On the Dynamics of an Inverted Flexible Pendulum With Tip Mass on a Cart

2012 ◽  
Author(s):  
Prasanna Gandhi ◽  
Ojas Patil
Keyword(s):  
Vertical Plane ◽  
Superior Performance ◽  
Positioning Systems ◽  
Proposed Model ◽  
Dynamics And Control ◽  
Stable Equilibria ◽  
Compact Design ◽  
And Control ◽  
Tip Mass ◽  
Method Approach

Flexible link systems are increasingly becoming popular for their superior performance in micro/nano positioning and several other advantages including less weight, compact design, lower power requirements and so on as compared to other precision micro-positioning systems. The dynamics and control of such systems is challenging, especially for cases where the system is in the vertical plane. A representative case, inverted flexible pendulum on cart system, is considered in this paper. A dynamic model for flexible pendulum with tip mass has been developed using the Euler Lagrange energy method with constraints for large deflection bending. The assumed modes method approach is used to represent significant contribution to dynamics by finite number of modes. For a lower tip mass, only one stable equilibrium in the center exists; however for higher mass this equilibrium becomes unstable and two stable equilibria on side emerge. An experimental setup of the system has also been developed and it is clear by measuring strain at the base of the pendulum that the nonlinear dynamics is captured well in the proposed model.

Robust Stabilization of Large Amplitude Ship Rolling in Beam Seas

1997 ◽  
Vol 122 (1) ◽  
pp. 108-113 ◽  
Author(s):  
Shyh-Leh Chen ◽  
Steven W. Shaw ◽  
Hassan K. Khalil ◽  
Armin W. Troesch
Keyword(s):  
Large Amplitude ◽  
Controller Design ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Vertical Plane ◽  
Singularly Perturbed Systems ◽  
Strongly Nonlinear ◽  
Beam Seas ◽  
Dynamics And Control ◽  
And Control

The dynamics and control of a strongly nonlinear 3-DOF model for ship motion are investigated. The model describes the roll, sway, and heave motions occurring in a vertical plane when the vessel is subjected to beam seas. The ship is installed with active antiroll tanks as a means of preventing large amplitude roll motions. A robust state feedback controller for the pumps is designed that can handle model uncertainties, which arise primarily from unknown hydrodynamic loads. The approach for the controller design is a combination of sliding mode control and composite control for singularly perturbed systems, with the help of the backstepping technique. It is shown that this design can effectively control roll motions of large amplitude, including capsize prevention. Numerical simulation results for an existing fishing vessel, the twice-capsized Patti-B, are used to verify the analysis. [S0022-0434(00)02701-5]

On the Dynamics and Multiple Equilibria of an Inverted Flexible Pendulum With Tip Mass on a Cart

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Ojas Patil ◽  
Prasanna Gandhi
Keyword(s):  
Dynamic Model ◽  
Multiple Equilibria ◽  
Chaotic Behavior ◽  
Elastic Beam ◽  
Superior Performance ◽  
Flexible Link ◽  
Equilibrium Solutions ◽  
Lagrange Formulation ◽  
Compact Design ◽  
Tip Mass

Flexible link systems are increasingly becoming popular for advantages like superior performance in micro/nanopositioning, less weight, compact design, lower power requirements, and so on. The dynamics of distributed and lumped parameter flexible link systems, especially those in vertical planes are difficult to capture with ordinary differential equations (ODEs) and pose a challenge to control. A representative case, an inverted flexible pendulum with tip mass on a cart system, is considered in this paper. A dynamic model for this system from a control perspective is developed using an Euler Lagrange formulation. The major difference between the proposed method and several previous attempts is the use of length constraint, large deformations, and tip mass considered together. The proposed dynamic equations are demonstrated to display an odd number of multiple equilibria based on nondimensional quantity dependent on tip mass. Furthermore, the equilibrium solutions thus obtained are shown to compare fairly with static solutions obtained using elastica theory. The system is demonstrated to exhibit chaotic behavior similar to that previously observed for vibrating elastic beam without tip mass. Finally, the dynamic model is validated with experimental data for a couple of cases of beam excitation.

Dynamics and Control of a Translating Flexible Beam With a Prismatic Joint

1992 ◽  
Vol 114 (3) ◽  
pp. 422-427 ◽  
Author(s):  
Sivakumar S. K. Tadikonda ◽  
Haim Baruh
Keyword(s):  
Rigid Body ◽  
The Other ◽  
Body Motion ◽  
Rigid Base ◽  
Flexible Beam ◽  
Positioning Control ◽  
Dynamics And Control ◽  
And Control ◽  
Tip Mass ◽  
Free Beam

The complete dynamic model of a translating flexible beam, with a tip mass at one end and emerging from or retracting into a rigid base at the other, is presented. The model considers the effect of elastic and translational motions of the beam on each other. The properties of the eigenfunctions of a fixed-free beam are exploited to obtain closed-form expressions for several domain integrals that arise in the model. It is shown that neglecting the effect of elastic motion on the rigid body motion leads to inaccuracies in positioning control. Issues associated with the feedback control of such a beam are discussed.

Dynamics and Control of Vertical-Plane Motion for an Electrohydraulically Actuated Single-Flexible-Link Arm

1992 ◽  
Vol 114 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Liang-Wey Chang
Keyword(s):  
Motion Tracking ◽  
Inverse Dynamics ◽  
Low Cost ◽  
Vertical Plane ◽  
Plane Motion ◽  
Flexible Link ◽  
Actuator Dynamics ◽  
Nonlinear Motion ◽  
Dynamics And Control ◽  
And Control

A research tool was developed for the dynamics and control of a single-flexible-link arm based on the Equivalent Rigid Link System (ERLS) dynamic model and the inverse dynamics of the arm and the actuator. The arm moved in a vertical plane and was actuated by an electrohydraulic motor. The required torque was computed based on the inverse dynamics of the ERLS model. The driving current was then predicted by the inverse actuator dynamics. This paper also presents a 16-bit microcomputer-based low-cost implementation of a nonlinear motion tracking control. The dynamic behavior of the control system was studied through the computer simulation and the experiment. Furthermore, the superiority of the flexible-body control was also proved through the comparison to the rigid-body control.

PROJECT ON ELECTRONIC STEERING SYSYTEM

2018 ◽  
Vol 4 (5) ◽  
pp. 7
Author(s):  
Shivam Dwivedi ◽  
Prof. Vikas Gupta
Keyword(s):  
Steering System ◽  
Essential Elements ◽  
Variable Pressure ◽  
Passenger Cars ◽  
Control Techniques ◽  
Steering Mechanism ◽  
Dynamics And Control ◽  
Active Research ◽  
Electronic Steering ◽  
And Control

As the four-wheel steering (4WS) system has great potentials, many researchers' attention was attracted to this technique and active research was made. As a result, passenger cars equipped with 4WS systems were put on the market a few years ago. This report tries to identify the essential elements of the 4WS technology in terms of vehicle dynamics and control techniques. Based on the findings of this investigation, the report gives a mechanism of electronically controlling the steering system depending on the variable pressure applied on it. This enhances the controlling and smoothens the operation of steering mechanism.

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