scholarly journals Stability Analysis of an Inverted Pendulum on a Cart with the Presence of Restoring and Frictional Forces Disturbance using Observer Based and Full State Feedback H2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Fiseha Bogale
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
System Stability ◽  
Lagrangian Equation ◽  
System Equation ◽  
Full State ◽  
Full State Feedback ◽  
Frictional Forces ◽  
The Stability

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

scholarly journals Stability Analysis of an Inverted Pendulum on a Cart with the Presence of Restoring and Frictional Forces Disturbance using Observer Based and Full State Feedback H2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Fiseha Bogale
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
System Stability ◽  
Lagrangian Equation ◽  
System Equation ◽  
Full State ◽  
Full State Feedback ◽  
Frictional Forces ◽  
The Stability

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

scholarly journals Stability Control of Double Inverted Pendulum on a Cart Using Full State Feedback with H infinity and H 2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Reta Degefa
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
State Feedback Control ◽  
Superior Performance ◽  
Lagrange Equations ◽  
H Infinity ◽  
Full State ◽  
Full State Feedback

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

scholarly journals Stability Control of Double Inverted Pendulum on a Cart using Full State Feedback with H infinity and H 2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Reta Degefa
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
State Feedback Control ◽  
Superior Performance ◽  
Lagrange Equations ◽  
H Infinity ◽  
Full State ◽  
Full State Feedback

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

Discussion On “Selective-Compliance-Based Lagrange Model and Multilevel Non-Collocated Feedback Control of a Humanoid Robot”

2020 ◽  
pp. 1-7
Author(s):  
Gustavo A. Medrano-Cerda
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Humanoid Robot ◽  
Velocity Feedback ◽  
Technical Errors ◽  
Full State ◽  
Full State Feedback ◽  
The Stability ◽  
Motor Velocity ◽  
Stability Results

Abstract The publication [1] makes unjustified claims, has many inconsistencies, numerous technical errors in the theoretical exposition and omitted proofs. The stability claim of the COM dynamics is incomplete and errors increase in time indicating that the robot is unstable and will eventually fall. The range of disturbances that the controller can handle is not suitably addressed. In addition the reported tracking stability results, for PDD control (motor position, motor velocity and link velocity feedback) and PPDD (full state feedback), have already been published by Lanari [1a], [2a] for a larger class of models and with full details of the corresponding Lagrange stability proofs.

scholarly journals Application of LQR Full-State Feedback Controller for Rotational Inverted Pendulum

2021 ◽  
Vol 2111 (1) ◽  
pp. 012006
Author(s):  
N Setiawan ◽  
G N P Pratama
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Equilibrium Points ◽  
Linear Quadratic Regulator ◽  
Feedback Controller ◽  
Control Law ◽  
Linear Quadratic ◽  
State Feedback Controller ◽  
Full State ◽  
Full State Feedback

Abstract The rotational inverted pendulum is an interesting subject for some researchers, especially control engineers. Its nonlinear and underactuated characteristic make it quite challenging to stabilize it. Hence, a proper control law is a must to make it stable. Here, in this paper, we present a control law using LQR (Linear-Quadratic Regulator) to stabilize the rotational inverted pendulum. The experiments are carried out by linearizing the model and simulate the response in MATLAB. The results show that the controller succeeds to stabilize the states of rotational inverted pendulum to their respective equilibrium points. Even more, it provides zero settling errors.

scholarly journals Calculation of the critical delay for the double inverted pendulum

2020 ◽  
pp. 107754632092690
Author(s):  
Csenge A Molnar ◽  
Tamas Balogh ◽  
Islam Boussaada ◽  
Tamas Insperger
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Dimensional Space ◽  
Computational Effort ◽  
Closed Loop System ◽  
Characteristic Roots ◽  
Full State ◽  
Full State Feedback ◽  
Delayed State Feedback

Single and double inverted pendulum systems subjected to delayed state feedback are analyzed in terms of stabilizability. The maximum (critical) delay that allows a stable closed-loop system is determined via the multiplicity-induced-dominancy property of the characteristic roots, that is the dominant (rightmost) roots are associated with higher multiplicity under certain conditions of the system parameters. Other methods such as tracking the changes of the D-curves with increasing delay and the Walton–Marshall method are also demonstrated for the example of the single pendulum. For the double inverted pendulum subjected to full state feedback, the number of control gains is four, and application of numerical methods requires therefore high computational effort (i.e. optimization in a four-dimensional space). It is shown that, with the multiplicity-induced-dominancy–based approach, the critical delay and the associated control gains can be determined directly using the characteristic equation and its derivatives.

scholarly journals Robust Full State Feedback Controller Design Using H∞ for Inverted Pendulum System

2018 ◽  
pp. 39-48
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Upright Position ◽  
Feedback Controller ◽  
Pendulum System ◽  
Integral Term ◽  
Inverted Pendulum System ◽  
Full State ◽  
Full State Feedback

This paper presents the design of a full state feedback H∞ controller to an inverted pendulum system. The nonlinear and linearized models of the system are obtained. The main goal of the proposed controller is to maintain the pendulum in the upright position and achieve a desirable tracking for the cart position. To achieve desirable tracking properties an integral term is added. The robustness of the proposed controller is examined when a 20% variation in the parameters of system is considered.

Flexible-Joint Humanoid Balancing Augmentation via Full-State Feedback Variable Impedance Control

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Emmanouil Spyrakos-Papastavridis ◽  
Jian S. Dai
Keyword(s):  
State Feedback ◽  
Position Control ◽  
Impedance Control ◽  
Humanoid Robots ◽  
Flexible Joint ◽  
Model Free ◽  
Floating Base ◽  
Full State ◽  
Full State Feedback ◽  
Series Elastic Actuators

Abstract This paper attempts to address the quandary of flexible-joint humanoid balancing performance augmentation, via the introduction of the Full-State Feedback Variable Impedance Control (FSFVIC), and Model-Free Compliant Floating-base VIC (MCFVIC) schemes. In comparison to rigid-joint humanoid robots, efficient balancing control of compliant bipeds, powered by Series Elastic Actuators (or harmonic drives), requires the design of more sophisticated controllers encapsulating both the motor and underactuated link dynamics. It has been demonstrated that Variable Impedance Control (VIC) can improve robotic interaction performance, albeit by introducing energy-injecting elements that may jeopardize closed-loop stability. To this end, the novel FSFVIC and MCFVIC schemes are proposed, which amalgamate both collocated and non-collocated feedback gains, with power-shaping signals that are capable of preserving the system's stability/passivity during VIC. The FSFVIC and MCFVIC stably modulate the system's collocated state gains to augment balancing performance, in addition to the non-collocated state gains that dictate the position control accuracy. Utilization of arbitrarily low-impedance gains is permitted by both the FSFVIC and MCFVIC schemes propounded herein. An array of experiments involving the COmpliant huMANoid reveals that significant balancing performance amelioration is achievable through online modulation of the full-state feedback gains (VIC), as compared to utilization of invariant impedance control.

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