Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

2006 ◽  
Vol 2 (1) ◽  
pp. 32-39 ◽  
Author(s):  
N. J. Peruzzi ◽  
J. M. Balthazar ◽  
B. R. Pontes ◽  
R. M. L. R. F. Brasil
Keyword(s):  
Equations Of Motion ◽  
Periodic Problem ◽  
Dc Motor ◽  
Transportation System ◽  
Stability Diagrams ◽  
Dynamics And Control ◽  
The Stability ◽  
Load Transportation ◽  
And Control ◽  
The Mathematical Model

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor. The governing equations of motion were derived via Lagrange’s equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial expansion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha’s theory.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

2011 ◽  
Vol 52-54 ◽  
pp. 13-18 ◽  
Author(s):  
Fábio Roverto Chavarette ◽  
Nelson José Peruzzi ◽  
José Manoel Balthazar ◽  
Luciano Barbanti ◽  
Berenice Carmargo Damasceno
Keyword(s):  
Inverted Pendulum ◽  
Equations Of Motion ◽  
Periodic Problem ◽  
Dc Motor ◽  
Transportation System ◽  
Linear Control ◽  
Governing Equations ◽  
Optimal Linear ◽  
Load Transportation ◽  
The Mathematical Model

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange’s equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

scholarly journals A unified approach to rigid body rotational dynamics and control

2011 ◽  
Vol 468 (2138) ◽  
pp. 395-414 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Aaron D. Schutte
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Equations Of Motion ◽  
Fundamental Equation ◽  
Rotational Dynamics ◽  
Constrained Motion ◽  
Dynamics And Control ◽  
Common Framework ◽  
The Stability ◽  
And Control

This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.

On a Control of a Non-Ideal Mono-Rail System With Periodic Coefficients

2005 ◽  
Author(s):  
N. J. Peruzzi ◽  
J. M. Balthazar ◽  
B. R. Pontes
Keyword(s):  
Iterative Method ◽  
Inverted Pendulum ◽  
Periodic Problem ◽  
Periodic Systems ◽  
Lagrange Equations ◽  
Floquet Multipliers ◽  
Stability Diagrams ◽  
Rail System ◽  
The Stability ◽  
And Control

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F transformation). This method was presented recently in [3–9].

Load transportation system based on autonomous small size helicopters

2010 ◽  
Vol 114 (1153) ◽  
pp. 191-198 ◽  
Author(s):  
M. Bernard ◽  
K. Kondak ◽  
G. Hommel
Keyword(s):  
Controller Design ◽  
Transportation System ◽  
Full Size ◽  
Distributed Sensor ◽  
Real World Application ◽  
Non Linear ◽  
Full Form ◽  
Space Limitation ◽  
Load Transportation ◽  
And Control

Abstract This paper is devoted to modelling and control algorithms for a slung load transportation system composed of one or multiple helicopters, where the load is coupled by the means of flexible ropes (see Fig. 1). The coupled helicopter system overcomes the payload limitation of a single small size helicopter, while keeping most of its advantages: small costs of operation, low maintenance costs and increased safeness. Therefore, the system can be utilised whenever the use of full size helicopters is impossible, too expensive or prohibited by law. We focus on the deployment and repairing of distributed sensor networks, using a transportation system based on multiple small size helicopters. A possible real world application is the deployment of fire fighting equipment, where space limitation of the fire trucks prohibits the application of bigger UAVs and using full size helicopters is too dangerous. The problem of load transportation using one or two full size helicopters (twin lift helicopter system), connected to the load by means of flexible ropes, has been discussed in the aerospace research community at least since 1960. We have shown in our previous work that there is a fundamental difference in the mathematical description between small and full size helicopters. Therefore, also the control design for the case of small size helicopters needs to be different. To our knowledge, the control of a slung load transportation system composed of multiple small size helicopters has not been studied until now. In this paper, the complete mechanical setup of the slung load transportation system based on one or more small size helicopters is presented. This includes a short description of the used UAVs, the additionally required sensors, and how the load is mounted. A model of one/multiple helicopters transporting a load is introduced. This model is used in a simplified form for the controller design and in full form for simulation. The controller for one and two helicopters, which is based on a state feedback controller, as well as the controller for three and more helicopters, which is based on a non linear controller, are explained in detail. Both controllers utilise an underlying non-linear orientation controller. We propose a feedback loop, based on forces measured in the ropes, to compensate for the influence of the rope. The controllers were tested in simulation and in real flight experiments. The world wide first flight experiment with three coupled helicopters was successfully conducted at the end of 2007.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

The Working Mechanism and Control Method of GL160C Metal Belt CVT

2010 ◽  
Vol 139-141 ◽  
pp. 1856-1859
Author(s):  
Lei Zhang ◽  
Xiu Min Yang ◽  
Tao Wei ◽  
Ying Di Shi
Keyword(s):  
Control Method ◽  
Bench Test ◽  
Speed Ratio ◽  
Clamping Force ◽  
Working Mechanism ◽  
Variable Transmission ◽  
Vehicle Test ◽  
The Stability ◽  
And Control ◽  
The Mathematical Model

On the foundation of the analysis of the working mechanism of the GL160C continuously variable transmission (CVT), the mathematical model of the axial clamping force of the driving and driven pulleys are constructed. The relationship between the pressure of the driving and driven cylinders and the speed ratio of the CVT are derived while the CVT is transmitting the unit torque. The control method of the axial clamping force between the driving and driven pulleys, the control model of the CVT speed ratio are given. The following conclusions are drawn from the bench test and integral vehicle test: the acceleration performance and the stability of the speed ratio of the GL160C CVT are good, the power output is stable and reliable, the controller could achieve every functional requirement, all of which could guarantee that the output of the engine could run as the designed ideal dynamic curve and the ideal economical curve.

