Modelling and control of flexible joint robot based on Takagi–Sugeno fuzzy approach and its stability analysis via sum of squares

Hosseinpour, M.; Nikdel, Parisa; Badamchizadeh, Mohammad Ali; Akbari, Mohammad

doi:10.1080/13873954.2012.731653

Cited by 10 publications

(3 citation statements)

References 10 publications

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“…Hence, the error dynamics in (18) becomesė = Je + Bv where −2σ ≤ e 1 ≤ 2σ (19) It is worth to note that there is no remarkable difference between the obtained results using the nonlinear system (18) or the linear system (19). However, the strategy developed in this work for the controller synthesis by considering the nonlinear dynamics (18) can be applied for more general constrained nonlinear systems for which the states evolve in a large region as for the case of the single-link rotary flexible joint robot studied in [67].…”

Section: Remarkmentioning

confidence: 88%

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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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Section: Remarkmentioning

confidence: 88%

“…3. The dynamics of the IWIP is a simple class of nonlinear systems with trigonometric nonlinearities, which can occur in robotic applications, such as the single-link flexible robot manipulator [66,67] and the pitch dynamics of a simplified helicopter model [68,69], and other nonlinear systems. 4.…”

Section: Motivationsmentioning

confidence: 99%

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

et al. 2017

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“…In the field of flexible parallel robot, the main researches include: stiffness model based on flexible hinge [2] , influence of mechanism parameters on the system stiffness [3] , mechanism error analysis and compensation [4] , dynamic characteristics [5] , the characteristics of flexible mechanism system and control method [6] and so on. But all these studies are all still in rigid motion range, which didn't considering the effect of flexible hinge deformation to structure movement.…”

Section: Introductionmentioning

confidence: 99%

The Analyse on Stiffness Model of 3-PPSR Flexible Parallel Robot

Luan

Wei

Sun

2014

AMM

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In order to achieve greater workspace motion, it’s designed a high aspect ratio 3-PPSR flexible parallel robot, driven by a piezoelectric motor, connected by flexible hinges, which has the advantages of simple structure, non singular, seamless, high motion precision. Because of the stiffness of the system directly affecting the motion accuracy, load bearing performance, according to the characteristics of high aspect ratio flexible hinge, It’s established the mathematical model of flexible hinge through finite element method. Using method of integral stiffness, conbined coordination equation with force balance equation, the flexible stiffness model of system is obtained. Finally, through using Ansys, it’s confirmed the validity of the theoretical model by comparing of the theoretical stiffness model results with the finite element analysis of the model results, to provide a reliable guarantee for optimization and analysis of kinematics and dynamics of flexible parallel robot.

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Fuzzy-Based Impulsive Synchronization of Different Complex Networks with Switching Topology and Time-Varying Dynamic

Behinfaraz

Ghaemi

Khanmohammadi

et al. 2020

Int. J. Fuzzy Syst.

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Modelling and control of flexible joint robot based on Takagi–Sugeno fuzzy approach and its stability analysis via sum of squares

Cited by 10 publications

References 10 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

The Analyse on Stiffness Model of 3-PPSR Flexible Parallel Robot

Fuzzy-Based Impulsive Synchronization of Different Complex Networks with Switching Topology and Time-Varying Dynamic

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