The stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motion

2021 ◽  
pp. 095440702110433
Author(s):  
Shuming Shi ◽  
Fanyu Meng ◽  
Minghui Bai ◽  
Nan Lin
Keyword(s):  
Stability Analysis ◽  
Quantitative Analysis ◽  
Lyapunov Exponents ◽  
Plane Motion ◽  
Vehicle Model ◽  
Motion Stability ◽  
Motion System ◽  
Nonlinear Vehicle Model ◽  
The Stability ◽  
Different Characteristics

The Lyapunov exponents method is an excellent approach for analyzing the vehicle plane motion stability, and the researchers demonstrated the effectiveness under 2-DOF vehicle model. However, whether the Lyapunov exponents approach can effectively reveal the characteristics of high-DOF nonlinear vehicle model is the key problem at present. In this paper, the Lyapunov exponents is applied to quantitatively analyze the stability of the nonlinear three and five degree of freedom vehicle plane motion system. The different characteristics between 2-DOF and high-DOF model are revealed and explained by using Lyapunov exponents. It illustrates the feasibility of using Lyapunov exponents to analyze the stability of high-DOF vehicle models, which supplements and perfects the existing quantitative analysis conclusion.

Coning motion stability of spinning missiles with strapdown seekers

2016 ◽  
Vol 120 (1232) ◽  
pp. 1566-1577 ◽  
Author(s):  
S. He ◽  
D. Lin ◽  
J. Wang
Keyword(s):  
Stability Analysis ◽  
Scaling Factor ◽  
Guidance System ◽  
Necessary Condition ◽  
Stability Conditions ◽  
Motion Stability ◽  
Model Derivation ◽  
The Stability ◽  
Stability Issues ◽  
Sufficient And Necessary Condition

ABSTRACTThis paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

Vibration stability analysis of dual motor harmonic synchronous excitation nonlinear vibration conveyer

2018 ◽  
Vol 42 (4) ◽  
pp. 419-426 ◽  
Author(s):  
Xiaohao Li ◽  
Yuanyuan Sun ◽  
Tao Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear Vibration ◽  
Vibration Machine ◽  
Nonlinear Dynamical ◽  
Motion Stability ◽  
Practical Applications ◽  
Nonlinear Force ◽  
The Stability ◽  
Parameter Perturbation Method ◽  
Compensation Function

To enhance the stability of a harmonic vibration synchronous conveyer, this paper establishes a nonlinear dynamical model for this kind of vibration machine, and the effects and compensation function on the stability produced by the nonlinearity of a master vibration spring have been analyzed. A small parameter perturbation method has been used to analyze the effects of a nonlinear force on the conveyer when a fluctuating impact was loaded onto the machine. The reaction between motion stability of the vibration conveyer and the synchronization of the two motors was also investigated. The results of experiments and practical applications demonstrated the correctness of the motion stability analysis of this nonlinear vibration conveyer and its application validity. In conclusion, significant reference values for design, dynamic analysis, testing, and application of the nonlinear vibration conveyer, with harmonic synchronous vibration, actuated by two motors have been achieved.

On stabilization of bipedal robots during disturbed standing using the concept of Lyapunov exponents

Robotica ◽  
2006 ◽  
Vol 24 (5) ◽  
pp. 621-624 ◽  
Author(s):  
Caixia Yang ◽  
Qiong Wu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponents ◽  
Stability Region ◽  
State Feedback ◽  
State Feedback Control ◽  
Bipedal Robots ◽  
The Stability ◽  
The One ◽  
Balancing Control ◽  
Switching State

Design of balancing control and the stability analysis of a biped during disturbed standing are investigated. A PD-based switching state feedback control is used to stabilize the biped at the upright position while satisfying the constraints between the feet and the ground. The concept of Lyapunov exponents is used for the stability analysis, and a stability region is determined. Furthermore, the stability region is compared and agrees well with the one from the previous work that predicts the feasible movement during which balance of human standing can be maintained. This agreement shows the potential of the concept of Lyapunov exponents to be used as a measure of balancing of human standing. The work contributes to bipedal balancing control, which is important in the development of bipedal robots.

scholarly journals Deriving a Control-Oriented Model for an Axisymmetric Vehicle With the Power-Law Revolution Nose

2020 ◽  
Author(s):  
Jun Huang ◽  
Zhigui Liu ◽  
Zhiqin Liu ◽  
Qingfeng Wang ◽  
Jie Fu
Keyword(s):  
Stability Analysis ◽  
Heating Rate ◽  
Power Law ◽  
Aerodynamic Force ◽  
Pseudospectral Method ◽  
Axisymmetric Body ◽  
Trajectory Design ◽  
Vehicle Model ◽  
The Stability ◽  
Fitting Model

The purpose of this paper is to construct a new general vehicle model as an open fundamental material for the guidance and control research. In this study, parameterized configuration, aerodynamics calculation, control-oriented modeling, stability analysis, and nominal trajectory design are performed for the general vehicle model. First, the aerodynamic configuration is parameterized as an axisymmetric body with a power-law revolution nose. Then, an engineering method considering inviscid flow, base drag and skin friction is used for the aerodynamics calculation, and a control-oriented fitting model of longitudinal aerodynamics is established based on the analysis of the correlation between aerodynamic force and the parameters of Mach number, attack angle, elevator deflection and height. Next, the aerothermodynamic environment prediction of power-law revolution axisymmetric hypersonic vehicle (PRAHV) is discussed, and the nose heating rate formula of PRAHV is established. The stability analysis and nominal trajectory design of PRAHV is performed based on the fitting model and the heating rate formula. The stability analysis shows that both the static stability and dynamic stability of the vehicle are unstable. The nominal trajectory of unpowered longitudinal maneuvering is achieved by the hp-adaptive pseudospectral method, which demonstrated that the availability of the control-oriented model established in this paper. In conclusion, this work provides a fundamental object for further study of vehicle guidance, control, and evaluation.

Passive Dynamic Biped Walking—Part II: Stability Analysis of the Passive Dynamic Gait

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Derek Koop ◽  
Christine Q. Wu
Keyword(s):  
Angular Momentum ◽  
Stability Analysis ◽  
Lyapunov Exponents ◽  
Basin Of Attraction ◽  
Dynamic Walking ◽  
Novel Method ◽  
The Stability ◽  
Dynamic Gait ◽  
Excellent Tool ◽  
The Basin Of Attraction

Passive dynamic walking is an excellent tool for evaluating biped stability measures, due to its simplicity, but an understanding of the stability, in the classical definition, is required. The focus of this paper is on analyzing the stability of the passive dynamic gait. The stability of the passive walking model, validated in Part I, was analyzed with Lyapunov exponents, and the geometry of the basin of attraction was determined. A novel method was created to determine the 2D projection of the basin of attraction of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of gait was examined. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Sign in / Sign up

Export Citation Format

Share Document