Stability and Bifurcation in Discrete Mechanical Systems: An Experimental and Analytical Study

The curse of dimensionality looms over many studies in science and engineering. Low-order systems provide conceptual clarity but often fail to reveal the extent of possible complexity, whereas high-order systems present a host of daunting challenges to the analyst, not least the classification and visualization of typical behavior. In this paper, we detail the behavior of systems that fall somewhere between a classification of low- and high-order. [Formula: see text][Formula: see text]We present both theoretical and experimental investigations into the nonlinear behavior of a couple of mechanical systems with three mechanical/structural degrees-of-freedom (DOF), with a special focus on bifurcation and multiple equilibria. Useful insight is provided by observation of transient trajectories as they meander about and between equilibria, especially revealing the influence of unstable equilibria, not normally accessible in an experimental context. For instance, the influences of index-1 saddles are mainly detected in three aspects: determining the systems capability to snap-through by generating accessible snap-though tubes, attracting nearby trajectories temporarily oscillating around it, and separating adjacent trajectories. Iso-potentials are 3D-printed to present the energy landscape. For these systems, the 3D configuration space allows considerable complexity, but is also somewhat amenable to geometric interpretation. By varying a mass/stiffness ratio as a control parameter, bifurcation structures and morphing potential energy landscapes exhibiting up to 11 equilibria are obtained. Finally, analytical and experimental studies reveal that parametric excitations can stabilize some unstable equilibria under the right amplitudes and frequencies.

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Using a Redundant User Interface in Teleoperated Surgical Systems for Task Performance Enhancement

Robotica ◽

10.1017/s0263574720000326 ◽

2020 ◽

Vol 38 (10) ◽

pp. 1880-1894 ◽

Cited By ~ 1

Author(s):

Ali Torabi ◽

Mohsen Khadem ◽

Koroush Zareinia ◽

Garnette Roy Sutherland ◽

Mahdi Tavakoli

Keyword(s):

Degrees Of Freedom ◽

Performance Enhancement ◽

Null Space ◽

Experimental Studies ◽

Geometric Interpretation ◽

Slave System ◽

Surgical Robots ◽

Control Effort ◽

User Simulation ◽

Master Slave System

SUMMARYThe enhanced dexterity and manipulability offered by master–slave teleoperated surgical systems have significantly improved the performance and safety of minimally invasive surgeries. However, effective manipulation of surgical robots is sometimes limited due to the mismatch between the slave and master robots’ kinematics and workspace. The purpose of this paper is first to formulate a quantifiable measure of the combined master–slave system manipulability. Next, we develop a null-space controller for the redundant master robot that employs the proposed manipulability index to enhance the performance of teleoperation tasks by matching the kinematics of the redundant master robot with the kinematics of the slave robot. The null-space controller modulates the redundant degrees of freedom of the master robot to reshape its manipulability ellipsoid (ME) towards the ME of the slave robot. The ME is the geometric interpretation of the kinematics of a robot. By reshaping the master robot’s manipulability, we match the master and slave robots’ kinematics. We demonstrate that by using a redundant master robot, we are able to enhance the master–slave system manipulability and more intuitively transfer the slave robot’s dexterity to the user. Simulation and experimental studies are performed to validate the performance of the proposed control strategy. Results demonstrate that by employing the proposed manipulability index, we can enhance the user’s control over the force/velocity of a surgical robot and minimize the user’s control effort for a teleoperated task.

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Dynamic Loads and Response of a Spar Buoy Wind Turbine with Pitch-Controlled Rotating Blades: An Experimental Study

Energies ◽

10.3390/en14123598 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3598

Author(s):

Sara Russo ◽

Pasquale Contestabile ◽

Andrea Bardazzi ◽

Elisa Leone ◽

Gregorio Iglesias ◽

...

Keyword(s):

Wind Speed ◽

Wind Turbine ◽

Degrees Of Freedom ◽

Large Scale ◽

Laboratory Data ◽

Nonlinear Behavior ◽

Offshore Wind ◽

Small Scale ◽

Wave Steepness ◽

Design Factor

New large-scale laboratory data are presented on a physical model of a spar buoy wind turbine with angular motion of control surfaces implemented (pitch control). The peculiarity of this type of rotating blade represents an essential aspect when studying floating offshore wind structures. Experiments were designed specifically to compare different operational environmental conditions in terms of wave steepness and wind speed. Results discussed here were derived from an analysis of only a part of the whole dataset. Consistent with recent small-scale experiments, data clearly show that the waves contributed to most of the model motions and mooring loads. A significant nonlinear behavior for sway, roll and yaw has been detected, whereas an increase in the wave period makes the wind speed less influential for surge, heave and pitch. In general, as the steepness increases, the oscillations decrease. However, higher wind speed does not mean greater platform motions. Data also indicate a significant role of the blade rotation in the turbine thrust, nacelle dynamic forces and power in six degrees of freedom. Certain pairs of wind speed-wave steepness are particularly unfavorable, since the first harmonic of the rotor (coupled to the first wave harmonic) causes the thrust force to be larger than that in more energetic sea states. The experiments suggest that the inclusion of pitch-controlled, variable-speed blades in physical (and numerical) tests on such types of structures is crucial, highlighting the importance of pitch motion as an important design factor.

