On the Control and Stability of One Class of Biped Locomotion Systems

The control and stability properties of a “simplified dynamic system” representing a particular biped gait are discussed. The simplified dynamic system consists of an algorithmically controlled lower limb system and a movable point mass. The concepts of repeatability and cyclicity are introduced by means of this model. These concepts provide the basis for control considerations in this class of systems. They lead to conditions which guarantee the maintenance of a gait. Stability of such nonlinear systems cannot be considered by classical techniques. To study stability, the concept of disturbance to nonlinear dynamic systems is introduced. This concept leads to a measure of stability by a quantity termed an “index of capability.” A method of computation for this index for this class of machines is shown.

Download Full-text

PARAMETRIC IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS USING COMBINED LEVENBERG–MARQUARDT AND GENETIC ALGORITHM

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455407002484 ◽

2007 ◽

Vol 07 (04) ◽

pp. 715-725 ◽

Cited By ~ 9

Author(s):

R. KISHORE KUMAR ◽

S. SANDESH ◽

K. SHANKAR

Keyword(s):

Genetic Algorithm ◽

Nonlinear Systems ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Parametric Identification ◽

Computational Effort ◽

Technical Note ◽

Nonlinear Dynamic Systems ◽

Levenberg Marquardt ◽

Time Accuracy

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.

Download Full-text

Diagnosing Irregularities of Nonlinear Dynamic Systems With Implementation of Periodicity-Ratio

Volume 11: Mechanical Systems and Control ◽

10.1115/imece2008-66041 ◽

2008 ◽

Author(s):

Liming Dai ◽

Guoqing Wang

Keyword(s):

Nonlinear Systems ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

The Other ◽

Nonlinear Dynamic Systems ◽

Deterministic System ◽

Final States ◽

Regular Motion ◽

Chaotic Vibrations ◽

Irregular Behavior

Among the irregular responses of nonlinear dynamic systems, chaotic responses of nonlinear systems are probably the most attractive phenomena along with the new observations in the last decades. A nonlinear deterministic system may behavior chaotically under regular such as periodic excitations. Regular motion of a system subjected to periodic exertions is usually periodic. In contrast with regular motions, final states of chaotic vibrations are extremely nonperiodic. This research is to analyzing the irregular behavior of dynamic systems with implementation of a newly developed criterion named Periodicity-Ratio. The development of a methodology for diagnosing the irregular motions from the regular motions of a dynamic system is presented. The Periodicity-Ratio describes the degree of periodicity of motion and can be conveniently used to distinguish a nonperiodic motion from a regular vibration or oscillation and to diagnose whether or not a motion is chaotic and the other irregular responses of the nonlinear dynamic systems, without plotting any figures. The analyses on the irregular behavior of nonlinear dynamic systems with the implementation of the Periodicity-Ratio will be demonstrated.

Download Full-text

Methods of Identification of Definite Degenerated and Nonlinear Dynamic System Using Specially Programmed Nonharmonic Enforce

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4036080 ◽

2017 ◽

Vol 139 (8) ◽

Cited By ~ 4

Author(s):

Miroslaw Bocian ◽

Krzysztof Jamroziak ◽

Mariusz Kosobudzki ◽

Maciej Kulisiewicz

Keyword(s):

Energy Balance ◽

Dynamic System ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Degrees Of Freedom ◽

Nonlinear Dynamic System ◽

Dynamic Structure ◽

Dynamic Loads ◽

Nonlinear Dynamic Systems ◽

Wide Range

The paper presents the new way of identification of complex nonlinear dynamic systems. The method has been explained with the use of a dynamic structure (degenerated one) with 1.5 degrees-of-freedom and some nonlinear restitution force. The applied method allows for the assessment of the dynamic behavior of material in a wide range of dynamic loads. The equation of energy balance when oscillations are set harmonic is applicable to the solution. It is possible when the loading force is adjustable. The method has been computer verified using a system with cubic spring characteristic.

Download Full-text

Assessment of Transient Stability of Nonlinear Dynamic Systems by the Method of Tangent Hyperplanes and the Method of Tangent Hypersurfaces

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3153086 ◽

1989 ◽

Vol 111 (3) ◽

pp. 540-541

Author(s):

A. M. Eskiciogˇlu

Keyword(s):

Asymptotic Stability ◽

Dynamic System ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Transient Stability ◽

Stability Boundary ◽

Direct Methods ◽

Nonlinear Dynamic System ◽

Nonlinear Dynamic Systems ◽

Stability Assessment

Two direct methods, the method of tangent hyperplanes and the method of tangent hypersurfaces, are applied to an elementary nonlinear dynamic system for transient stability assessment. The former method is based on the approximation of the asymptotic stability boundary by hyperplanes at a certain class of unstable singular points in the state-space, and the latter replaces hyperplanes by hypersurfaces. The applicability and accuracy of both methods are evaluated through a comparison of results.

Download Full-text

Characterizing Nonlinear Dynamic Systems With Periodicity Ratio and Statistic Hypothesis

Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B ◽

10.1115/imece2011-62109 ◽

2011 ◽

Author(s):

Lu Han ◽

Liming Dai

Keyword(s):

Nonlinear Systems ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Poincaré Map ◽

Numerical Results ◽

Present Approach ◽

Nonlinear Dynamic Systems ◽

Statistical Hypothesis ◽

Poincare Map ◽

Nonlinear Characteristics

By introducing a statistical hypothesis to Periodicity Ratio, the efficiency and accuracy of diagnosing the nonlinear characteristics of dynamic systems are improved. Overlapping points in a Poincare map are verified on a statistically sound basis. The characteristics of nonlinear systems are investigated by using the present approach. The numerical results generated by the approach are compared with that of the conventional approaches.

Download Full-text