Friction and the Inverted Pendulum Stabilization Problem

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Sue Ann Campbell ◽  
Stephanie Crawford ◽  
Kirsten Morris
Keyword(s):  
Small Amplitude ◽  
Viscous Friction ◽  
Experimental System ◽  
Linear Quadratic Regulator ◽  
Poor Performance ◽  
Friction Model ◽  
Linear Quadratic ◽  
Stick Slip ◽  
And Performance ◽  
Friction Parameters

We consider an experimental system consisting of a pendulum, which is free to rotate 360deg, attached to a cart. The cart can move in one dimension. We study the effect of friction on the design and performance of a feedback controller, a linear quadratic regulator, that aims to stabilize the pendulum in the upright position. We show that a controller designed using a simple viscous friction model has poor performance—small amplitude oscillations occur when the controller is implemented. We consider various models for stick slip friction between the cart and the track and measure the friction parameters experimentally. We give strong evidence that stick slip friction is the source of the small amplitude oscillations. A controller designed using a stick slip friction model stabilizes the system, and the small amplitude oscillations are eliminated.

scholarly journals Time Delay and Feedback Control of an Inverted Pendulum With Stick Slip Friction

2007 ◽  
Author(s):  
Sue Ann Campbell ◽  
Stephanie Crawford ◽  
Kirsten Morris
Keyword(s):  
Time Delay ◽  
Basin Of Attraction ◽  
Critical Time ◽  
Viscous Friction ◽  
Experimental System ◽  
Friction Model ◽  
Stable Equilibrium Point ◽  
Feedback Controllers ◽  
Stick Slip ◽  
The Basin Of Attraction

We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart which can move in one dimension. There is stick slip friction between the cart and the track on which it moves. Using two different models for this friction we design feedback controllers to stabilize the pendulum in the upright position. We show that controllers based on either friction model give better performance than one based on a simple viscous friction model. We then study the effect of time delay in this controller, by calculating the critical time delay where the system loses stability and comparing the calculated value with experimental data. Both models lead to controllers with similar robustness with respect to delay. Using numerical simulations, we show that the effective critical time delay of the experiment is much less than the calculated theoretical value because the basin of attraction of the stable equilibrium point is very small.

scholarly journals System design for inverted pendulum using LQR control via IoT

2020 ◽  
Vol 11 ◽  
pp. 12
Author(s):  
Dechrit Maneetham ◽  
Petrus Sutyasadi
Keyword(s):  
Inverted Pendulum ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Lqr Controller ◽  
Model Tuning ◽  
And Performance ◽  
Performance Results ◽  
And Control

This research proposes control method to balance and stabilize an inverted pendulum. A robust control was analyzed and adjusted to the model output with real time feedback. The feedback was obtained using state space equation of the feedback controller. A linear quadratic regulator (LQR) model tuning and control was applied to the inverted pendulum using internet of things (IoT). The system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone. Finally, the inverted pendulum was able to be controlled using the LQR controller and the IoT communication developed will monitor to check the all conditions and performance results as well as help the inverted pendulum improved various operations of IoT control is discussed.

ACTIVE VIBRATION CONTROL OF SEISMICALLY EXCITED STRUCTURES BY ATMDS: STABILITY AND PERFORMANCE ROBUSTNESS PERSPECTIVE

2010 ◽  
Vol 10 (03) ◽  
pp. 501-527 ◽  
Author(s):  
ARASH MOHTAT ◽  
AGHIL YOUSEFI-KOMA ◽  
EHSAN DEHGHAN-NIRI
Keyword(s):  
Vibration Control ◽  
Structural Damage ◽  
Fuzzy Logic Controller ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Structural Vibration ◽  
Linear Quadratic ◽  
And Performance ◽  
Performance Robustness

