Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach

2016 ◽  
Vol 39 (11) ◽  
pp. 1721-1734 ◽  
Author(s):  
Abdul Jabbar ◽  
Fahad Mumtaz Malik ◽  
Shahzad Amin Sheikh
Keyword(s):  
Inverted Pendulum ◽  
Coupled System ◽  
System Model ◽  
Control Law ◽  
Second Stage ◽  
Backstepping Approach ◽  
Stabilizing Control ◽  
Control Scheme ◽  
Backstepping Controller ◽  
Two Stages

Modified backstepping control is proposed for an under-actuated rotary double inverted pendulum. The system has actuated rotary base joint with which two unactuated links are attached. The proposed control design is a three step process for de-coupled system model. In the first stage, a backstepping controller is designed for each of the active and passive joints. In the second stage, compensation is introduced in the respective control efforts to cater for uncertain terms based on Lyapunov function for each joint. Finally, the controllers obtained in the two stages are combined to form a total control law. The performance of the proposed control scheme is evaluated by convergence analysis and simulations.

scholarly journals Swinging up the Furuta Pendulum and its Stabilization Via Model Predictive Control

2013 ◽  
Vol 64 (3) ◽  
pp. 152-158 ◽  
Author(s):  
Pavol Seman ◽  
Boris Rohal’-Ilkiv ◽  
Martin Juh´as ◽  
Michal Salaj
Keyword(s):  
Predictive Control ◽  
Inverted Pendulum ◽  
Control Law ◽  
Classical Approach ◽  
Second Stage ◽  
Total Potential ◽  
Predictive Controller ◽  
Power Law Function ◽  
Two Stages ◽  
Rotary Inverted Pendulum

This paper deals with certain options on controlling an inverted rotary pendulum also known as the Furuta pendulum. Controlling an inverted pendulum involves two stages. The first stage is the swing up of the pendulum and the second stage is its balancing in the up-right position. The paper describes two possibilities on swinging up the pendulum. First one is the classical approach based on comparing the current total (potential and kinetic) energy of the system with the energy in its stabilized up-right position. The second option uses an exponentiation operation over the pendulum position since the trend of power law function is very convenient for determining the amount of required energy to be delivered to the system. For the purposes of balancing the pendulum in the up-right position a predictive controller based on optimal control law with perturbation was proposed, which is an LQ controller with control signal corrections when constraints are exceeded. The results are illustrated by real-time experiments on a laboratory rotary inverted pendulum setup.

Design and development of a backstepping controller autopilot for fixed-wing UAVs

2021 ◽  
pp. 1-27
Author(s):  
D. Sartori ◽  
F. Quagliotti ◽  
M.J. Rutherford ◽  
K.P. Valavanis
Keyword(s):  
Real Time ◽  
Control Law ◽  
Parametric Uncertainties ◽  
Hardware In The Loop ◽  
Aircraft Control ◽  
Backstepping Approach ◽  
Small Uav ◽  
Backstepping Controller ◽  
Definition Of ◽  
Performance Results

Abstract Backstepping represents a promising control law for fixed-wing Unmanned Aerial Vehicles (UAVs). Its non-linearity and its adaptation capabilities guarantee adequate control performance over the whole flight envelope, even when the aircraft model is affected by parametric uncertainties. In the literature, several works apply backstepping controllers to various aspects of fixed-wing UAV flight. Unfortunately, many of them have not been implemented in a real-time controller, and only few attempt simultaneous longitudinal and lateral–directional aircraft control. In this paper, an existing backstepping approach able to control longitudinal and lateral–directional motions is adapted for the definition of a control strategy suitable for small UAV autopilots. Rapidly changing inner-loop variables are controlled with non-adaptive backstepping, while slower outer loop navigation variables are Proportional–Integral–Derivative (PID) controlled. The controller is evaluated through numerical simulations for two very diverse fixed-wing aircraft performing complex manoeuvres. The controller behaviour with model parametric uncertainties or in presence of noise is also tested. The performance results of a real-time implementation on a microcontroller are evaluated through hardware-in-the-loop simulation.

