Motion control of planar parallel robot using the fuzzy descriptor system approach

Vermeiren, Laurent; Dequidt, Antoine; Afroun, Mohamed; Guerra, Thierry Marie

doi:10.1016/j.isatra.2012.04.001

Cited by 55 publications

(25 citation statements)

References 33 publications

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“…In practice, some mechanical systems, such as, double inverted pendulum model of human standing in [43], twowheeled self-balanced transporter in [44] and 2-DOF planar parallel robot in [45], can be modelled as nonlinear descriptor systems (43). Applying the established sliding mode control methodology [7], [9], [12], [35], [36] to system (43) involves transformatiom to the nonlinear normal system described bẏ…”

Section: Application To a Class Of Mechanical Systemsmentioning

confidence: 99%

“…For mechanical systems, this assumption may be restrictive because it may be possible to only measure a sub-set of the states in practice. It should be noted that the difference in the input matrices in (45) results from the inverse operation of the derivative-term coefficient E(x(t)), which makes the sliding mode control problem difficult. In addition, the descriptor model of the system (43) has a more simple structure than its normal model (44) and inverse operation of derivative-term matrix is avoid.…”

Section: Application To a Class Of Mechanical Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Zhang

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the T-S fuzzy descriptor systems are developed. A two step design is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities, and the results are used to facilitate the development of a single step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.Index Terms-Observer-based stabilization, T-S fuzzy descriptor systems, integral sliding mode control, mechanical systems.

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Section: Application To a Class Of Mechanical Systemsmentioning

confidence: 99%

Section: Application To a Class Of Mechanical Systemsmentioning

confidence: 99%

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Zhang

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…[Vermeiren et al, 2012] The D-LPV system(1) is admissible. It means that there exists a Lyapunov function…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

Fault Diagnosis Based on Robust Observer for Descriptor-LPV Systems with Unmeasurable Scheduling Functions

López‐Estrada

Ponsart

Theilliol

et al. 2014

IFAC Proceedings Volumes

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“…The advantage of this representation is that it provides a systematic framework for designing control laws through the LMI constrain formulation [13]. In this work we are interested to a TS fuzzy descriptor, which is different from state space expression and have attracted attention in control system design [14]. The descriptor system describes a wider class of system, including physical models and nondynamic constraints [15].…”

Section: B Ts Fuzzy Descriptor Approachmentioning

confidence: 99%

Robust control of two-wheeled self-balanced transporter on sloping ground: A Takagi-Sugeno descriptor approach

Allouche

Vermeiren

Dequidt

et al. 2013

3rd International Conference on Systems and Control

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A commonly asked question in the field of autonomous robotics and intelligent vehicles is : How to design and control an urban transporter able to investigate narrow spaces ? From a mechanical point of view, a two wheeled transporter seems to be a good alternative due to its small footprint and its ability to manoeuvre on tight turns. However, the design of this vehicle requires two level of control : One, for the auto-balancing. The second ensures a velocity tracking. The use of linear control law requires a linearisation of the model around an a priori known equilibrium point under the assumption that the vehicle moves on a plane surface. Now, assume that the vehicle is moving along an unknown slope. Then, the equilibrium point is not known while designing the controller. The linearized model becomes unrepresentative. This work present a control of self-balanced two wheeled transporter. The aim is to design a robust controller able to stabilize the transporter on its natural equilibrium along an unknown slope. A quasi LPV approach, through the so-called TS fuzzy model and LMI constraints will be proposed. Moreover, The natural descriptor form of the mechanical system will be used to design the control law. This last choice allows reducing the conservatism of the LMI conditions. Finally a simulation tests showed the effectiveness of our approach.

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Motion control of planar parallel robot using the fuzzy descriptor system approach

Cited by 55 publications

References 33 publications

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Fault Diagnosis Based on Robust Observer for Descriptor-LPV Systems with Unmeasurable Scheduling Functions

Robust control of two-wheeled self-balanced transporter on sloping ground: A Takagi-Sugeno descriptor approach

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