Minimizing Residual Vibration for Point-to-Point Motion

1985 ◽  
Vol 107 (4) ◽  
pp. 378-382 ◽  
Author(s):  
P. H. Meckl ◽  
W. P. Seering
Keyword(s):  
Minimum Energy ◽  
Residual Vibration ◽  
Test Fixture ◽  
Square Wave ◽  
Wave Forcing ◽  
Forcing Function ◽  
Point Motion ◽  
Minimum Residual ◽  
Order Of Magnitude ◽  
Point To Point

This paper describes an appropriately shaped forcing function for moving a dynamic system over an incremental distance with minimum residual vibration. The function is constructed by combining harmonics of a “ramped sinusoid” function so that minimum energy is introduced to the system at its resonant frequencies. A test fixture to evaluate this approach is described and experimental results are given. Residual vibration amplitudes for the ramped sinusoid function are compared with those for a square wave input and a bang-bang function. In practice, the ramped sinusoid achieves nearly an order-of-magnitude reduction in residual vibration amplitude as compared to the square wave forcing function.

Friction-Compensating Command Shaping for Vibration Reduction

2004 ◽  
Vol 127 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Jason Lawrence ◽  
William Singhose ◽  
Keith Hekman
Keyword(s):  
Steady State ◽  
Coulomb Friction ◽  
Vibration Reduction ◽  
Input Shaping ◽  
Residual Vibration ◽  
Command Shaping ◽  
Point Motion ◽  
Common Operation ◽  
Point To Point ◽  
Theoretical Developments

Fast and accurate point-to-point motion is a common operation for industrial machines, but vibration will frequently corrupt such motion. This paper develops commands that can move machines without vibration, even in the presence of Coulomb friction. Previous studies have shown that input shaping can be used on linear systems to produce point-to-point motion with no residual vibration. This paper extends command-shaping theory to nonlinear systems, specifically systems with Coulomb friction. This idea is applied to a PD-controlled mass with Coulomb friction to ground. The theoretical developments are experimentally verified on a solder cell machine. The results show that the new commands allow the proportional gain to be increased, resulting in reduced rise time, settling time, and steady-state error.

Point-to-Point Motion Planning for Servosystems With Elastic Transmission Via Optimal Dynamic Inversion1

2001 ◽  
Vol 123 (4) ◽  
pp. 733-736 ◽  
Author(s):  
Aurelio Piazzi ◽  
Antonio Visioli
Keyword(s):  
Optimization Procedure ◽  
Dynamic Inversion ◽  
Residual Vibration ◽  
Inversion Point ◽  
Stiffness Constant ◽  
Point Motion ◽  
Optimal Dynamic ◽  
A New Technique ◽  
Point To Point ◽  
Definition Of

A new technique, based on dynamic inversion, for the residual vibration reduction in the point-to-point motion of servosystems with elastic transmission is presented. The methodology consists of defining a suitable motion law for the load, and subsequently determining, via dynamic inversion, the corresponding command function for the system. The method inherently assures the robustness of the control scheme despite inaccuracies in the estimation of the stiffness constant and of the damping of the transmission. The main contribution of the paper lies in the definition of a simple optimization procedure which allows the system inversion point that minimizes the residual vibration to be found. Experimental results show that in this way the identification phase is less critical and performances can be significantly improved.

Effective Feedforward/Feedback Controller Design With Command Shaping to Reduce Residual Vibration

Manufacturing ◽  
2003 ◽  
Author(s):  
Peter H. Meckl ◽  
Young Joo Shin
Keyword(s):  
Control Strategy ◽  
High Speed ◽  
Controller Design ◽  
High Volume ◽  
Feedback Controller ◽  
Residual Vibration ◽  
Command Shaping ◽  
Minimum Residual ◽  
High Volume Production ◽  
Point To Point

Many manufacturing devices must execute motions as quickly as possible to achieve profitable high-volume production. This paper develops a control strategy that combines feedforward and feedback control with command shaping. First, the feedback controller is designed to increase damping and eliminate steady-state error. Next, the feedforward controller is designed to speed up the transient response. Finally, an appropriate reference profile is generated using command-shaping techniques to ensure fast point-to-point motions with minimum residual vibration. The particular focus of the paper is to understand the interactions between these individual control components. The resulting control strategy is demonstrated on a model of a high-speed semiconductor manufacturing machine.

