Experimental Verification of Critical Speed Ranges for Elastic Closed Loop Linkage Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 126-130 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Critical Speed ◽  
Closed Loop ◽  
Local Maximum ◽  
Experimental Methods ◽  
Strain Response ◽  
Maximum Value ◽  
Speed Range ◽  
The Stability

In this work critical speed ranges are determined and verified for an elastic four bar crank rocker mechanism where all links are modeled as elastic members. The procedure used for the dynamic stability analysis is described in Nagarajan and Turcic (1991). The speed range of interest where the stability analysis is performed is 195–390 rpm. The values of the critical speeds obtained in the above speed range are then verified using independent theoretical and experimental methods of analysis. The steady state strain response is obtained both theoretically and experimentally for a number of speeds in the speed range of 195–390 rpm. From these responses plots different strain characteristics versus operating speeds are obtained. These plots exhibit peaks in the response at certain speeds indicating that the dynamic response at these speeds reaches a local maximum value. The critical speed ranges determined are found to correspond quite closely to the speeds where the peaks occur. This indicates that the critical speed ranges are indeed speeds where the response of the system is larger when compared to neighboring speeds and that the methods of determining them are accurate for the application considered.

scholarly journals Experimental Study on the Stability and Transient Behavior of a Closed-Loop Two-Phase Thermosyphon (CLTPT) Charged with NOVEC 649

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7920
Author(s):  
Ana Larrañaga ◽  
Miguel A. Gómez ◽  
David Patiño ◽  
Jacobo Porteiro
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Stability Analysis ◽  
Closed Loop ◽  
Transient Behavior ◽  
Power Input ◽  
Heat Transfer Analysis ◽  
Two Phase ◽  
Flow Circulation ◽  
The Stability

Currently, the growing need for efficient refrigeration resources in the industrial sector has led to an increasing interest in finding technologies with a higher heat removal potential and better cooling performance. Along these lines, two-phase liquid cooling appears to be a very interesting solution, with the CLTPT (closed-loop two-phase thermosyphon) being one of the leading alternatives. Most works in the scientific literature study loop thermosyphons that work in flow boiling conditions in steady state. The present paper analyzes the transient thermal behavior of a pool boiling CLTPT gravitational channel as a passive cooling system using NOVEC 649 as working fluid. The evaporator works with two submerged cylindrical heaters that represent different heat sources located in different positions. The initial transient behavior and consequent instabilities of a laboratory-scale facility were studied, followed by a stability analysis for various power inputs. Parameters such as temperature and pressure along the experimental setup were monitored, and the effects of internal pressure and room conditions were also tested. The results show some instabilities in the process to start the flow circulation and a relative stability and quick adaptation to changes when circulation is reached. The temperature in the evaporator chamber was highly homogeneous during the whole process; however, the temperature changes in the riser and the loop top were delayed with respect to the evaporator zone. The analysis shows several pressure and temperature raises before the vapor flux reaches the condenser. When the flow circulation is established, the system becomes highly stable and thermally homogeneous, decreasing the thermal resistance when increasing the power input. The stability analysis also showed that, when the system reaches the steady state, the changes in the power input produce a transient increase in the pressure and temperature of the fluid, followed by a quick decrease of the previous steady state values. The heat transfer analysis in the evaporator shows a higher heat flux on the upper heater caused by the buoyancy flow that rises from the lower heater. It was also observed that the lower heater reaches the CHF point with a lower heat flux.