This paper demonstrates the trade-off between nominal performance and robustness in intelligent and conventional structural vibration control schemes; and, proposes a systematic treatment of stability robustness and performance robustness against uncertainty due to structural damage. The adopted control strategies include an intelligent genetic fuzzy logic controller (GFLC) and reduced-order observer-based (ROOB) controllers based on pole-placement and linear quadratic regulator (LQR) conventional schemes. These control strategies are applied to a seismically excited truss bridge structure through an active tuned mass damper (ATMD). Response of the bridge-ATMD control system to earthquake excitation records under nominal and uncertain conditions is analyzed via simulation tests. Based on these results, advantages of exploiting heuristic intelligence in seismic vibration control, as well as some complexities arising in realistic conventional control are highlighted. It has been shown that the coupled effect of spill-over (due to reduction and observation) and mismatch between the mathematical model and the actual plant (due to uncertainty and modeling errors) can destabilize the conventional closed-loop system even if each is alone tolerated. Accordingly, the GFLC proves itself to be the dominant design in terms of the compromise between performance and robustness.

scholarly journals Estimating Friction Parameters in Reaction Wheels for Attitude Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Valdemir Carrara ◽  
Hélio Koiti Kuga
Keyword(s):  
Attitude Control ◽  
Deterministic Model ◽  
High Reliability ◽  
Viscous Friction ◽  
Static Friction ◽  
Friction Model ◽  
Artificial Satellites ◽  
Wide Range ◽  
The Stability ◽  
Friction Parameters

The ever-increasing use of artificial satellites in both the study of terrestrial and space phenomena demands a search for increasingly accurate and reliable pointing systems. It is common nowadays to employ reaction wheels for attitude control that provide wide range of torque magnitude, high reliability, and little power consumption. However, the bearing friction causes the response of wheel to be nonlinear, which may compromise the stability and precision of the control system as a whole. This work presents a characterization of a typical reaction wheel of 0.65 Nms maximum angular momentum storage, in order to estimate their friction parameters. It used a friction model that takes into account the Coulomb friction, viscous friction, and static friction, according to the Stribeck formulation. The parameters were estimated by means of a nonlinear batch least squares procedure, from data raised experimentally. The results have shown wide agreement with the experimental data and were also close to a deterministic model, previously obtained for this wheel. This model was then employed in a Dynamic Model Compensator (DMC) control, which successfully reduced the attitude steady state error of an instrumented one-axis air-bearing table.

Design and Performance Analysis of LQR Controller for Stabilizing Double Inverted Pendulum System

2017 ◽  
Vol 2 (9) ◽  
pp. 1-5
Author(s):  
Ghassan A. Sultan ◽  
Ziyad K. Farej
Keyword(s):  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum Model ◽  
Inverted Pendulum System ◽  
Pendulum Model ◽  
Lqr Controller ◽  
And Performance ◽  
Performance Results

Double inverted pendulum (DIP) is a nonlinear, multivariable and unstable system. The inverted pendulum which continually moves toward an uncontrolled state represents a challenging control problem. The problem is to balance the pendulum vertically upward on a mobile platform that can move in only two directions (left or right) when it is offset from zero stat. The aim is to determine the control strategy that deliver better performance with respect to pendulum's angles and cart's position. A Linear-Quadratic-Regulator (LQR) technique for controlling the linearized system of double inverted pendulum model is presented. Simulation studies conducted in MATLAB environment show that the LQR controller are capable of controlling the multi output double inverted pendulum system. Also better performance results are obtained for controlling heavy driven part DIP system.

scholarly journals Impact Behavior of a Rotating Rigid Body with Impact and Viscous Friction

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Dorian Cojocaru ◽  
Dan B. Marghitu
Keyword(s):  
Viscous Friction ◽  
Friction Model ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Impact Behavior ◽  
Element Analysis ◽  
Friction Parameters ◽  
Friction Function ◽  
Coulomb Dry Friction ◽  
The Impact

The impact between a rotating link and a solid flat surface is considered. For the impact, we consider three distinct periods: elastic period, elastoplastic period, and restitution period. A Hertzian contact force is considered for the elastic period. Nonlinear contact forces developed from finite element analysis are used for the remaining two phases. The tangential effect is taken into account considering a friction force that combines the Coulomb dry friction model and a viscous friction function of velocity. Simulations results are obtained for different friction parameters. An experimental setup was designed to measure the contact time during impact. The experimental and simulation results are compared for different lengths of the link.

scholarly journals Humanoid robot solving a task of balancing on a tilting platform

