Two relay controller for real time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum via quasi‐continuous HOSM

Estrada, Antonio; Aguilar, Luis T.; Iriarte, Rafael

doi:10.1002/asjc.339

Cited by 10 publications

(7 citation statements)

References 20 publications

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“…The latter condition on the nonvanishing perturbation 2 requires it to have a bounded derivative (where it exists), that is, it is a Lipschitz function of time. These conditions (11) are clearly satisfied (at least locally) for the situation considered in (10). In the generalized form (11) further uncertain and/or perturbation effects can be considered.…”

Section: Problem Statementmentioning

confidence: 84%

Reaction wheel pendulum control using fourth‐order discontinuous integral algorithm

Gutiérrez‐Oribio

Mercado‐Uribe

Moreno

2020

Intl J Robust & Nonlinear

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The fourth-order model of the reaction wheel pendulum is considered and a fourth-order discontinuous integral algorithm is used for stabilization and tracking of the system, using a continuous control signal. The states reach the origin or a reference signal in finite-time, even in presence of uncertain control coefficient and a kind of matched and unmatched uncertainties/disturbances. A homogeneous Lyapunov function is designed to ensure local finite-time stability of the system, which can be used for designing the controller gains. Simulations and experimental results illustrate the performance and advantages of the presented algorithm. K E Y W O R D S finite-time convergence, higher-order sliding-mode control, nonlinear control, tracking control, wheel pendulum Abbreviations: 3-DIA, third order discontinuous integral algorithm; 4-DIA, fourth order discontinuous integral algorithm; RWP, reaction wheel pendulum.

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Section: Problem Statementmentioning

confidence: 84%

Reaction wheel pendulum control using fourth‐order discontinuous integral algorithm

Gutiérrez‐Oribio

Mercado‐Uribe

Moreno

2020

Intl J Robust & Nonlinear

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“…Another interesting and challenging task with the IWIP is the stabilization of periodic motions. Authors in [41][42][43][44][45][46] developed a (quasi-continuous) high(second)-order sliding mode control to solve the tracking control problem for the IWIP. These authors developed a reference model (trajectory) based on a two-relay controller, which was introduced to produce oscillations where the desired amplitude and frequency were reached by choosing the control gains properly.…”

Section: Literature Reviewmentioning

confidence: 99%

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

et al. 2017

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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.

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“…Then the sliding surface parameters in (35) i.e. k1, k2, k3 and amust be chosen such that all the roots of (39) satisfy the condition arg( ) λ π > 2L [45].…”

Section: S T Ke T K D E T K D E T K E Tmentioning

confidence: 99%

“…In , an adaptive dynamic sliding‐mode neural control (ADSNC) system composed of a neural controller and a fuzzy compensator has been proposed. A quasi‐continuous high‐order sliding mode (QC‐HOSM) control has been developed in to solve the tracking control problem for an inertia wheel pendulum. The synchronization problem for a class of uncertain chaotic systems has been investigated in .…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Controller Design for A Flexible Link Manipulator Robot

Delavari¹,

Lanusse²,

Sabatier³

2013

Asian Journal of Control

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In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single‐link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.

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Two relay controller for real time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum via quasi‐continuous HOSM

Cited by 10 publications

References 20 publications

Reaction wheel pendulum control using fourth‐order discontinuous integral algorithm

Reaction wheel pendulum control using fourth‐order discontinuous integral algorithm

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

Fractional Order Controller Design for A Flexible Link Manipulator Robot

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