Journal ArticleDOI

# A novel fractional-order model and controller for vibration suppression in flexible smart beam

01 Jul 2018-Nonlinear Dynamics (Springer Netherlands)-Vol. 93, Iss: 2, pp 525-541

TL;DR: The mathematical framework used to derive a fractional-order impedance lumped model for capturing frequency response of a flexible beam system exposed to a multisine excitation is described, and it is shown that the fractional order model outperforms an integer order model of the smart beam.

AbstractVibration suppression represents an important research topic due to the occurrence of this phenomenon in multiple domains of life. In airplane wings, vibration can cause discomfort and can even lead to system failure. One of the most frequently used means of studying vibrations in airplane wings is through the use of dedicated flexible beams, equipped with sensing and actuating mechanisms powered by suitable control algorithms. In order to optimally reject these vibrations by means of closed-loop control strategies, the availability of a model is required. So far, the modeling of these smart flexible beams has been limited to deliver integer order transfer functions models. This paper, however, describes the mathematical framework used to derive a fractional-order impedance lumped model for capturing frequency response of a flexible beam system exposed to a multisine excitation. The theoretical foundation stems from fractional calculus applied in combination with transmission line theory and wave equations. The simplified model reduces to a minimal number of parameters when converging to a limit value. It is shown that the fractional-order model outperforms an integer order model of the smart beam. Based on this novel fractional-order model, a fractional-order $$\hbox {PD}^\mu$$ controller is then tuned. The controller design is based on shaping the frequency response of the closed-loop system such that the resonant peak is reduced in comparison to the uncompensated smart beam system and disturbances are rejected. Experimental results, considering a custom-built smart beam system, are provided, considering both passive and active control situations, showing that a significant improvement in the closed-loop behavior is obtained using the proposed controller. Comparisons with a fractional-order $$\hbox {PD}^\mu$$ controller, tuned according to classical open-loop frequency domain design specifications, are provided. The experimental results show that the proposed tuning technique leads to similar results as the classical approach. Thus, the proposed method is a viable alternative, being based on closed-loop specifications, which is more intuitive for practitioners.

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TL;DR: The research carried out in the past five years, in the areas of modeling, and optimal positioning of piezoelectric actuators/sensors, for active vibration control, are covered.
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TL;DR: The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates.
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Journal ArticleDOI
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### Cites background from "A novel fractional-order model and ..."

• ...Several researchers have used fractional order tools to model more accurately viscoelastic phenomena [1], aerodynamics [2], structural engineering [3], non-Newtonian characteristics in blood [4,5], type 1 diabetes [6], diffusion phenomena in magnetic resonance imaging [7], post-exposure prophylaxis model in HIV [8], epidemic models for infectious diseases [9], biochemical phenomena [10], etc....

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Journal ArticleDOI
TL;DR: Simulation results validate the advantages of proposed fractional order impedance control and it can be also employed to absorb/increase, hold/keep, and dissipate/decrease system energy to achieve jumping, bouncing and friendly contact, respectively.
Abstract: This paper proposes a novel fractional order impedance control. In traditional impedance control model, the orders of inertia, damping, and stiffness are integers and the contact force can be reduced effectively to some extent in robots and manipulators. However, there exists a tracking error of end-effector at the stable state due to the existence of stiffness, which is not conducive to tackle tasks based on high performance position control for robots and manipulators. Thus, an integral item is added into the traditional impedance model to eliminate the tracking error. Besides, the idea of fractional order is introduced to make the orders of inertia, damping, and stiffness change from integers to fractions to achieve more significant compliant performance. Simulation results validate the advantages of proposed fractional order impedance control and it can be also employed to absorb/increase, hold/keep, and dissipate/decrease system energy to achieve jumping, bouncing and friendly contact, respectively. Also, three criterions of choosing and tuning all these 14 parameters in the proposed fractional order impedance control are given out. This provides an insight for robot dynamic interaction, bouncing and jumping control.

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##### References
More filters
Book
01 Jan 1970

17,588 citations

Journal ArticleDOI
TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.

2,154 citations

BookDOI
Concepción A. Monje
01 Jan 2010

1,478 citations

Book
Concepción A. Monje
01 Jan 2010
TL;DR: Fractional-order control strategies for Power Electronic Buck Converters have been discussed in this paper, as well as some nonlinear Fractionalorder Control Strategies for nonlinear control strategies.
Abstract: Fundamentals of Fractional-order Systems and Controls.- Fundamentals of Fractional-order Systems.- State-space Representation and Analysis.- Fundamentals of Fractional-order Control.- Fractional-order PID-Type Controllers.- Fractional-order Proportional Integral Controller Tuning for First-order Plus Delay Time Plants.- Fractional-order Proportional Derivative Controller Tuning for Motion Systems.- Fractional-order Proportional Integral Derivative Controllers.- Fractional-order Lead-lag Compensators.- Tuning of Fractional-order Lead-lag Compensators.- Auto-tuning of Fractional-order Lead-lag Compensators.- Other Fractional-order Control Strategies.- Other Robust Control Techniques.- Some Nonlinear Fractional-order Control Strategies.- Implementations of Fractional-order Controllers: Methods and Tools.- Continuous-time and Discrete-time Implementations of Fractional-order Controllers.- Numerical Issues and MATLAB Implementations for Fractional-order Control Systems.- Real Applications.- Systems Identification.- Position Control of a Single-link Flexible Robot.- Automatic Control of a Hydraulic Canal.- Mechatronics.- Fractional-order Control Strategies for Power Electronic Buck Converters.

700 citations