Experimental evaluation of time-varying impulse shaping with a two-link flexible manipulator

Robotica ◽  
1996 ◽  
Vol 14 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Jung-Keun Cho ◽  
Youn-Sik Park
Keyword(s):  
Vibration Reduction ◽  
Vertical Plane ◽  
Joint Stiffness ◽  
Flexible Manipulator ◽  
Input Shaping ◽  
Time Varying ◽  
Modal Properties ◽  
Revolute Joints ◽  
Point Motion ◽  
Point To Point

SUMMARYIn the authors' previous paper,10 an input shaping method was presented to reduce motion-induced vibrations effectively for various classes of flexible systems. In this paper, the effectiveness of the shaping method is experimentally demonstrated with a two-link flexible manipulator systemThe manipulator for experiments includes two revolute joints and two flexible links, and moves on a vertical plane under gravity. An analytic model is developed considering the flexibility of the system and its joint stiffness in order to derive an appropriate estimation of dynamic modal properties. The input shaping method used in this work utilizes time-varying modal properties obtained from the model instead of the conventional input shaping method which employs time-invariant modal properties. A point-to-point motion is tested in order to show the effectivess of the proposed shaping method in vibration reduction during and after a given motion. The given reference trajectories are shaped to suppress the motion induced vibration. The test results demonstrate that the link vibration can be greatly suppressed during and after a motion, and the residual vibration reduction was observed more than 90% by employing this time-varying impulse shaping technique.

Minimum Energy Control of a Unicycle Model Robot

2021 ◽  
Author(s):  
Youngjin Kim ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Minimum Energy ◽  
Kinematic Model ◽  
Elliptic Functions ◽  
Terminal Point ◽  
Jacobi Elliptic Functions ◽  
Differential Drive ◽  
Terminal Constraints ◽  
Differential Drive Robot ◽  
Point To Point

Abstract Point-to-point path planning for a kinematic model of a differential-drive wheeled mobile robot (WMR) with the goal of minimizing input energy is the focus of this work. An optimal control problem is formulated to determine the necessary conditions for optimality and the resulting two point boundary value problem is solved in closed form using Jacobi elliptic functions. The resulting nonlinear programming problem is solved for two variables and the results are compared to the traditional shooting method to illustrate that the Jacobi elliptic functions parameterize the exact profile of the optimal trajectory. A set of terminal constraints which lie on a circle in the first quadrant are used to generate a set of optimal solutions. It is noted that for maneuvers where the angle of the vector connecting the initial and terminal point is greater than a threshold, which is a function of the radius of the terminal constraint circle, the robot initially moves into the third quadrant before terminating in the first quadrant. The minimum energy solution is compared to two other optimal control formulations: (1) an extension of the Dubins vehicle model where the constant linear velocity of the robot is optimized for and (2) a simple turn and move solution, both of whose optimal paths lie entirely in the first quadrant. Experimental results are used to validate the optimal trajectories of the differential-drive robot.

Kinematics Analysis and Motion Control of a Mobile Robot Driven by Three Tracked Vehicles

2018 ◽  
Author(s):  
Xin-Jun Liu ◽  
Zhao Gong ◽  
Fugui Xie ◽  
Shuzhan Shentu
Keyword(s):  
Mobile Robot ◽  
Motion Planning ◽  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Planning Method ◽  
Tracked Vehicles ◽  
Loop Control ◽  
Point Motion ◽  
Point To Point ◽  
Motion Mode

In this paper, a mobile robot named VicRoB with 6 degrees of freedom (DOFs) driven by three tracked vehicles is designed and analyzed. The robot employs a 3-PPSR parallel configuration. The scheme of the mechanism and the inverse kinematic solution are given. A path planning method of a single tracked vehicle and a coordinated motion planning of three tracked vehicles are proposed. The mechanical structure and the electrical architecture of VicRoB prototype are illustrated. VicRoB can achieve the point-to-point motion mode and the continuous motion mode with employing the motion planning method. The orientation precision of VicRoB is measured in a series of motion experiments, which verifies the feasibility of the motion planning method. This work provides a kinematic basis for the orientation closed loop control of VicRoB whether it works on flat or rough road.

Optimal Design Methodology of Point-to-Point Servo Systems for Minimization of Energy Consumption

1992 ◽  
Vol 206 (1) ◽  
pp. 35-43
Author(s):  
S W Kim ◽  
J S Park
Keyword(s):  
Design Methodology ◽  
Design Problems ◽  
Servo Systems ◽  
Speed Reduction ◽  
Point Motion ◽  
Actual Design ◽  
Profile Optimization ◽  
Point To Point ◽  
Selection Of

An optimum design methodology is presented for point-to-point motion control servo systems in which d.c. permanent magnetic motors are used as the main actuators. Emphasis is focused on establishing a series of comprehensive decision-making practices in dealing with three major design subjects: determination of the velocity profile, optimization of the speed reduction ratio, and selection of the motor. Finally, a practical design example is discussed to illustrate how the suggested design methodology may be applied to actual design problems.

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