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.

Feedforward and Feedback Optimal Control of Autonomous Profiling Monitoring Underwater Vehicle with Disturbance

2014 ◽  
Vol 602-605 ◽  
pp. 970-973 ◽  
Author(s):  
Hua Mu ◽  
Jian Yuan
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Feedback Linearization ◽  
Vertical Plane ◽  
Underwater Vehicle ◽  
Linearization Method ◽  
Control Law ◽  
Control Scheme ◽  
System States ◽  
Feedback Optimal Control

The optimal control of autonomous profiling monitoring underwater vehicle (APMUV) is investigated. Firstly, dynamics equations in vertical plane with disturbances are constructed, and the equations are converted into a linear system by feedback linearization method and then feedforward and feedback optimal control (FFOC) law is designed for the linear system. To solve the unpractical problem of the control law, we construct a disturbance observer to observe the system states to make a quick convergance of the observed system states. Numerical simulations show the effectiveness of the control scheme

scholarly journals Combination of Two Nonlinear Techniques Applied to a 3-DOF Helicopter

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
P. Ahmadi ◽  
M. Golestani ◽  
S. Nasrollahi ◽  
A. R. Vali
Keyword(s):  
Convergence Rate ◽  
Feedback Linearization ◽  
Sliding Mode ◽  
Control Law ◽  
Sliding Mode Controller ◽  
Control Methods ◽  
Control Effort ◽  
Control Techniques ◽  
Control Scheme ◽  
Feedback Linearization Control

A combination of two nonlinear control techniques, fractional order sliding mode and feedback linearization control methods, is applied to 3-DOF helicopter model. Increasing of the convergence rate is obtained by using proposed controller without increasing control effort. Because the proposed control law is robust against disturbance, so we only use the upper bound information of disturbance and estimation or measurement of the disturbance is not required. The performance of the proposed control scheme is compared with integer order sliding mode controller and results are justified by the simulation.

scholarly journals Design controler of the quasi-time optimization approach for stabilizing and trajectory tracking of inverted pendulum

2018 ◽  
Vol 226 ◽  
pp. 02007 ◽  
Author(s):  
Nguyen Xuan Chiem ◽  
Hai Nguyen Phan
Keyword(s):  
Inverted Pendulum ◽  
External Disturbance ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Vertical Position ◽  
Control Law ◽  
Optimization Approach ◽  
Time Control ◽  
Time Optimization ◽  
Better Than

This article describes the method of stabilizing and tracking the trajectory of the inverted pendulum with the quasi-time optimization approach. The controller proposed in this paper is not only to stabilize the inverted pendulum in a vertical position but also to cause the inverted pendulum to follow a predetermined reference signal even when there is an interference effect. The focus of this project is the design of a quasi-time control law based on the quasi-time optimization approach and Lyapunov stability theory. The simulation and experimental results suggest that the proposed controller controls the inverted pendulum balance and cart position stability which are better than the LQR method even when there is an external disturbance effect.

Kinematics, Dynamics and Control of a Planar 3-DOF Tensegrity Robot Manipulator

2007 ◽  
Author(s):  
Rafael E. Vasquez ◽  
Julio C. Correa
Keyword(s):  
Nonlinear Control ◽  
Feedback Linearization ◽  
Robot Manipulator ◽  
Equation Of Motion ◽  
Tensegrity Systems ◽  
Control Scheme ◽  
Dynamics And Control ◽  
Cartesian Coordinate ◽  
Three Degree Of Freedom ◽  
And Control

In this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar three-degree-of-freedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedback-linearization-based nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.

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.

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.

scholarly journals Tracking of periodic oscillations in an underactuated system via adaptive neural networks

2018 ◽  
Vol 37 (1) ◽  
pp. 128-143 ◽  
Author(s):  
Sergio A Puga-Guzmán ◽  
Carlos Aguilar-Avelar ◽  
Javier Moreno-Valenzuela ◽  
Víctor Santibáñez
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Mechanical System ◽  
Feedback Linearization ◽  
Control Technique ◽  
Underactuated System ◽  
Periodic Oscillations ◽  
Underactuated Mechanical System ◽  
Model Based ◽  
Adaptive Neural Networks

In this paper, the tracking control of periodic oscillations in an underactuated mechanical system is discussed. The proposed scheme is derived from the feedback linearization control technique and adaptive neural networks are used to estimate the unknown dynamics and to compensate uncertainties. The proposed neural network-based controller is applied to the Furuta pendulum, which is a nonlinear and nonminimum phase underactuated mechanical system with two degrees of freedom. The new neural network-based controller is experimentally compared with respect to its model-based version. Results indicated that the proposed neural algorithm performs better than the model-based controller, showing that the real-time adaptation of the neural network weights successfully estimates the unknown dynamics and compensates uncertainties in the experimental platform.

scholarly journals Nonlinear Control System Design for Active Lubrication of Hydrostatic Thrust Bearing

Coatings ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 426
Author(s):  
Yuanpeng Sha ◽  
Changhou Lu ◽  
Wei Pan ◽  
Shujiang Chen ◽  
Peiqi Ge
Keyword(s):  
Nonlinear Control ◽  
Feedback Linearization ◽  
Thrust Bearing ◽  
Control Method ◽  
Sliding Mode ◽  
Linearization Method ◽  
Control Law ◽  
Machining Accuracy ◽  
Control Input ◽  
Vibration Absorption

The active controlled hydrostatic bearing is becoming more and more popular because of its accuracy, safety, as well as low vibration and noise. In this paper, we present a design approach for a hydrostatic thrust bearing system, where the analytical nonlinear state space equation of the system is established first, and then three kinds of control inputs are investigated and compared to each other. It is found that, by selecting the supply pressure as the control input, we could obtain an affine nonlinear system, which could be linearized by the feedback linearization method, and its robustness could be enhanced by the sliding mode control method. The tracking control law could be easily obtained with the linearized system. The simulation verifies the effectiveness of the nonlinear control law. The proposed nonlinear control model might have a positive effect on the improvement of the machining accuracy, safety, and vibration absorption.

Passivity Based Control of a Cart with Inverted Pendulum

2013 ◽  
Vol 332 ◽  
pp. 339-344 ◽  
Author(s):  
Matthias Jörgl ◽  
Kurt Schlacher ◽  
Hubert Gattringer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lyapunov Function ◽  
Mechanical System ◽  
Simple Proof ◽  
Control Strategy ◽  
Inverted Pendulum ◽  
Equation Of Motion ◽  
Control Law ◽  
Passivity Based Control

This paper deals with passivity based control of a cart , which can moves on a skew plain. On the cart a non actuated pendulum is assembled. Therefore, the mechanical system is non-linear, one degree under actuated and instable. The equation of motion is derived by the method of Lagrange. The goal of the control strategy is to stabilize the cart and the upper position of the pendulum. The applied control strategy is called Interconnection Damping Assignment Passivity Based Control (IDA-PBC). This method allows a physical approach with a simple proof of stability having appropriate Lyapunov function on hand. The simple proof of stability is an advantage of this theory. However, the proof of stability is fulfilled, challenging partial differential equation have to be solved to get the control law. Measurements results are presented.

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