On unsolvability of nonlinear system stability

1997 ◽  
Author(s):  
Heikki Hyotyniemi
Keyword(s):  
Nonlinear System ◽  
System Stability

scholarly journals A Controller Combining Positive Velocity Feedback with Negative Angle Feedback for a Two-Wheeled Robot

2015 ◽  
Vol 15 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Lingyan Hu ◽  
Henry Leung Ieee ◽  
Shaoping Xu ◽  
Hua Zhang
Keyword(s):  
Nonlinear System ◽  
Negative Feedback ◽  
Tilt Angle ◽  
Positive Feedback ◽  
Pid Controller ◽  
System Stability ◽  
Velocity Control ◽  
Velocity Feedback ◽  
Wheeled Robot ◽  
The Stability

Abstract The two-wheeled robot is a nonlinear system of multi-variables, higherorder and strong coupling. This paper presented a PID Controller with Double Loops (PCDL) to control the tilt angle and velocity of a two-wheeled robot. The angle controller is the regular negative feedback, while the velocity control is the positive feedback. The Double Loops work cooperatively to endow the system with strong anti-interference ability. The stability of the whole system is analyzed and the criterion of the system stability is developed. The simulation and experiments showed that the two-wheeled robot can self-balance and move at an expected velocity and the system has strong anti-interference ability.

scholarly journals Stability Analysis and Variational Integrator for Real-Time Formation Based on Potential Field

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Shengqing Yang ◽  
Jianqiao Yu
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Dynamic System ◽  
Real Time ◽  
Potential Field ◽  
Lagrange Equation ◽  
System Stability ◽  
Damping Force ◽  
Variational Integrator ◽  
Error Dynamic

This paper investigates a framework of real-time formation of autonomous vehicles by using potential field and variational integrator. Real-time formation requires vehicles to have coordinated motion and efficient computation. Interactions described by potential field can meet the former requirement which results in a nonlinear system. Stability analysis of such nonlinear system is difficult. Our methodology of stability analysis is discussed in error dynamic system. Transformation of coordinates from inertial frame to body frame can help the stability analysis focus on the structure instead of particular coordinates. Then, the Jacobian of reduced system can be calculated. It can be proved that the formation is stable at the equilibrium point of error dynamic system with the effect of damping force. For consideration of calculation, variational integrator is introduced. It is equivalent to solving algebraic equations. Forced Euler-Lagrange equation in discrete expression is used to construct a forced variational integrator for vehicles in potential field and obstacle environment. By applying forced variational integrator on computation of vehicles' motion, real-time formation of vehicles in obstacle environment can be implemented. Algorithm based on forced variational integrator is designed for a leader-follower formation.

scholarly journals Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1727 ◽  
Author(s):  
Susmita Das ◽  
Dalia Nandi ◽  
Biswarup Neogi ◽  
Biswajit Sarkar
Keyword(s):  
Nonlinear System ◽  
System Design ◽  
Lower Limb ◽  
Hardware Design ◽  
System Stability ◽  
Behavioral Analysis ◽  
Stability Factor ◽  
Artificial System ◽  
Effective Implementation ◽  
The Stability

System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems. The stability checking of the proposed artificial lower extremity is the newer approach needed to take decisions on output implementation in the system design.

scholarly journals Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Zhanshan Zhao ◽  
Jing Zhang ◽  
Liankun Sun ◽  
Dakun Zhang
Keyword(s):  
Nonlinear System ◽  
Sliding Mode ◽  
Second Order ◽  
System Stability ◽  
Order System ◽  
Unmodeled Dynamics ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Adaptive Law ◽  
Nonsingular Terminal Sliding Mode

A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.

scholarly journals Analyzing Nonlinear System Stability of a New Hydraulic Bilateral Rolling Shear

2016 ◽  
Vol 56 (10) ◽  
pp. 1789-1795 ◽  
Author(s):  
HeYong Han ◽  
HongZhou Li ◽  
Jia Li ◽  
KeJun Miao ◽  
Jing Wang ◽  
...  
Keyword(s):  
Nonlinear System ◽  
System Stability ◽  
Rolling Shear

Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

2011 ◽  
Vol 330 (24) ◽  
pp. 6006-6022 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Mohamed H. Zaher ◽  
Antonio M. Recuero ◽  
Cheta Rathod
Keyword(s):  
Nonlinear System ◽  
Eigenvalue Analysis ◽  
System Stability ◽  
Gyroscopic Motion
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