scholarly journals Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sang-Myeong Kim ◽  
Heungseob Kim ◽  
Kwangsuck Boo
Keyword(s):  
Design Methodology ◽  
Flexible Manipulator ◽  
Flexible Beam ◽  
Fundamental Vibration ◽  
Zener Model ◽  
Closed Form Solutions ◽  
Mechanical Analogy ◽  
Lumped Element ◽  
Mechanical Elements ◽  
Proportional Derivative Controller

A study is presented in this paper that uses a simple mechanical analogy to analytically tune the PD (proportional-derivative) controller of a linear flexible manipulator system. More specifically, the aim is to give simple closed-form solutions of the optimal P and D gains to yield the maximum bandwidth under a given damping requirement or conversely the maximum damping under a given bandwidth requirement. The idea of this study is based on the observation that the performance of the complete manipulator system is largely determined by the operational dynamics of the fundamental vibration mode. A lumped element method is thus applied to model this dynamics in terms of simple lumped mechanical elements. It subsequently turns out that the original servo control problem is analogous to a conventional Zener mount design problem, that is, mathematically, to optimize a third-order dynamic system consisting of the Zener model of a viscoelastic mount and an inertial object upon it. A design methodology is finally established to analytically determine the optimal elements of the mount, corresponding to the optimal control gains. Simulations and experiments were also conducted with a single-link flexible beam to support the model and the design methodology developed.

scholarly journals The Study of Dynamic Modeling and Multivariable Feedback Control for Flexible Manipulators with Friction Effect and Terminal Load

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1522
Author(s):  
Fuli Zhang ◽  
Zhaohui Yuan
Keyword(s):  
Dynamic Model ◽  
Vibration Suppression ◽  
Control Method ◽  
Coupling Effect ◽  
Flexible Manipulator ◽  
Flexible Beam ◽  
Robot Dynamics ◽  
Joint Friction ◽  
Balance Principle ◽  
Multivariable Feedback

The flexible manipulato is widely used in the aerospace industry and various other special fields. Control accuracy is affected by the flexibility, joint friction, and terminal load. Therefore, this paper establishes a robot dynamics model under the coupling effect of flexibility, friction, and terminal load, and analyzes and studies its control. First of all, taking the structure of the central rigid body, the flexible beam, and load as the research object, the dynamic model of a flexible manipulator with terminal load is established by using the hypothesis mode and the Lagrange method. Based on the balance principle of the force and moment, the friction under the influence of flexibility and load is recalculated, and the dynamic model of the manipulator is further improved. Secondly, the coupled dynamic system is decomposed and the controller is designed by the multivariable feedback controller. Finally, using MATLAB as the simulation platform, the feasibility of dynamic simulation is verified through simulation comparison. The results show that the vibration amplitude can be reduced with the increase of friction coefficient. As the load increases, the vibration can increase further. The trajectory tracking and vibration suppression of the manipulator are effective under the control method of multi-feedback moment calculation. The research is of great significance to the control of flexible robots under the influence of multiple factors.

scholarly journals Vibration Response and Power Flow Characteristics of a Flexible Manipulator with a Moving Base

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yufei Liu ◽  
Wei Li ◽  
Xuefeng Yang ◽  
Mengbao Fan ◽  
Yuqiao Wang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Power Flow ◽  
Flow Characteristics ◽  
Flexible Manipulator ◽  
Rigid Base ◽  
Flexible Beam ◽  
Noticeable Effect ◽  
Moving Base ◽  
Vibration Responses ◽  
Motion Characteristics

Flexible manipulator generally can be modeled as a coupling system with a flexible beam and a rigid moving base. This paper investigates the vibration responses and power flow of a flexible manipulator with a moving base (FMMB). Considering the motion characteristics of the rigid base, the moving base is modeled to have a motion with disturbances, and the dynamic model of the FMMB is established. With the dynamic model, vibration responses of the FMMB for the rigid base having disturbance velocities and accelerations are specifically presented. Subsequently, to investigate the effect of the disturbances on the vibration energy distributions of the FMMB, power flow of the FMMB is exhibited. To verify the dynamic model, an ADAMS physical model of the FMMB is constructed. It reveals that the motion characteristics of the rigid base have a noticeable effect on the vibration responses and power flow of the FMMB and should be considered. The results are significant and contribute to the vibration control of flexible manipulators.

