1,484 research outputs found
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model
Fractional-order controller design with partial pole-zero cancellation
Master´s thesis in Mechatronics (MAS500
Fractional vs. ordinary control systems: What does the fractional derivative provide?
[EN] The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.Conejero, JA.; Franceschi, J.; Picó-Marco, E. (2022). Fractional vs. ordinary control systems: What does the fractional derivative provide?. Mathematics. 10(15):1-18. https://doi.org/10.3390/math10152719118101
Closed-Loop Identification of Stabilized Models Using Dual Input-Output Parameterization
This paper introduces a dual input-output parameterization (dual IOP) for the
identification of linear time-invariant systems from closed-loop data. It draws
inspiration from the recent input-output parameterization developed to
synthesize a stabilizing controller. The controller is parameterized in terms
of closed-loop transfer functions, from the external disturbances to the input
and output of the system, constrained to lie in a given subspace. Analogously,
the dual IOP method parameterizes the unknown plant with analogous closed-loop
transfer functions, also referred to as dual parameters. In this case, these
closed-loop transfer functions are constrained to lie in an affine subspace
guaranteeing that the identified plant is \emph{stabilized} by the known
controller. Compared with existing closed-loop identification techniques
guaranteeing closed-loop stability, such as the dual Youla parameterization,
the dual IOP neither requires a doubly-coprime factorization of the controller
nor a nominal plant that is stabilized by the controller. The dual IOP does not
depend on the order and the state-space realization of the controller either,
as in the dual system-level parameterization. Simulation shows that the dual
IOP outperforms the existing benchmark methods
Fractional Order Identification Method and Control: Development of Control for Non-Minimum Phase Fractional Order System
The increasing use of renewable energy has resulted in the need for improved a dc-dc converters. This type of electronic-based equipment is needed to interface the dc voltages normally encountered with solar arrays and battery systems to voltage levels suitable for connecting three phase inverters to distribution level networks. As grid-connected solar power levels continue to increase, there is a corresponding need for improved modeling and control of power electronic converters. In particular, higher levels of boost ratios are needed to connect low voltage circuits (less than 1000 V) to medium voltage levels in the range of 13 kV to 34 kV. With boost ratios now exceeding a factor of 10, the inherent nonlinearities of boost converter circuits become more prominent and thereby lead to stability concerns under variable load conditions. This dissertation presents a new method for analyzing dc-dc converters using fractional order calculus. This provides control systems designers the ability to analyze converter frequency response with Bode plots that have pole-zero contributions other than +/- 20 dB/decade. This dissertation details a systematic method of deriving the optimal frequency-domain fit of nonlinear dc-dc converter operation by use of a modified describing function technique. Results are presented by comparing a conventional linearization technique (i.e., integer-order transfer functions) to the describing-function derived equivalent fractional-order model. The benefits of this approach in achieving improved stability margins with high-ratio dc-dc converters are presented
Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview
Disturbance Observer has been one of the most widely used robust control
tools since it was proposed in 1983. This paper introduces the origins of
Disturbance Observer and presents a survey of the major results on Disturbance
Observer-based robust control in the last thirty-five years. Furthermore, it
explains the analysis and synthesis techniques of Disturbance Observer-based
robust control for linear and nonlinear systems by using a unified framework.
In the last section, this paper presents concluding remarks on Disturbance
Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure
Application of fractional calculus in the system modelling and control
Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of several systems.N/
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