters which are constants. According to the characteristics of the tailings dam, the pore water pressure of the tailings dam can be divided into the slope dam segment, dry beach segment, and artificial lake segment. The pore water pressure is obtained through solving the partial differential equation by separation variable method. On this basis, the dissipation and accumulation of pore water pressure of the upstream tailings dam are analyzed. The example of typical tailings is introduced to elaborate the applicability of the analytic solution. What is more, the application of pore water pressure in tailings dam is discussed. The research results have important scientific and engineering application value for the stability of tailings dam.

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