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Experimental Evaluation of Airlift Performance for Vertical Pumping of Water in Underground Mines

Mine Water and the Environment ◽

10.1007/s10230-021-00807-w ◽

2021 ◽

Author(s):

Parviz Enany ◽

Oleksandr Shevchenko ◽

Carsten Drebenstedt

Keyword(s):

Water Flow ◽

High Efficiency ◽

Experimental Studies ◽

Theoretical Models ◽

Injection System ◽

Experimental Investigations ◽

Flow Mode ◽

New Device ◽

Riser Pipe ◽

Airlift Pump

AbstractThis paper presents experimental studies on the optimization of air–water flow in an airlift pump. Airlift pumps use compressed gas to verticall transport liquids and slurries. Due to the lack of theoretical equations for designing and predicting flow regimes, experimental investigations must be carried out to find the best condition to operate an airlift pump at high efficiency. We used a new air injection system and different submergence ratios to evaluate the output of a simple pump for vertical displacement of water in an underground mine. The tests were carried out in a new device with 5.64 m height and 10.2 cm circular riser pipe. Three air-jacket pipes, at different gas flows in the range of 0.002–0.09 m3/s were investigated with eight submergence ratios. It was found that with the same air flow rate, the most efficient flow of water was achieved when an air jacket with 3 mm diameter holes was used with a submergence ratio between 0.6 and 0.75. In addition, a comparison of practical results with two theoretical models proposed by other investigators showed that neither was able to accurately predict airlift performance in air–water flow mode.

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Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211031396 ◽

2021 ◽

pp. 014233122110313

Author(s):

Afef Hfaiedh ◽

Ahmed Chemori ◽

Afef Abdelkrim

Keyword(s):

Real Time ◽

Error Control ◽

Degrees Of Freedom ◽

Sliding Mode ◽

Mechanical Systems ◽

Class I ◽

Control Input ◽

Underactuated Mechanical Systems ◽

Control Scheme ◽

And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

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Nonlinear Behavior of a Magnetic Bearing System

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2814135 ◽

1995 ◽

Vol 117 (3) ◽

pp. 582-588 ◽

Cited By ~ 29

Author(s):

L. N. Virgin ◽

T. F. Walsh ◽

J. D. Knight

Keyword(s):

Degrees Of Freedom ◽

Initial Conditions ◽

Nonlinear Behavior ◽

Analytical Techniques ◽

Magnetic Bearing ◽

Forced Response ◽

The Mathematical Model ◽

Two Degree Of Freedom ◽

Sensitivity To Initial Conditions ◽

Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

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Model Calibration for a Rigid Hexapod-Based End-Effector with Integrated Force Sensors

Sensors ◽

10.3390/s21103537 ◽

2021 ◽

Vol 21 (10) ◽

pp. 3537

Author(s):

Christian Friedrich ◽

Steffen Ihlenfeldt

Keyword(s):

Parameter Identification ◽

Degrees Of Freedom ◽

Force Measurement ◽

Experimental Studies ◽

Measurement Model ◽

Calibration Procedure ◽

Force Sensors ◽

End Effector ◽

Measurement Models ◽

Fast Procedure

Integrated single-axis force sensors allow an accurate and cost-efficient force measurement in 6 degrees of freedom for hexapod structures and kinematics. Depending on the sensor placement, the measurement is affected by internal forces that need to be compensated for by a measurement model. Since the parameters of the model can change during machine usage, a fast and easy calibration procedure is requested. This work studies parameter identification procedures for force measurement models on the example of a rigid hexapod-based end-effector. First, measurement and identification models are presented and parameter sensitivities are analysed. Next, two excitation strategies are applied and discussed: identification from quasi-static poses and identification from accelerated continuous trajectories. Both poses and trajectories are optimized by different criteria and evaluated in comparison. Finally, the procedures are validated by experimental studies with reference payloads. In conclusion, both strategies allow accurate parameter identification within a fast procedure in an operational machine state.

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A high-order three-dimensional numerical manifold method enriched with derivative degrees of freedom

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2017.07.010 ◽

2017 ◽

Vol 83 ◽

pp. 229-241 ◽

Cited By ~ 6

Author(s):

Huo Fan ◽

Jidong Zhao ◽

Hong Zheng

Keyword(s):

Degrees Of Freedom ◽

Three Dimensional ◽

High Order ◽

Numerical Manifold Method ◽

Numerical Manifold

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Design and Analysis of a 1D Actively Stabilized System with Viscoelastic Damping Support

Actuators ◽

10.3390/act8020033 ◽

2019 ◽

Vol 8 (2) ◽

pp. 33

Author(s):

Josef Passenbrunner ◽

Gerald Jungmayr ◽

Wolfgang Amrhein

Keyword(s):

Degrees Of Freedom ◽

Nonlinear Behavior ◽

Axial Rotation ◽

Test System ◽

Axial Position ◽

Viscoelastic Damping ◽

Temperature Dependent ◽

Temperature Dependent Properties ◽

Rotor Dynamic ◽

Damping Capability

Passively magnetically stabilized degrees of freedom yield the benefit of reduced complexity and therefore costs. However, the application of passive magnetic bearings (PMBs) also features some drawbacks. The poor damping capability leads to exaggerated deflection amplitudes when passing the resonance speeds of the applied system. This results in the necessity of external damping. Complying with the goal of costs and complexity, viscoelastic materials offer a suitable solution. However, these materials show high frequency and temperature dependent properties which induce the necessity of a proper model. Thus, the design of systems, as presented in this paper, requires accurate modeling of the dynamic behavior including the nonlinear characteristic of damping elements to predict the system displacements. In the investigated setup only two degrees of freedom remain to be controlled actively. These are the axial rotation and the axial position of the rotor which are controlled by the motor and an active magnetic axial bearing (AMB). This article focuses on the rotor dynamic modeling of a radial passively magnetically stabilized system especially considering the nonlinear behavior of viscoelastic damping elements. Finally, the results from the analytic model are verified by measurements on a manufactures test system.

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