Dynamic Stability Considerations in Elastic Closed Loop Linkage Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 131-136 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Dynamic Stability ◽  
Experimental Verification ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Closed Loop ◽  
Theoretical Method ◽  
Efficient Implementation ◽  
Theoretical Methods ◽  
Critical Speeds ◽  
Large Numbers

In this work a theoretical method is developed to identify critical speeds for elastic linkage systems. Critical speeds are input operating speeds where the response of the system is larger when compared to neighboring noncritical speeds. A survey of the literature reveals that theoretical methods of determining the critical operating speeds with experimental verification have not been applied by researchers for linkage systems with large number of elastic degrees of freedom and with all links considered as elastic members. Research works that address this problem are usually limited to mechanisms with only one link treated as an elastic member. The method of determining critical speeds in this work is an efficient implementation of Floquet theory, and is applicable for mechanism systems with large numbers of elastic degrees of freedom and with all links considered as elastic members. Experimental verification for the results obtained using this approach is provided in Nagarajan and Turcic (1991).

scholarly journals Software Sensor to Enhance Online Parametric Identification for Nonlinear Closed-Loop Systems for Robotic Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3653
Author(s):  
Lilia Sidhom ◽  
Ines Chihi ◽  
Ernest Nlandu Kamavuako
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Parametric Identification ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Closed Loop Identification ◽  
Input Variables ◽  
Robotic Applications

This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differentiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algorithm’s effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 658-667 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Bearing

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

Demonstration of aircraft dynamic stability and response for aeronautical engineering students

1994 ◽  
Vol 98 (975) ◽  
pp. 192-193
Author(s):  
A.W. Bloy
Keyword(s):  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Engineering Students ◽  
Six Degrees Of Freedom ◽  
Stability And Control ◽  
Good Grasp ◽  
Aircraft Motion ◽  
Aeronautical Engineering ◽  
And Control ◽  
Aircraft Stability And Control

The teaching of aircraft stability and control at university usually progresses to the complexity of six degrees of freedom with a large array of aerodynamic, gravitational and inertial terms. It is therefore essential to ensure that students have a good grasp of fundamental dynamic characteristics such as damping and natural frequency, and any demonstration in which students observe aircraft motion is particularly helpful. At Manchester University this is achieved by a windtunnel demonstration of aircraft dynamic stability and response in pitch to a sinusoidal gust generator.

scholarly journals Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sameer Gupta ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Medical Surgery ◽  
Natural Motion ◽  
Hybrid Manipulator ◽  
Contour Plots ◽  
Kinematic Singularities ◽  
And Control ◽  
Optimal Configurations

Abstract This paper presents the singularity analysis of a 7-degrees of freedom (DOF) hybrid manipulator consisting of a closed-loop within it. From the past studies, it is well-known that the kinematic singularities play a significant role in the design and control of robotic manipulators. Kinematic singularities pose two-fold effects – first, they can induce the loss of one or more DOF of the manipulator and cause infinite joint rates at that particular joint, and second, they help to determine the trajectory or zone with high mechanical advantage. In current work, a 7-DOF hybrid manipulator is considered which is being developed at Council Of Scientific And Industrial Research–Central Scientific Instruments Organisation (CSIR–CSIO) Chandigarh to assist a surgeon during a medical-surgical task. To emulate the natural motion of a surgeon, the challenging configuration with redundant DOF is utilized. Jacobian has been computed analytically and analyzed at each instantaneous configuration with the evaluation of manipulability. Effect of a closed loop in the hybrid configurations is focused at, and utilizing the contour plots, good and worst working zones are identified in the workspace of the manipulator. The verification and validation of best and worst manipulability points (singularities) are done with the help of genetic algorithms, to determine locally and globally optimal configurations. Finally, on the basis of the singularity analysis, the present work concludes with few guidelines to the surgeon about the best and worst working zones for surgical tasks.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

Trajectory Tracking of Underactuated Surface Vessels Based on Hierarchical Sliding Mode

2014 ◽  
Author(s):  
Cheng Liu ◽  
Zaojian Zou ◽  
Jianchuan Yin
Keyword(s):  
Trajectory Tracking ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Underactuated System ◽  
Sliding Mode Controller ◽  
Control Field ◽  
Surface Vessels ◽  
Underactuated Surface Vessels ◽  
Hierarchical Sliding Mode

Trajectory tracking is an importance practice in ship motion control field. It attracts more attention recently due to its difficulties. Trajectory tracking requires the ship to arrive pinpoint location at exact time. It is a underactuated system because the degrees of freedom of control inputs are fewer than the degrees of freedom that needed to be controlled. In this paper, a hierarchical sliding mode controller and a common sliding mode controller are proposed to deal with the trajectory tracking problem of underactuated surface vessels. Simulation results validate the tracking performance of the proposed controllers. The closed-loop stability is testified by the Lyapunov stability theorem.

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