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Switching Control Design for Switched Fuzzy Discrete-Time Systems

2014 ◽  
Vol 1006-1007 ◽  
pp. 711-714
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Control Method ◽  
Control Design ◽  
Switching Control ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

This paper investigates the problems of stability analysis and stabilization for a class of switched fuzzy discrete-time systems. Based on a common Lyapunov functional, a switching control method has been developed for the stability analysis of switched discrete-time fuzzy systems. A new stabilization approach based on a switching parallel distributed compensation scheme is given for the closed-loop switched fuzzy systems. Finally, the illustrative example is provided to demonstrate the effectiveness of the techniques proposed in this paper.

scholarly journals Computation of time-delay for Delayed Network Controlled Temperature Control System

2021 ◽  
Vol 2070 (1) ◽  
pp. 012102
Author(s):  
V Venkatachalam ◽  
M Ramasubramanian ◽  
M Thirumarimurugan ◽  
D Prabhakaran
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Temperature Control ◽  
Closed Loop ◽  
Simulation Software ◽  
Loop System ◽  
Temperature Control System ◽  
Closed Loop System ◽  
The Stability ◽  
Time Invariant

Abstract This paper presents an Investigation on the stability of network controlled temperature control system having Time-Invariant feedback delays, by utilizing a direct method for TDS stability analysis. A PI controller based stability analysis for temperature control system with Time invariant feedback loop delay has been constructed in this paper. The stability problem has been formulated based on the transfer function model of the closed loop system with various time delays. For different subsets of the controller parameters, based on the stability criterion’s maximal permissible bound of the network link delay that the closed loop system can accommodate without losing the stability has been computed. The effectiveness of the obtained result was validated on a benchmark temperature control system using MATLAB simulation software.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Robust Stability Clearance of Flight Control Law Based on Global Sensitivity Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Liuli Ou ◽  
Lei Liu ◽  
Shuai Dong ◽  
Yongji Wang
Keyword(s):  
Sensitivity Analysis ◽  
Stability Analysis ◽  
Robust Stability ◽  
Flight Control ◽  
Closed Loop ◽  
Strong Nonlinearity ◽  
Uncertain Model ◽  
Sobol’S Method ◽  
The Stability ◽  
Global Uncertainty

To validate the robust stability of the flight control system of hypersonic flight vehicle, which suffers from a large number of parametrical uncertainties, a new clearance framework based on structural singular value (μ) theory and global uncertainty sensitivity analysis (SA) is proposed. In this framework, SA serves as the preprocess of uncertain model to be analysed to help engineers to determine which uncertainties affect the stability of the closed loop system more slightly. By ignoring these unimportant uncertainties, the calculation ofμcan be simplified. Instead of analysing the effect of uncertainties onμwhich involves solving optimal problems repeatedly, a simpler stability analysis function which represents the effect of uncertainties on closed loop poles is proposed. Based on this stability analysis function, Sobol’s method, the most widely used global SA method, is extended and applied to the new clearance framework due to its suitability for system with strong nonlinearity and input factors varying in large interval, as well as input factors subjecting to random distributions. In this method, the sensitive indices can be estimated via Monte Carlo simulation conveniently. An example is given to illustrate the efficiency of the proposed method.

scholarly journals Stability Analysis of a Gear Pair System Supported by Squeeze-Film Dampers

2001 ◽  
Vol 7 (2) ◽  
pp. 143-151 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Harmonic Balance Method ◽  
Squeeze Film ◽  
Hybrid Technique ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Squeeze Film Dampers ◽  
The Stability

This paper examines the stability of the steady-state periodic response of a gear pair system supported by squeeze-film dampers. The steady-state response of the system is obtained by using the hybrid technique of Harmonic Balance Method and Time Collocation. The Fioquet-Liapunov theory is used to perform the stability analysis of the first variation equations with periodic coefficients, which is generated by the perturbation technique. The stability charts on gear mesh stiffness, spin ratio, disk unbalance, gravity, and squeeze-film damper are used to perform parameter studies. The numerical results show that the unstable region always occurs when the spin ratio is near the second coupled mode of the gear pair system. Furthermore, the mesh stiffness has a significant influence on the coupled critical speeds. Therefore, it plays an important role in determining the spin ratio stability range.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

2011 ◽  
Vol 225 (12) ◽  
pp. 2804-2818 ◽  
Author(s):  
A Amamou ◽  
M Chouchane
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Critical Speed ◽  
Design Parameters ◽  
Stable Limit ◽  
Non Linear ◽  
The Stability

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

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