2020 ◽  
pp. 5-12
Author(s):  
Svyatoslav Golousov ◽  
Sergei Savin ◽  
Semen Kurkin ◽  
Artem Badarin ◽  
Vladimir Khorev ◽  
...  
Keyword(s):  
Control System ◽  
Horizontal Plane ◽  
Human Subject ◽  
Humanoid Robot ◽  
Inverse Dynamics ◽  
Viscous Friction ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Model Based Control ◽  
Model Based

This study focuses on the control of a humanoid robot in a new environment, whose parameters were not accounted for during the design of the robot’s control system. The environments in question are an active and a passive tilting platform. The study shows that the humanoid robot behaves similar to a human subject in the experiments with low viscous friction. In the experiment with high viscous friction, it was demonstrated that the robot is capable of balancing on the platform. Same result was achieved in the case of an active platform. The paper provides a discussion of how the task of standing on a passive platform deviated from the model-based control formulation with constrained linear quadratic regulator and projected inverse dynamics, designed for the case of walking on stationary horizontal plane. The results in the paper suggest that while there are limitations to how well standard control approaches can adapt to the unknown environments, it is still possible to use them directly.

scholarly journals A New Efficient Adaptive Control of Torsional Vibrations Induced by Switched Nonlinear Disturbances

2019 ◽  
Vol 29 (2) ◽  
pp. 285-303 ◽  
Author(s):  
Maciej Wasilewski ◽  
Dominik Pisarski ◽  
Robert Konowrocki ◽  
Czesław I. Bajer
Keyword(s):  
Linear Quadratic Regulator ◽  
Drill String ◽  
Friction Torque ◽  
Nonlinear Behaviour ◽  
Torsional Vibrations ◽  
Linear Quadratic ◽  
Stick Slip ◽  
Direct Measurements ◽  
Excited Vibration ◽  
The Impact

Abstract Torsional vibrations induced in drilling systems are detrimental to the condition of the machine and to the effectiveness of the engineering process. The cause of vibrations is a nonlinear and unknown friction between a drill string and the environment, containing jumps in its characteristics. Nonlinear behaviour of the friction coefficient results in self-excited vibration and causes undesirable stick-slip oscillations. The aim of this paper is to present a novel adaptive technique of controlling vibrating systems. The scheme is based on the linear quadratic regulator and uses direct measurements of the friction torque to synthesize its linear dynamic approximation. This approach allows generating a control law that takes into account the impact of the friction on the system dynamics and optimally steers the system to the desired trajectory. The controller’s performance is examined via numerical simulations of the stabilization of the drilling system. The proposed solution outperforms the comparative LQG regulator in terms of the minimization of the assumed cost functional and the overall stability of the control system under the nonlinear disturbance.

Polynomial-Chaos-Based Numerical Method for the LQR Problem With Uncertain Parameters in the Formulation

2010 ◽  
Author(s):  
Emmanuel Blanchard ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Numerical Method ◽  
Polynomial Chaos ◽  
Linear Quadratic Regulator ◽  
Mean Value ◽  
Optimal Controller ◽  
Linear Quadratic ◽  
Case Scenario ◽  
Worst Case ◽  
Lqr Problem ◽  
And Performance

This paper proposes a polynomial chaos based numerical method providing an optimal controller for the linear-quadratic regulator (LQR) problem when the parameters in the formulation are uncertain, i.e., a controller minimizing the mean value of the LQR cost function obtained for a certain distribution of the uncertainties which is assumed to be known. The LQR problem is written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and an iterative algorithm converges to the optimal answer. The algorithm is applied to a simple example for which the answer is already known. Polynomial chaos based methods have the advantage of being computationally much more efficient than Monte Carlo simulations. The Linear-Quadratic Regulator controller is not very well adapted to robust design, and the optimal controller does not guarantee a minimum performance or even stability for the worst case scenario. Stability robustness and performance robustness in the presence of uncertainties are therefore not guaranteed. However, this is a first step aimed at designing more judicious controllers if combined with other techniques in the future. The next logical step would be to extend this numerical method to H2 and then H-infinity problems.

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