On a Control of a Non-Ideal Mono-Rail System With Periodic Coefficients

2005 ◽  
Author(s):  
N. J. Peruzzi ◽  
J. M. Balthazar ◽  
B. R. Pontes
Keyword(s):  
Iterative Method ◽  
Inverted Pendulum ◽  
Periodic Problem ◽  
Periodic Systems ◽  
Lagrange Equations ◽  
Floquet Multipliers ◽  
Stability Diagrams ◽  
Rail System ◽  
The Stability ◽  
And Control

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F transformation). This method was presented recently in [3–9].

On Non-Linear Dynamics and a Periodic Control Design Applied to the Potential of Membrane Action

2006 ◽  
Vol 5-6 ◽  
pp. 47-54 ◽  
Author(s):  
Fabio R. Chavarette ◽  
N.J. Peruzzi ◽  
José Manoel Balthazar ◽  
H.A. Hermini
Keyword(s):  
Action Potential ◽  
Control Design ◽  
Periodic Problem ◽  
Test Bed ◽  
Membrane Action ◽  
Floquet Multipliers ◽  
Linear Dynamics ◽  
Stability Diagrams ◽  
Complex Models ◽  
The Stability

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

2006 ◽  
Vol 2 (1) ◽  
pp. 32-39 ◽  
Author(s):  
N. J. Peruzzi ◽  
J. M. Balthazar ◽  
B. R. Pontes ◽  
R. M. L. R. F. Brasil
Keyword(s):  
Equations Of Motion ◽  
Periodic Problem ◽  
Dc Motor ◽  
Transportation System ◽  
Stability Diagrams ◽  
Dynamics And Control ◽  
The Stability ◽  
Load Transportation ◽  
And Control ◽  
The Mathematical Model

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor. The governing equations of motion were derived via Lagrange’s equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial expansion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha’s theory.

scholarly journals Turning Gait Planning Method for Humanoid Robots

2018 ◽  
Vol 8 (8) ◽  
pp. 1257 ◽  
Author(s):  
Tianqi Yang ◽  
Weimin Zhang ◽  
Xuechao Chen ◽  
Zhangguo Yu ◽  
Libo Meng ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Translational Motion ◽  
Humanoid Robots ◽  
Inverted Pendulum Model ◽  
Straight Line ◽  
Pendulum Model ◽  
The Stability ◽  
And Control ◽  
Present Simulation

The most important feature of this paper is to transform the complex motion of robot turning into a simple translational motion, thus simplifying the dynamic model. Compared with the method that generates a center of mass (COM) trajectory directly by the inverted pendulum model, this method is more precise. The non-inertial reference is introduced in the turning walk. This method can translate the turning walk into a straight-line walk when the inertial forces act on the robot. The dynamics of the robot model, called linear inverted pendulum (LIP), are changed and improved dynamics are derived to make them apply to the turning walk model. Then, we expend the new LIP model and control the zero moment point (ZMP) to guarantee the stability of the unstable parts of this model in order to generate a stable COM trajectory. We present simulation results for the improved LIP dynamics and verify the stability of the robot turning.

An Approximate Analysis of Quasi-Periodic Systems Via Floquét Theory

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Parametric Excitation ◽  
Periodic System ◽  
Floquet Theory ◽  
Picard Iteration ◽  
Periodic Systems ◽  
Transition Matrices ◽  
Frequency Spectra ◽  
Periodic Coefficients ◽  
Stability Diagrams ◽  
The Stability

Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases, the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices (STMs) are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.

Modeling and Control of a Spherical Inverted Pendulum With Actuator Saturation

2019 ◽  
Author(s):  
Geovani Bondo ◽  
Chengzhi Yuan ◽  
Chang Duan
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Actuator Saturation ◽  
Control Strategies ◽  
Mathematic Model ◽  
Disturbance Attenuation ◽  
Modeling And Control ◽  
Advanced Control ◽  
The Stability ◽  
And Control

Abstract This paper studies the modeling and control of a spherical inverted pendulum (SIP). The SIP is deemed to be a reasonable model for rocket-propelled body and is often used to test advanced control strategies. The mathematic model is derived based on a Quanser two degrees-of-freedom inverted pendulum commercial product. The pendulum is mounted on a five-bar mechanism that is actuated by two rotary servo base units. Unlike conventional assumption that the two motors are allowed to rotate simultaneously, we assume a more challenging scenario that at one time only one motor is working. The system is hence modeled as a switched system as two motors have to be switched in order to balance the pendulum at its unstable equilibrium. Switched controllers, together with a switching strategy are developed to ensure the stability of the system and satisfy a disturbance attenuation performance index. Simulation results are presented to show the effectiveness of the proposed method.

scholarly journals Development of Graphical Interface System for Inverted Pendulum Stabilization

2019 ◽  
pp. 150
Author(s):  
Erwin Susanto
Keyword(s):  
Inverted Pendulum ◽  
Control Design ◽  
Mathematic Model ◽  
Graphical Interface ◽  
Control Engineering ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Interface System ◽  
The Stability ◽  
And Control

Currently, most of basic control engineering lectures teach both mathematic model and control of an inverted pendulum to explain stability problems in dynamic systems. The inverted pendulum system is a pendulum controlled with a certain force in order to stand in balance around vertical equilibrium line. Hence this system is a highly unstable system and needs stabilization methods using a  kind of controller. This paper describes how to design a Proportional Derivative Integral (PID) controller via root locus technique to stabilize it and realization of its interface system for monitoring angle trajectory. This visualization is needed to observe the stability and  effectiveness of its mathematic model and control design. Experimental results and analysis show that control design and interface system can be implemented well.

Dynamic Modeling and Control of a Novel One-Legged Hopping Robot

Robotica ◽  
2021 ◽  
pp. 1-19
Author(s):  
Amin Khakpour Komarsofla ◽  
Ehsan Azadi Yazdi ◽  
Mohammad Eghtesad
Keyword(s):  
Sliding Mode ◽  
Main Body ◽  
Lagrange Equations ◽  
Flat Foot ◽  
Modeling And Control ◽  
System A ◽  
Hopping Robot ◽  
Hopping Robots ◽  
The Stability ◽  
And Control

SUMMARY In this article, a novel mechanism for planar one-legged hopping robots is proposed. The robot consists of a flat foot which is pinned to the leg and a reciprocating mass which is connected to the leg via a prismatic joint. The proposed mechanism performs the hopping by transferring linear momentum between the reciprocating mass and its main body. The nonlinear equations of the motion of the robot are derived using the Euler–Lagrange equations. To accomplish a stable jump, appropriate trajectories have been planned. To guarantee a stable response for this nonlinear system, a sliding-mode controller is implemented. The performance of the hopping robot is investigated through numerical simulations. The results confirm the stability of the hopping robot through the jump cycle on a flat surface and in climbing up and down ramp and stairs.

scholarly journals Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

2021 ◽  
Vol 11 (4) ◽  
pp. 1829
Author(s):  
Davide Grande ◽  
Catherine A. Harris ◽  
Giles Thomas ◽  
Enrico Anderlini
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Short Term Memory ◽  
Moving Average ◽  
Machine Learning Algorithms ◽  
Physical Models ◽  
Data Driven ◽  
The Stability ◽  
And Control ◽  
Nonlinear Autoregressive

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.

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