On the Stability of PD Control for a Two-Link Rigid-Flexible Manipulator

1994 ◽  
Vol 116 (2) ◽  
pp. 208-215 ◽  
Author(s):  
Ahmet S. Yigit
Keyword(s):  
Controller Design ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Simulation Studies ◽  
Parameter Uncertainties ◽  
Pd Control ◽  
System Parameters ◽  
Flexible System ◽  
The Stability

Controller design for a rigid-flexible two-link manipulator is considered. Robustness of independent joint PD control is investigated. It has been shown that the stability of independent joint PD control does not depend explicitly on the system parameters. No discretization or linearization of the equations of motion is required to assure the stability. Simulation studies also show that independent joint PD control gives reasonably good results for the flexible system, and is robust to parameter uncertainties.

A Preliminary Investigation of the Dynamic Stability of Flexible Manipulators Performing Repetitive Tasks

1986 ◽  
Vol 108 (3) ◽  
pp. 206-214 ◽  
Author(s):  
D. A. Streit ◽  
C. M. Krousgrill ◽  
A. K. Bajaj
Keyword(s):  
Parametric Excitation ◽  
Floquet Theory ◽  
Equations Of Motion ◽  
Preliminary Investigation ◽  
Zero Solution ◽  
Flexible Manipulator ◽  
Governing Equations ◽  
Repetitive Tasks ◽  
The Stability ◽  
Two Degree Of Freedom

The governing equations of motion for the compliant coordinates describing a flexible manipulator performing repetitive tasks contain parametric excitation terms. The stability of the zero solution to these equations is investigated using Floquet theory. Analytical and numerical results are presented for a two-degree-of-freedom model of a manipulator with one prismatic joint and one revolute joint.

Delayed-Acceleration Feedback for Active-Multimode Vibration Control of Cantilever Beams

2007 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Ali H. Nayfeh ◽  
Mohammed F. Daqaq
Keyword(s):  
Cantilever Beam ◽  
Controller Design ◽  
Equations Of Motion ◽  
Time Integration ◽  
Free Vibrations ◽  
Delayed Feedback Control ◽  
Vibration Modes ◽  
Stability Boundaries ◽  
Single Input Single Output ◽  
The Stability

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly-coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.

scholarly journals Dynamic Modelling And Predictive Control For Insect-Like Flapping Wing Aerial Micro Robots

2021 ◽  
Author(s):  
Alborz Sakhaei
Keyword(s):  
Predictive Control ◽  
Controller Design ◽  
Equations Of Motion ◽  
Dynamic Modelling ◽  
Scale Insect ◽  
Flapping Wing ◽  
Confined Space ◽  
Simulation Framework ◽  
The Stability ◽  
Technological Limitations

The outstanding potential capability of flapping-wing aerial micro robots to perform gamut [sic] of applications ranging from indoor and confined space missions to perilous environment explorations elevates them from conventional fixed and rotary wing micro aerial vehicles. Despite the remarkable progress in development of manufacturing paradigms to fabricate an at-scale insect-like aerial micro robot, the existing methods are still incompetent to mimic even the most basic maneuvers [sic] of the flying insects. This incompetency comes from technological limitations in terms of size and power density as well as lack of thorough insight into the complex neuromuscular actuation mechanism of the insects' wing. These limitations raise the motivation to develop a simulation framework to be used to analyze the stability and flight dynamics of the insect-like aerial micro robots, and provide a means by which the controller design for these systems could be accomplished. This thesis describes the development of such simulation framework in the context of dynamic modelling and controller design. A consistent set of dynamic and kinematic equations of motion are developed, and the application of the model predictive control strategy for insect-like flapping wing aerial micro robots is investsigated.

Integrated Design and PD Control of High-Speed Closed-loop Mechanisms

2002 ◽  
Vol 124 (4) ◽  
pp. 522-528 ◽  
Author(s):  
F. X. Wu ◽  
W. J. Zhang ◽  
Q. Li ◽  
P. R. Ouyang
Keyword(s):  
High Speed ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Design ◽  
Integrated Design ◽  
Pd Controller ◽  
Pd Control ◽  
Link Mechanism ◽  
Mass Redistribution ◽  
The Stability

The performance of an electromechanical system not only depends on its controller design, but also on the design of its mechanical structure. In order to achieve the excellent performance of the four-bar-link mechanism by employing the simple PD control, we redesign the structure of the four-bar-link mechanism by a mass-redistribution scheme to simplify the dynamic model. Theoretically, we analyze the stability of the closed-loop system consisting of the PD controller and several kinds of four-bar-link mechanisms, and discuss the relations between the performance of the PD controller and its gains and the mechanical design. The obtained results show that the performance of the PD controller may be significantly improved by using the methodology of Design For Control (DFC). The effectiveness of the proposed methodology has also been verified by some simulation studies.

