Stable limit cycle generation for underactuated mechanical systems, application: Inertia wheel inverted pendulum

Andary, S.; Chemori, Ahmed; Krut, Sébastien

doi:10.1109/iros.2008.4650994

Cited by 10 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gruber and Hofbaur [51] employed the same method for planning periodic motions and designing a stabilizing controller based on a thorough analysis of the dynamics transversal to the resulting limit cycle. In addition, Andary et al [52] proposed a control approach dedicated to stable limit cycle generation for the IWIP. The proposed approach was based on partial nonlinear feedback linearization and dynamic control for optimal periodic reference trajectories tracking.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The proposed approach was based on partial nonlinear feedback linearization and dynamic control for optimal periodic reference trajectories tracking. The feedback controller presented in [52] is enhanced in [53,54] to handle constant disturbances in limit cycle tracking by using online iterative estimation of an equivalent disturbance which is easily compensated by adding the estimated value to the output of the system. Moreover, Zayane-Aissa et al [55] introduced a high order sliding mode structure to solve the problem of trajectory tracking problem of the IWIP in presence of unknown input perturbation.…”

Section: Literature Reviewmentioning

confidence: 99%

“…2. According to [34,35,[52][53][54], the motion of the IWIP is constrained. Indeed, the planar swing motion of the pendulum body is subject to unilateral contacts (constraints) [65], for which its angular position reaches a certain maximum/minimum value at standstill.…”

Section: Motivationsmentioning

confidence: 99%

See 2 more Smart Citations

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

et al. 2017

View full text Add to dashboard Cite

This paper deals with the tracking approach of a self-generated stable limit cycle for an underactuated mechanical system: The Inertia Wheel Inverted Pendulum (IWIP). Such system is subject to unilateral constraints limiting its swing motion. It is known that an Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) can be employed to control such pendulum to its upright position. In this work, we briefly show first that the IWIP can generate a stable period-1 limit cycle through a Hopf bifurcation by varying some gain parameter of the IDA-PBC. Thus, such self-generated limit cycle is used as a reference trajectory, which is chosen to be tracked by the IWIP. To achieve the tracking problem, a supplementary control input is added. Such tracking problem is reformulated as an asymptotic stabilization of the tracking error. Our fundamental approach hinges mainly on the use of the S-procedure to introduce the unilateral constraints, and the Schur complement and the matrix inversion lemma to transform Bilinear Matrix Inequalities (BMI) into Linear Matrix Inequalities (LMI). Several simulations have been presented to corroborate the mathematical results and to show the efficiency of the proposed tracking scheme of the self-generated stable limit cycle of the controlled IWIP, even if it is subject to external disturbances, or in the presence of uncertainties in the friction parameters.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

et al. 2017

View full text Add to dashboard Cite

show abstract

“…The coaxial two-wheeled robot is inherent unstable and underactuated system (Andary, Chemori et al 2008), all of the positions such as keep balance and running are realized by the torque of the two driving wheels, shown in Fig.6. Theoretically, when the two driving wheels are fed by the same torque, the robot will only move in one direction (with a small forward and backward movement before the settlement is achieved) (Ahmad, Tokbi et al 2009).…”

Section: Controller Designmentioning

confidence: 99%

Smooth Control the Coaxial Self-Balance Robot under Impact Disturbances

Gao

2011

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

The purpose of this paper is to propose a systematic smooth control method for improving the stability of the two-wheeled self-balance robot under impact disturbances. For enhancing the robtot stability, a blend controller based on states feedback control embedded with the PID speed synchronization is estabilished, as well as a hybrid filter composes of RC network and Kalman algorithm. With the hybrid filter, disturbance signals are maximally attenuated or directly eliminated, and the system sensitivity to the impact disturbances significantly declines ; under the blend motion controller, the robot can not only keep balance under impacts but also achieve synchronization of the two driving wheels. The dynamic model, the blend controller, hybrid filter, and experimental results including application to transport are described, both of the simulation and experimental results are provided to verify the analysis.

show abstract

“…An Underactuated Mechanical System (UMS) is this which possesses fewer control inputs than degrees of freedom [15,16]. UMSs have been arosen in many different real-life applications, such as: helicopters, aircrafts, spacecrafts, vertical take-off and landing aircrafts, under water vehicles, mobile robots, walking robots and so on.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Dynamic Behaviour of an Inverted Pendulum with Bounded Control

Николов¹,

Nedev²

2016

Journal of Theoretical and Applied Mechanics

View full text Add to dashboard Cite

Abstract. This paper presents an investigation on the behaviour of conventional inverted pendulum with an inertia disk in its free extreme. The system is actuated by means of torques applied to the disk by a DC motor, mounted on the pendulum's arm. Thus, the system is underactuated since the pendulum can rotate freely around its pivot point. The dynamical model is given with three ordinary nonlinear differential equations. Using Poincare-Andronov-Hopf's theory, we find a new analytical formula for the first Lyapunov's value at the boundary of stability. It enables one to study in detail the bifurcation behaviour of the above dynamic system. We check the validity of our analytical results on the first Lyapunov's value by numerical simulations. Hence, we find some new results.

show abstract

Stable limit cycle generation for underactuated mechanical systems, application: Inertia wheel inverted pendulum

Cited by 10 publications

References 8 publications

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

Smooth Control the Coaxial Self-Balance Robot under Impact Disturbances

Bifurcation Analysis and Dynamic Behaviour of an Inverted Pendulum with Bounded Control

Contact Info

Product

Resources

About