Conservation Laws -- a Source for Distortionless Propagation and Time Delays

2021 ◽  
Vol 1 (2) ◽  
pp. 1-11
Author(s):  
Vladimir Rasvan
Keyword(s):  
Conservation Laws ◽  
Transmission Lines ◽  
Time Delays ◽  
Functional Equations ◽  
Neutral Type ◽  
Initial Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Control Approach ◽  
Dynamics And Control ◽  
And Control

Since the very first paper of J. Bernoulli in 1728, a connection exists between initial boundary value problems for hyperbolic Partial Differential Equations (PDE) in the plane (with a single space coordinate accounting for wave propagation) and some associated Functional Equations (FE). From the point of view of dynamics and control (to be specific, of dynamics for control) both type of equations generate dynamical and controlled dynamical systems. The functional equations may be difference equations (in continuous time), delay-differential (mostly of neutral type) or even integral/integro-differential. It is possible to discuss dynamics and control either for PDE or FE since both may be viewed as self contained mathematical objects. A more recent topic is control of systems displaying conservation laws. Conservation laws are described by  nonlinear hyperbolic PDE belonging to the class ``lossless'' (conservative); their dynamics and control theory is well served by the associated energy integral. It is however not without interest to discuss association of some FE. Lossless implies usually distortionless propagation hence one would expect here also lumped time delays. The paper contains some illustrating applications from various fields: nuclear reactors with circulating fuel, canal flows control, overhead crane, drilling devices, without forgetting the standard classical example of the nonhomogeneous transmission lines for distortionless and lossless propagation. Specific features of the control models are discussed in connection with the control approach wherever it applies.

Electrospinning Nanofibers: Measurements, Dynamics, and Control Strategy Development

2014 ◽  
Author(s):  
Yunshen Cai ◽  
Michael Gevelber
Keyword(s):  
Controller Design ◽  
Fiber Diameter ◽  
Operating Regime ◽  
Strategy Development ◽  
Process Conditions ◽  
Control Approach ◽  
Process Dynamics ◽  
Wide Range ◽  
Dynamics And Control ◽  
And Control

Electrospinning produces submicron fibers for a variety of applications using a wide range of polymers. Achieving the desired fiber diameter, maximizing productivity, and minimizing variation are important production objectives. This paper addresses several important areas needed to develop a general electrospinning control approach including: developing a correlation between measurements, process conditions, and the resulting fiber diameter, developing a method to determine an operating regime that meets manufacturing objectives, and identifying process dynamics for controller design.

Dynamics and Control of a Helicopter Carrying a Payload Using a Cable-Suspended Robot

2005 ◽  
Author(s):  
So-Ryeok Oh ◽  
Ji-Chul Ryu ◽  
Sunil K. Agrawal
Keyword(s):  
Control Method ◽  
Dual System ◽  
Robust Controller ◽  
Robot System ◽  
Control Approach ◽  
Cable Robot ◽  
Dynamics And Control ◽  
Position And Orientation ◽  
And Control ◽  
Scale Control

This paper presents a study of the dynamics and control of a helicopter carrying a payload through a cable-suspended robot. The helicopter can perform gross motion, while the cable suspended robot underneath the helicopter can modulate a platform in position and orientation. Due to the under-actuated nature of the helicopter, the operation of this dual system consisting of the helicopter and the cable robot is challenging. We propose here a two time scale control method, which makes it possible to control the helicopter and the cable robot independently. In addition, this method provides an effective estimation on the bound of the motion of the helicopter. Therefore, even in the case where the helicopter motion is unknown, the cable robot can be stabilized by implementing a robust controller. Simulation results of the dual system show that the proposed control approach is effective for such a helicopter-robot system.

scholarly journals Control of Conservation Laws – An Application

2018 ◽  
Vol 71 (1) ◽  
pp. 155-174
Author(s):  
Vladimir Răsvan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Power Plants ◽  
Main Tool ◽  
Nonlinear Boundary Conditions ◽  
Point Of View ◽  
Hyperbolic Partial Differential Equations ◽  
Hydroelectric Power ◽  
And Control

Abstract We present here three types of controlled boundary value problems for conservation laws arising from energy co-generation, hydraulic flows and water hammer for hydroelectric power plants and control of the open channel flows (shallow water). The novelty of these models, from the mathematical point of view, is that they are described by nonlinear hyperbolic partial differential equations of the conservation laws with (possibly) nonlinear boundary conditions. At their turn these boundary conditions are controlled by some systems of ordinary differential equations. The engineering requirements for such systems are asymptotic stability and disturbance rejection: these properties have to be achieved by feedback control. In our setting the main tool for tackling these problems is a suitable Lyapunov functional arising from the energy identity. The hints for “guessing” this functional are to be found in the linearized version of the aforementioned mathematical objects.