Study on Joint Characteristics and the Stability of the Flexible Manipulator Considering the Control Performance

2010 ◽  
Vol 34-35 ◽  
pp. 1119-1123
Author(s):  
Wei Guo Shen ◽  
Jin Tian Yun
Keyword(s):  
Boundary Conditions ◽  
Controller Design ◽  
Flexible Manipulator ◽  
Control Performance ◽  
Joint Characteristics ◽  
The Stability

For flexible manipulator, the analysis of the joint characteristics and the stability become very important for controller design. The boundary conditions of the flexible manipulator with noncollocated P controller and collocated P controller are developed in this paper. And the stability of the flexible manipulator is also discussed.

Finite Element-Based Control of a Single-Link Flexible Hydraulic Manipulator

2017 ◽  
Author(s):  
Petri Mäkinen ◽  
Jouni Mattila
Keyword(s):  
Finite Element ◽  
Controller Design ◽  
Hydraulic Cylinder ◽  
Flexible Manipulator ◽  
Flexible Link ◽  
Hydraulic Actuator ◽  
Single Link ◽  
Dynamics And Control ◽  
The Stability ◽  
And Control

In this study, a stability-guaranteed, nonlinear, finite element-based control is presented for a single-link flexible manipulator with hydraulic actuation, subject to experimental validation. The strong, inherent nonlinearities of the hydraulic cylinder and fluid dynamics, coupled with flexible link dynamics, cause remarkable challenges in controlling the system effectively. In an attempt to cope with these challenges, a controller based on the Virtual Decomposition Control (VDC) approach is introduced. The VDC approach takes advantage of subsystem-dynamics-based control, enabling the handling of the dynamics and control of the hydraulic actuator and the flexible link separately, thus keeping the controller design relatively simple. The rigorous stability theory of the VDC approach guarantees the stability of the entire system. The experiments demonstrate the VDC controller’s performance in end-point control with built-in vibration dampening.

scholarly journals Spreading Control in Two-Layer Multiplex Networks

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1157
Author(s):  
Roberto Bernal Jaquez ◽  
Luis Angel Alarcón Ramos ◽  
Alexander Schaum
Keyword(s):  
Transition Rates ◽  
Simulation Studies ◽  
Central Question ◽  
Spreading Process ◽  
Multilayer Network ◽  
Time Model ◽  
System Parameters ◽  
Multiplex Networks ◽  
The Stability ◽  
Stability Results

The problem of controlling a spreading process in a two-layer multiplex networks in such a way that the extinction state becomes a global attractor is addressed. The problem is formulated in terms of a Markov-chain based susceptible-infected-susceptible (SIS) dynamics in a complex multilayer network. The stabilization of the extinction state for the nonlinear discrete-time model by means of appropriate adaptation of system parameters like transition rates within layers and between layers is analyzed using a dominant linear dynamics yielding global stability results. An answer is provided for the central question about the essential changes in the step from a single to a multilayer network with respect to stability criteria and the number of nodes that need to be controlled. The results derived rigorously using mathematical analysis are verified using statical evaluations about the number of nodes to be controlled and by simulation studies that illustrate the stability property of the multilayer network induced by appropriate control action.

scholarly journals Stabilization and Controller Design of 2D Discrete Switched Systems with State Delays under Asynchronous Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shipei Huang ◽  
Zhengrong Xiang ◽  
Hamid Reza Karimi
Keyword(s):  
Switched Systems ◽  
Dwell Time ◽  
State Feedback ◽  
Controller Design ◽  
Robust Stabilization ◽  
Asynchronous Switching ◽  
Parameter Uncertainties ◽  
State Delays ◽  
Discrete Switched Systems ◽  
The Stability

This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.

Lateral Dynamics and Stability of Two Full Vehicles in Tandem

1998 ◽  
Vol 120 (1) ◽  
pp. 50-56 ◽  
Author(s):  
N. A. El-Esnawy ◽  
J. F. Wilson
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Mean Square ◽  
Critical System ◽  
Lateral Dynamics ◽  
System Parameters ◽  
Vehicle System ◽  
Articulated Vehicle ◽  
The Stability ◽  
Oscillatory Instabilities

The lateral dynamics and stability of two full vehicles in tandem are investigated. The nonlinear differential equations of motion of this four-axle articulated vehicle system are presented in matrix form and then linearized. The critical forward velocity of the steady state for oversteering conditions is derived in a closed form, and the criteria for understeer, neutral steer, or oversteer are given. Uncertainty of the critical forward velocity and its sensitivity to errors in the system parameters are evaluated using the root mean square method. Conditions for nonoscillatory and oscillatory instabilities of the linearized vehicle system are given. Effects of the critical system parameters (mainly the mass distribution) on the stability are investigated.

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