Dynamics of Elastic Manipulators With Prismatic Joints

1992 ◽  
Vol 114 (1) ◽  
pp. 41-49 ◽  
Author(s):  
K. W. Buffinton
Keyword(s):  
Equations Of Motion ◽  
Elastic Beam ◽  
Alternative Form ◽  
Specific System ◽  
Beam Equations ◽  
Prismatic Joints ◽  
Dynamics And Control ◽  
And Control ◽  
Two Degree Of Freedom ◽  
Elastic Beam Equations

The purpose of this investigation is to study the formulation of equations of motion for flexible robots containing translationally moving elastic members that traverse a finite number of distinct support points. The specific system investigated is a two-degree-of-freedom manipulator whose configuration is similar to that of the Stanford Arm and whose translational member is regarded as an elastic beam. Equations of motion are formulated by treating the beam’s supports as kinematical constraints imposed on an unrestrained beam, by discretizing the beam by means of the assumed modes technique, and by applying an alternative form of Kane’s method which is particularly well suited for systems subject to constraints. The resulting equations are programmed and are used to simulate the system’s response when it performs tracking maneuvers. The results provide insights into some of the issues and problems involved in the dynamics and control of manipulators containing highly elastic members connected by prismatic joints.

scholarly journals ANALYZE THE EFFECT OF TIME DELAY ON THE STABILITY OF HYBRID ACTIVE POWER FILTER

2022 ◽  
Vol 36 (06) ◽  
Author(s):  
CHAU MINH THUYEN
Keyword(s):  
Time Delay ◽  
Active Power Filter ◽  
Active Power ◽  
Practical Significance ◽  
Stable Domain ◽  
Power Filter ◽  
Hybrid Active Power Filter ◽  
The Stability ◽  
And Control ◽  
The Mathematical Model

Hybrid Active Power Filter (HAPF) has highly effective in improving the power quality of power system. In this paper, a stable analysis of HAPF considering the time delay was made. The mathematical model of HAPF with time delay has been established. Based on that, the stable domain of the HAPF parameters was determined based on the Routh’s stability standard. Simulation results based on Matlab software have shown that: time delay has a marked impact on the stability of the HAPF system. This research has practical significance in the design and control of HAPF in real system.

Flight mechanics of a free-wing tilt-body aircraft

2008 ◽  
Vol 112 (1137) ◽  
pp. 625-640
Author(s):  
K. Ro ◽  
J. W. Kamman ◽  
J. B. Barlow
Keyword(s):  
Mathematical Model ◽  
Incidence Angle ◽  
Equations Of Motion ◽  
Dynamic Modelling ◽  
Flight Simulation ◽  
The Body ◽  
Flight Mechanics ◽  
Short Takeoff And Landing ◽  
And Control ◽  
The Mathematical Model

Abstract The free-wing tilt-body aircraft refers to a vehicle configuration in which the wing, fuselage, and empennage are in a longitudinally articulated connection. This allows the main wing to freely rotate relative to the body, while the empennage, which is in the form of a long twin boom connected to the rear of the body, changes its incidence angle relative to the body in response to external commands. The principal advantages claimed for the configuration are short takeoff and landing capability, and reduced gust sensitivity. The aerodynamics of the free-wing tilt-body configuration has been previously studied, but analysis of its flight mechanics is limited. In this paper we present derivations of the flight dynamic equations of motion using multi-body dynamic modelling techniques, and combine the resulting equations of motion with experimental aerodynamic data to achieve a nonlinear mathematical model for flight simulation of a generic free-wing tilt-body vehicle. The mathematical model is suitable for the study of detailed dynamic characteristics as well as for model based control law synthesis. Key flight performance, and stability and control characteristics of a generic configuration are obtained from the mathematical model.

Dynamic Stability Characteristics of Axially Accelerated Beams

2006 ◽  
Vol 321-323 ◽  
pp. 1654-1658 ◽  
Author(s):  
Hong Hee Yoo ◽  
Sung Jin Eun
Keyword(s):  
Dynamic Stability ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Stability Diagram ◽  
Accelerated Motion ◽  
Stability Diagrams ◽  
Divergence Type ◽  
The Stability ◽  
Direct Numerical Integration ◽  
Free Beam

Dynamic stability of axially accelerated beams is investigated in this paper. The equations of motion of a fixed-free beam undergoing axially accelerated motion are derived. Unstable regions due to the acceleration are obtained by using the Floquet’s theory. Stability diagrams are presented to illustrate the influence of the acceleration characteristics. Large unstable regions of flutter type instability exist around the first, twice the first, and twice the second bending natural frequencies. Divergence type instability also occurs when the acceleration exceeds a certain value. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

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