LMI-based 2-DoF control design of a manipulator via T-S descriptor approach

Nguyen, Van-Anh; Nguyen, Anh‐Tu; Dequidt, Antoine; Vermeiren, Laurent; Dambrine, Michel

doi:10.1016/j.ifacol.2018.11.525

Cited by 3 publications

(3 citation statements)

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“…From all of the previous references, we can conclude that either the work presented is only applicable to the plant for which they are making the design of the controller, as in [6][7][8], or the controller requires such extensive computing [9] that makes it prohibitive its application in typical industrial robot manipulators, or it could be applied to robots if their work can be extended to more than one link [11]. Additionally, in only half of the papers, a full stability analysis was presented, and none of the previous works have found a strict Lyapunov function for the stability analysis of its control approach.…”

Section: Introduction 1motivationmentioning

confidence: 96%

“…All of these control approaches use a Mamdani type SFC as its core element; nevertheless, there exists the Takagi-Sugeno (T-S) counterpart of fuzzy controllers that has been applied to the control of mechanical or mechatronics systems: in [6], a T-S descriptor was employed to control a 2-DOF robotic manipulator with elastic joints and dry friction. The tracking control design and stability assurance is reformulated as optimization problem based in the solution of a Linear Matrix Inequality (LMI).…”

Section: Introduction 1motivationmentioning

confidence: 99%

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Sectorial Fuzzy Controller Plus Feedforward for the Trajectory Tracking of Robotic Arms in Joint Space

et al. 2021

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In this paper, we propose a Sectorial Fuzzy Controller (SFC) with a feedforward compensation of the robot dynamics in joint space, evaluated at the desired angular positions, velocities, and accelerations, applied to the trajectory tracking of all revolute joints robotic arms. Global uniform asymptotic stability proof applying the direct Lyapunov theorem, is introduced for this new control scheme by using a strict Lyapunov function. This strict Lyapunov function is the first one within the field of fuzzy control that is applied to the trajectory control of robotic manipulators. With this strict Lyapunov function, a sensitivity analysis was also computed for this novel control scheme. Additionally, physical and simulation experimental results are given in comparison to the original control scheme, in which this new controller is inspired: the Proportional-Derivative (PD) controller plus feedforward compensation. The experimental results yielded better performance for the new fuzzy control scheme when compared to the classical structure, in both the joint position errors for similar or smaller values of applied torques, showing the expected tolerance to parametric deviations and uncertainties that all fuzzy controllers possess.

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Section: Introduction 1motivationmentioning

confidence: 96%

Section: Introduction 1motivationmentioning

confidence: 99%

Sectorial Fuzzy Controller Plus Feedforward for the Trajectory Tracking of Robotic Arms in Joint Space

et al. 2021

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“…The parallel distributed compensation (PDC) scheme combined with linear matrix inequalities (LMIs) technique is then utilized in order to construct global controller and ensure system's stability. In [10] a TS fuzzy controller is studied to guarantee the H-infinity performance for tracking problem of a 2 DOF manipulators. Akka et al [11] express the kinematic model of mobile robot in TS form, then PDC with each local controller being linear quadratic regular (LQR) combined with fuzzy controller is constructed to make the robot track the desired trajectories while avoiding obstacles.…”

Section: Introductionmentioning

confidence: 99%

Takagi-Sugeno Fuzzy Approach with Compressed Representation for Overhead Crane System

2022

JST: SSAD

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This paper proposes a Takagi-Sugeno (TS) fuzzy approach for 2-dimensional of freedom overhead crane. Since this system is underactuated with nonlinear mathematical dynamic model, the requirement of achieving accurate positioning while eliminating oscillation is a challenging issue. The nonlinear sector decomposition is taken into implementation which uses the nonlinear terms in the dynamic model as scheduling variables to transform the initial system to TS representation. However, the number of TS fuzzy rules is exponential in the number of nonlinear elements in the system, leading to the increase of computational expense. Therefore, the reduced complexity method is introduced to minimize the scheduling variables in TS system. In addition, the uncertain system’s components are also taken into consideration to enhance the robust property of the system when working in practical environment. The controller is constructed based on parallel distributed compensation (PDC) approach while the linear matrix inequalities (LMIs) technique is employed to analyse the system’s stability. The effectiveness of the proposed method is demonstrated through numeral simulations.

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