On the control of a single flexible arm robot via Youla-Kucera parameterization

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 150-172 ◽  
Author(s):  
Habib Esfandiar ◽  
Saeed Daneshmand ◽  
Roozbeh Dargahi Kermani
Keyword(s):  
Closed Loop ◽  
Optimization Techniques ◽  
Loop System ◽  
Flexible Manipulator ◽  
Order System ◽  
Flexible Beam ◽  
Closed Loop System ◽  
Stabilizing Controller ◽  
Main Challenge ◽  
Tip Mass

SUMMARYIn this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Executive options with inflated equity prices

2014 ◽  
Vol 10 (3) ◽  
pp. 266-292 ◽  
Author(s):  
Linus Wilson ◽  
Yan Wendy Wu
Keyword(s):  
Boards Of Directors ◽  
Stock Price ◽  
Design Methodology ◽  
Ceo Compensation ◽  
Managerial Compensation ◽  
Equity Prices ◽  
Content Type ◽  
Closed Form Solutions ◽  
Compensation Package ◽  
Applied Game Theory

Purpose – The purpose of this paper is to solve the optimal managerial compensation problem when shareholders are either naïvely optimistic or rational. Design/methodology/approach – The paper uses applied game theory to derive the optimal CEO compensation package with over optimistic shareholders. Findings – The results suggest that boards of directors should decrease option grants to CEOs when equity is likely to be irrationally overvalued at the date when the CEO's options vest. Research limitations/implications – The implications of the model are consistent with the available empirical evidence. In addition, the model generates new testable predictions about managerial stock price manipulation, the number of options granted, and the magnitude of the options’ strike prices that have not yet been formally tested. Originality/value – This is the only paper to derive closed-form solutions to optimal CEO compensation when shareholders are naïvely optimistic.

General inverse solution of six-degrees-of-freedom serial robots based on the product of exponentials model

2018 ◽  
Vol 38 (3) ◽  
pp. 361-367 ◽  
Author(s):  
Haixia Wang ◽  
Xiao Lu ◽  
Wei Cui ◽  
Zhiguo Zhang ◽  
Yuxia Li ◽  
...  
Keyword(s):  
Design Methodology ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Complex Problem ◽  
Content Type ◽  
Geometrical Properties ◽  
Closed Form Solutions ◽  
Six Degrees Of Freedom ◽  
Serial Robots ◽  
Six Dof

Purpose Developing general closed-form solutions for six-degrees-of-freedom (DOF) serial robots is a significant challenge. This paper thus aims to present a general solution for six-DOF robots based on the product of exponentials model, which adapts to a class of robots satisfying the Pieper criterion with two parallel or intersecting axes among its first three axes. Design/methodology/approach The proposed solution can be represented as uniform expressions by using geometrical properties and a modified Paden–Kahan sub-problem, which mainly adopts the screw theory. Findings A simulation and experiments validated the correctness and effectiveness of the proposed method (general resolution for six-DOF robots based on the product of exponentials model). Originality/value The Rodrigues rotation formula is additionally used to turn the complex problem into a solvable trigonometric function and uniformly express six solutions using two formulas.

Hybrid vibration and rest-to-rest control of a two-link flexible robotic arm using H∞ loop-shaping control design

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Mostafa sayahkarajy ◽  
Z Mohamed ◽  
A.A.M. Faudzi ◽  
E. Supriyanto
Keyword(s):  
Vibration Control ◽  
Design Methodology ◽  
Flexible Manipulator ◽  
Structural Vibration ◽  
Joint Angles ◽  
Shaping Filter ◽  
Loop Shaping ◽  
Space Manipulators ◽  
Feed Forward Controller ◽  
Practical Implications