Nonlinear Dynamics and Control of the Scan Process in Noncontacting Atomic Force Microscopy

2005 ◽  
Author(s):  
S. Hornstein ◽  
O. Gottlieb ◽  
L. Ioffe
Keyword(s):  
Nonlinear Dynamics ◽  
Atomic Force Microscopy ◽  
Numerical Study ◽  
Initial Boundary ◽  
Atomic Interaction ◽  
Force Microscopy ◽  
Atomic Force ◽  
Dynamics And Control ◽  
And Control ◽  
Nonlinear Dynamics And Control

The focus of this paper is on the nonlinear dynamics and control of the scan process in noncontacting atomic force microscopy. An initial-boundary-value problem is consistently formulated to include both nonlinear dynamics of a microcantilever with a localized atomic interaction force for the surface it is mapping, and a horizontal boundary condition for a constant scan speed and its control. The model considered is obtained using the extended Hamilton’s principle which yields two partial differential equations for the combined horizontal and vertical motions. Isolation of a Lagrange multiplier describing the microbeam fixed length enables construction of a modified equation of motion which is reduced to a single mode dynamical system via Galerkin’s method. The analysis includes a numerical study of the strongly nonlinear system leading to a stability map describing an escape bifurcation threshold where the tip, at the free end of the microbeam, ‘jumps-to-contact’ with the sample. Results include periodic ultrasubharmonic and quasiperiodic solutions corresponding to primary and secondary resonances.

On Dynamics and Control of Multi-Link Flexible Manipulators

1995 ◽  
Vol 117 (2) ◽  
pp. 134-142 ◽  
Author(s):  
W. Gawronski ◽  
C.-H. C. Ih ◽  
S. J. Wang
Keyword(s):  
Rigid Body ◽  
Inverse Dynamics ◽  
Linear Time ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Link Length ◽  
Joint Torques ◽  
Control Approach ◽  
Dynamics And Control ◽  
And Control

This paper presents solutions of dynamics, inverse dynamics, and control problems of multi-link flexible manipulators. In deriving the manipulator dynamics, flexible deformations are assumed to be small in relation to the link length, angular rates of the links are assumed to be much smaller than their fundamental frequencies, and nonlinear terms (centrifugal and Coriolis forces) in the flexible manipulator model are assumed to be the same as those in the rigid body model. Flexible displacements are measured with respect to the rigid body configuration, obtained from its rigid body inverse kinematics. As a result, a linear time-varying system is obtained. The inverse dynamics problem consists of determination of joint torques for a given tip trajectory such that joint angles in the flexible configuration are equal to the angles in the rigid body configuration. The manipulator control system consists of the feedforward compensation and feedback control loops. Simulation results of a two-link space crane with a large payload show that the performance of this linearized dynamics and control approach is accurate, and at the same time is robust when subjected to parameter variations during slew operations.

scholarly journals Dynamics and Control of a Free-Piston Diesel Engine

2003 ◽  
Vol 125 (3) ◽  
pp. 468-474 ◽  
Author(s):  
Tor A. Johansen ◽  
Olav Egeland ◽  
Erling Aa. Johannessen ◽  
Rolf Kvamsdal
Keyword(s):  
Diesel Engine ◽  
Control Structure ◽  
Piston Motion ◽  
Free Piston ◽  
Control Approach ◽  
Engine Design ◽  
Dynamics And Control ◽  
Scale Test ◽  
Freely Moving ◽  
And Control

Free-piston diesel engines are characterized by freely moving pistons without any crankshaft or camshaft connected to the pistons. This allows a compact and efficient engine design, but requires automatic control of the piston motion. This paper present a dynamic mathematical model of a free-piston diesel engine, and a control oriented dynamic analysis leading to a piston motion control structure. Experimental results using a full scale test cylinder are included and show feasibility of the suggested control approach.

Dynamics and Control of a Helicopter Carrying a Payload Using a Cable-Suspended Robot

2005 ◽  
Vol 128 (5) ◽  
pp. 1113-1121 ◽  
Author(s):  
So-Ryeok Oh ◽  
Ji-Chul Ryu ◽  
Sunil K. Agrawal
Keyword(s):  
Control Method ◽  
Dual System ◽  
Robust Controller ◽  
Robot System ◽  
Control Approach ◽  
Cable Robot ◽  
Dynamics And Control ◽  
Position And Orientation ◽  
And Control ◽  
Scale Control

In this paper we present a study of the dynamics and control of a helicopter carrying a payload through a cable-suspended robot. The helicopter can perform gross motion, while the cable suspended robot underneath the helicopter can modulate a platform in position and orientation. Due to the underactuated nature of the helicopter, the operation of this dual system consisting of the helicopter and the cable robot is challenging. We propose here a two time scale control method, which makes it possible to control the helicopter and the cable robot independently. In addition, this method provides an effective estimation on the bound of the motion of the helicopter. Therefore, even in the case where the helicopter motion is unknown, the cable robot can be stabilized by implementing a robust controller. Simulation results of the dual system show that the proposed control approach is effective for such a helicopter-robot system.

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