Control of Two-Link Flexible Structures

Volume 1 ◽  
2004 ◽  
Author(s):  
Clarice Wagner-Nachshoni ◽  
Yoram Halevi
Keyword(s):  
Transfer Function ◽  
Time Delays ◽  
Wave Motion ◽  
Controller Design ◽  
Flexible Structures ◽  
Infinite Dimensional ◽  
Second Stage ◽  
Finite Dimensional ◽  
Control Scheme ◽  
Two Stages

A method of noncollocated controller design for non-uniform flexible structures, governed by the wave equation, is proposed. An exact, infinite dimensional, transfer function, relating the actuation and measurement points, with general boundary conditions, is derived for the multi-link case. Three modeling methods are presented and discussed. A key element of the model is the existence of time delays, due to the wave motion, which play a major role in the controller design. The design consists of two stages. First an inner rate loop is closed in order to improve the system dynamic behavior. It leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated position loop is closed. It has the structure of an observer–predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order, with arbitrarily assigned dynamics, plus delay.

Backstepping Controller Design for a 5 DOF Spherical Inverted Pendulum

2019 ◽  
Vol 41 ◽  
pp. 37-50 ◽  
Author(s):  
Soukaina Krafes ◽  
Zakaria Chalh ◽  
Abdelmjid Saka
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Virtual Reality Environment ◽  
Linear Quadratic ◽  
Control Scheme ◽  
Linearized System ◽  
Backstepping Controller

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.

Nonlinear Control of an Inverted Pendulum on a Cart by a Single Control Law

2013 ◽  
Vol 464 ◽  
pp. 279-284 ◽  
Author(s):  
Aydın Özbey ◽  
Erol Uzal ◽  
Hüseyin Yildiz
Keyword(s):  
Nonlinear Control ◽  
Global Stability ◽  
Mechanical System ◽  
Feedback Linearization ◽  
Numerical Experiments ◽  
Inverted Pendulum ◽  
Vertical Position ◽  
Control Law ◽  
Underactuated Mechanical System ◽  
Control Scheme

Stabilization at the top vertical position of an inverted pendulum on a cart, while bringing the cart to a desired position, by applying a force to the cart is considered. This is an underactuated mechanical system for which the main nonlinear control scheme, feedback linearization, fails. A single control law producing the force on the cart using cart velocity, and position and velocity of the pendulum is developed and shown, by numerical experiments, to asymptotically stabilize the pendulum at the top position while bringing the cart to its origin, although no attemp is made for a proof of global stability.

COMPARISON OF AN X4-AUV PERFORMANCE USING A BACKSTEPPING AND INTEGRAL BACKSTEPPING APPROACH

2016 ◽  
Vol 78 (6-11) ◽  
Author(s):  
Nur Fadzillah Harun ◽  
Zainah Md. Zain
Keyword(s):  
Autonomous Underwater Vehicle ◽  
Control Method ◽  
Underwater Vehicle ◽  
Control Technique ◽  
Underactuated System ◽  
Control Law ◽  
Backstepping Approach ◽  
Highly Nonlinear ◽  
Backstepping Controller ◽  
Propose Control System

X4-AUV is a type of an autonomous underwater vehicle (AUV) which has 4 inputs with six degrees of freedoms (6-DOFs) in motion and is classified under an underactuated system. Controlling an underactuated system is difficult tasks because of the highly nonlinear dynamic, uncertainties in hydrodynamics behaviour and mostly those systems fails to satisfy Brockett’s Theorem. It usually required nonlinear control technique and this paper proposed an integral backstepping controller for stabilizing an underactuated X4-AUV. A control law is designed for the system in new state space using integral backstepping. The performance of the proposed control method is examined through simulation and results demonstrate all motion is stabilized and convergence into desired point. We also compared the results with backstepping approach to see the effectiveness of the propose control system.

Global Stability Study of a Compliant Double-Inverted Pendulum Based on Hamiltonian Modeling

2012 ◽  
Author(s):  
Emmanouil Spyrakos-Papastavridis ◽  
Gustavo Medrano-Cerda ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Global Stability ◽  
Inverted Pendulum ◽  
Physical Structure ◽  
Stability Study ◽  
Dynamical Model ◽  
Hamiltonian Equations ◽  
Stabilizing Control ◽  
Control Scheme ◽  
Simulation Results ◽  
Insight Into

This paper presents a dynamical model of a compliant double-inverted pendulum that is used to approximate the physical structure of the compliant humanoid (COMAN) robot, using both the Hamiltonian and the Lagrangian approaches. A comparison between the two aims at providing insight into the various advantages and/or disadvantages associated to each approach. Through manipulation of the resulting formulae, it is shown that the Hamiltonian equations possess certain characteristics, such as the allowance of the tracking of global stability, that render this method of representation suitable for legged robotics applications. Finally, an asymptotically stabilizing control scheme is presented together with simulation results.

Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions

2004 ◽  
Vol 127 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Yoram Halevi
Keyword(s):  
Wave Equation ◽  
Transfer Function ◽  
Transfer Functions ◽  
Controller Design ◽  
Flexible Structures ◽  
Infinite Dimensional ◽  
Second Stage ◽  
Finite Dimensional ◽  
Control Scheme ◽  
Two Stages

A method of noncollocated controller design for flexible structures, governed by the wave equation, is proposed. First an exact, infinite dimension, transfer function is derived and its properties are investigated. A key element in that part is the existence of time delays due to the wave motion. The controller design consists of two stages. The first one is an inner collocated rate loop. It is shown that there exists a controller that leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated position loop is closed. It has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order, with arbitrarily assigned dynamics, plus delay.

Altered Fine Structure of B Lymphocytes Correlated with Defective Terminal Differentiation

1973 ◽  
Vol 31 ◽  
pp. 386-387
Author(s):  
Dale E. Bockman ◽  
L. Y. Frank Wu ◽  
Alexander R. Lawton ◽  
Max D. Cooper
Keyword(s):  
Immune Deficiency ◽  
B Lymphocytes ◽  
Plasma Cells ◽  
Present Report ◽  
Specific Antigen ◽  
Terminal Differentiation ◽  
Second Stage ◽  
Two Stages ◽  
Deficiency Diseases ◽  
Cell Line Generation

B-lymphocytes normally synthesize small amounts of immunoglobulin, some of which is incorporated into the cell membrane where it serves as receptor of antigen. These cells, on contact with specific antigen, proliferate and differentiate to plasma cells which synthesize and secrete large quantities of immunoglobulin. The two stages of differentiation of this cell line (generation of B-lymphocytes and antigen-driven maturation to plasma cells) are clearly separable during ontogeny and in some immune deficiency diseases. The present report describes morphologic aberrations of B-lymphocytes in two diseases in which second stage differentiation is defective.

Distributed Entropy Energy-Efficient Clustering algorithm for cluster head selection (DEEEC)

2020 ◽  
Vol 39 (6) ◽  
pp. 8139-8147
Author(s):  
Ranganathan Arun ◽  
Rangaswamy Balamurugan
Keyword(s):  
Energy Efficient ◽  
Clustering Algorithm ◽  
Cluster Head ◽  
Residual Energy ◽  
Energy Utilization ◽  
Sensor Nodes ◽  
Second Stage ◽  
Energy Efficient Clustering ◽  
Two Stages ◽  
Ch Selection

In Wireless Sensor Networks (WSN) the energy of Sensor nodes is not certainly sufficient. In order to optimize the endurance of WSN, it is essential to minimize the utilization of energy. Head of group or Cluster Head (CH) is an eminent method to develop the endurance of WSN that aggregates the WSN with higher energy. CH for intra-cluster and inter-cluster communication becomes dependent. For complete, in WSN, the Energy level of CH extends its life of cluster. While evolving cluster algorithms, the complicated job is to identify the energy utilization amount of heterogeneous WSNs. Based on Chaotic Firefly Algorithm CH (CFACH) selection, the formulated work is named “Novel Distributed Entropy Energy-Efficient Clustering Algorithm”, in short, DEEEC for HWSNs. The formulated DEEEC Algorithm, which is a CH, has two main stages. In the first stage, the identification of temporary CHs along with its entropy value is found using the correlative measure of residual and original energy. Along with this, in the clustering algorithm, the rotating epoch and its entropy value must be predicted automatically by its sensor nodes. In the second stage, if any member in the cluster having larger residual energy, shall modify the temporary CHs in the direction of the deciding set. The target of the nodes with large energy has the probability to be CHs which is determined by the above two stages meant for CH selection. The MATLAB is required to simulate the DEEEC Algorithm. The simulated results of the formulated DEEEC Algorithm produce good results with respect to the energy and increased lifetime when it is correlated with the current traditional clustering protocols being used in the Heterogeneous WSNs.

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