The fractional order state equations for the control of viscoelastically damped structures

Bagley, Ronald L.; Calico, Robert A.

doi:10.2514/6.1989-1213

Cited by 144 publications

(199 citation statements)

References 9 publications

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“…In [12], the control of viscoelastic damped structure is presented. Control applications to a flexible transmission [13], an active suspension [14], a buck converter [15], a robotic manipulator [16], and a thermal system [17] are also found in the literature.…”

Section: Fractional Order Calculus Definition and Applicationsmentioning

confidence: 99%

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

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Abstract:One of the key issues in control design for Active Magnetic Bearing (AMB) systems is the tradeoff between the simplicity of the controller structure and the performance of the closed-loop system. To achieve this tradeoff, this paper proposes the design of a fractional order Proportional-Integral-Derivative (FOPID) controller. The FOPID controller consists of only two additional parameters in comparison with a conventional PID controller. The feasibility of FOPID for AMB systems is investigated for rotor suspension in both the radial and axial directions. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with a conventional PID controller, as well as with some advanced controllers such as Linear Quadratic Gausian (LQG) and H ∞ controllers. The comparison is made in terms of various stability and robustness specifications, as well as the dimensions of the controllers as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings. The results show that, with a proper selection of gains and fractional orders, the performance of the resulting FOPID is similar to those of the advanced controllers.

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Section: Fractional Order Calculus Definition and Applicationsmentioning

confidence: 99%

Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings

Anantachaisilp¹,

Lin

2017

Actuators

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“…(see, for instance, [10], [26] and [6]). Among these we can mention applications on viscoelasticity [3], analysis of electrode processes [11] and Lorenz systems [8]. Therefore, currently fractional systems (i.e., equations involving fractional derivatives and/or integrals) have been studied by several authors, among them we can mention Hilfer [10], Kilbas et al [13], Miller and Ross [20], Podlubny [26], Samko et al [30], etc.…”

Section: Introductionmentioning

confidence: 99%

Stability for some linear stochastic fractional systems

Fiel¹,

León²,

Márquez-Carreras³

2014

COSA

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Abstract. We obtain a closed expression for the solution of a linear Volterra integral equation with an additive Hölder continuous noise, which is a fractional Young integral, and with a function as initial condition. This solution is given in terms of the Mittag-Leffler function. Then we study the stability of the solution via the fractional calculus. As an application we analyze the stability in the mean of some stochastic fractional integral equations with a functional of the fractional Brownian motion as an additive noise.

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“…On the other hand, fractional calculus provides a powerful tool for the description of memory and hereditary effects in various substances and in modeling dynamical processes in fractal media [6]. For more knowledge of the applications of fractional calculus in modern science and engineering, please consult [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%