Purpose This study presents a method for simultaneous motion and vibration control of light-weight slender robotic arms, known as flexible manipulators. In this paper, a new control algorithm is proposed for a two-link manipulator with elastic links. Design/methodology/approach The controller includes a MIMO H∞ Loop-Shaping Design (H∞LSD) as the feedback controller, and a command pre-shaping filter as the feed-forward controller. The conventional inputs and outputs of a typical two-link manipulator , that consists of the torques applied by the actuators at the joints, and the joint angles are chosen for the feedback control. Findings It is shown that by selecting a proper desired loop shape, the H∞LSD is able to control the joint angles of the manipulator, and simultaneously, suppress vibrations of the system so that the high frequency chatter due to the structural vibration modes does not appear at the outputs. Then it is shown that when the H∞LSD is equipped with a command pre-shaping filter, more efficient suppression of the chatter at the tip of the manipulator is achieved. The capability and effectiveness of the proposed control strategy in driving and stabilizing the manipulator to desired positions and simultaneously suppressing structural vibrations is shown by the simulation of the flexible manipulator in rest-to-rest maneuvers. Practical implications Flexible Manipulator, Space Manipulators Originality/value A robust MIMO controller is proposed for simultaneous motion and vibration control of flexible manipulator.

Improving the tie force method for progressive collapse design of RC frames

2018 ◽  
Vol 9 (4) ◽  
pp. 520-531 ◽  
Author(s):  
Arash Naji
Keyword(s):  
Design Methodology ◽  
Progressive Collapse ◽  
Limit State ◽  
Content Type ◽  
Catenary Action ◽  
Closed Form Solutions ◽  
Rc Frames ◽  
Orthogonal Beams ◽  
Similar Equation ◽  
Good Agreement

Purpose The purpose of this paper is to recover the deficiency of existing tie force (TF) methods by considering the decrease in section strength due to cracking and by selecting limit state of collapse according to section properties. Design/methodology/approach A substructure is selected by isolating the connected beams from the entire structure. For interior joints, the TFs in the orthogonal beams are obtained by catenary action. For corner joints, the TFs are assessed by beam action. For edge joints, however, the resistance is gained by greater of the resistance under catenary action for periphery beams and beam action for all the connecting beams in both directions. For catenary action, the TF capacities must satisfy Equation (20). On the other hand, for beam action, the TF must satisfy Equation (16), while R is calculated from Equation (17). In the case where the length of the connecting beams is similar, Equation (19) can be used. Findings Closed form solutions are available for TFs on both beam and catenary stages. Originality/value The proposed formulation makes designing more practical and convenient. However, the proposed formulation had good agreement with experimental results.

Effect of Payload on the Dynamics of a Flexible Manipulator—Modeling for Control

1991 ◽  
Vol 113 (3) ◽  
pp. 409-418 ◽  
Author(s):  
T. R. Parks ◽  
H. A. Pak
Keyword(s):  
Transfer Functions ◽  
Order Reduction ◽  
Qualitative Change ◽  
Flexible Manipulator ◽  
Flexible Beam ◽  
Model Order ◽  
Modeling And Control ◽  
Prior Literature ◽  
And Control ◽  
Substantial Change

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

scholarly journals Computer aided design of ferrite lumped element circulators

2021 ◽  
Vol 23 (4) ◽  
pp. 74-84
Author(s):  
Vladimir N. Borodin ◽  
Valery A. Kozlov ◽  
Evgeny A. Mikhalitsyn ◽  
Alexander V. Sorokin
Keyword(s):  
Computer Aided Design ◽  
Design Methodology ◽  
Ultra Wideband ◽  
Design System ◽  
Resonant Circuit ◽  
Lumped Element ◽  
Computer Aided ◽  
Impedance Calculation ◽  
Aided Design ◽  
Theoretical Results

The results of integrity of narrowband and wideband lumped element circulators design methodology to the computer aided design system of microwave devices AWR Microwave Office are presented in the article. The calculation method of narrow band circulators circuits which consist of serious and shunt tuning capacities is investigated. The simple and visual method of wideband ferrite isolators optimize design based on circulation impedance calculation is described here. The results of design of the ultra wideband circulator with shunt capacity, serious resonant matching circuit and serious resonant circuit between common terminal and ground are considered. The new theoretical results of calculation of two schematics of wideband high power circulators with serious tuning capacity are presented. The first schematic is formed with matching resonant network being connected in serious at each terminal. It is shown that double hump characteristic is realized. The second schematic is formed with serious resonant network connected between common terminal and the ground. It is shown that four-order Tchebycheff characteristic is realized.

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