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 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.

SYSTEM CHARACTERISTICS OF DISTRIBUTED PARAMETER SYSTEMS

2020 ◽  
Vol 70 (3) ◽  
pp. 34-44
Author(s):  
Kamen Perev
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Initial Conditions ◽  
Distributed Parameter Systems ◽  
Point Of View ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Special Cases ◽  
The Green Function ◽  
Set Up

The paper considers the problem of distributed parameter systems modeling. The basic model types are presented, depending on the partial differential equation, which determines the physical processes dynamics. The similarities and the differences with the models described in terms of ordinary differential equations are discussed. A special attention is paid to the problem of heat flow in a rod. The problem set up is demonstrated and the methods of its solution are discussed. The main characteristics from a system point of view are presented, namely the Green function and the transfer function. Different special cases for these characteristics are discussed, depending on the specific partial differential equation, as well as the initial conditions and the boundary conditions.

Exact and approximate controllability for distributed parameter systems

Acta Numerica ◽  
1994 ◽  
Vol 3 ◽  
pp. 269-378 ◽  
Author(s):  
R. Glowinski ◽  
J.L. Lions
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Controllability ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Control Functions

We consider a system whose state is given by the solution y to a Partial Differential Equation (PDE) of evolution, and which contains control functions, denoted by v.

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