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The paper presents a comparative analysis of extended horizon model predictive control deployed for two various state prediction algorithms designed for discrete-time fractional-order state space systems. The first one is a finite fractional difference state predictor derived on the basis of a finite-length approximation of the fractional-order state space system. The second one is a BTA-based integer-order...
In this paper, controversial views on the use of an integer- and fractional-order derivatives in the theory and practice of electric circuits are discussed. Maxwell's equations are definitely useful in classical circuit analyses but empirical, fractional-order modeling is advocated in specific applications, including an exemplary supercapacitor charging circuit. Thus, both methodologies can be employed...
This paper presents a new approach to approximation of linear time-invariant (LTI) discrete-time fractional-order state space SISO systems by means of the SVD-originated balanced truncation (BT) method applied to an FIR-based representation of the fractional-order system. This specific representation of the system enables to introduce simple, analytical formulas for determination of the Cholesky factorizations...
This paper introduces a method for modeling and identification of a simple dynamical system described by fractional-order differential equation. The Grünwald-Letnikov fractional-order derivative is approximated by a discrete-time Laguerre-based model, giving rise to a new discrete-time integerorder equation modeling the considered system. An application example involves a supercapacitor charging circuit...
This paper presents a new method for modeling and identification of a simple electric circuit described by fractional-order differential equation. The Grunwald-Letnikov fractional-order derivative is approximated by its effective discrete-time model based on Laguerre filters, giving rise to a new discrete-time integer-order equation modeling the considered electric circuit. High accuracy of modeling...
In this paper, a Grünwald-Letnikov-originated fractional-order difference (FD) is modeled with finite-length approximators called a finite fractional difference (FFD) and a normalized finite fractional difference (NFFD), whose time-domain structure enables their effective employment in the prediction process for linear discrete-time fractional-order state-space systems. The main, original contribution...
This paper presents a general, modified framework for various time-domain approximations to the Grünwald-Letnikov fractional difference, namely finite fractional and Laguerre-based differences. The approximations are applied in the modeling problem for linear fractional-order state space systems, with two different implementation schemes presented.
In this paper, a new definition of a right inverse of nonsquare parameter matrices is derived from MVC-related inverses of nonsquare polynomial matrices. The new definition is employed in a stabilizing state-space perfect control law for nonsquare LTI MIMO systems. A simulation example shows that the new inverse outperforms the classical minimum-norm right inverse.
This paper presents a new implementable strategy for modeling and identification of a fractional-order discrete-time nonlinear block-oriented SISO Wiener system. The concept of modeling of a linear dynamics by means of orthonormal basis functions (OBF) is employed to separate linear and nonlinear submodels, which enables a linear regression formulation of the parameter estimation problem. Finally,...
This paper presents new results in the reduction of a steady-state error in modeling of the Grünwald-Letnikov (GL) discrete-time fractional difference by means of discrete-time Laguerre filters. A discussion of various approximation criteria contributes to the steady-state accuracy problem. The paper is culminated with the presentation of finite fractional/Laguerre-based difference (FFLD), whose excellent...
This paper presents a new concept of modeling of LTI SISO discrete-time fractional-order systems, in which the Laguerre filters are employed to model both 1) the Grünwald-Letnikov fractional difference and 2) a dynamics of the LTI SISO fractional-order system. Such a ‘double-Laguerre’ concept yields original accuracy and computational results at both modeling stages, illustrated with a series of simulation...
Normalized finite fractional differences are considered as an approximation to the Grunwald-Letnikov fractional difference. In particular, adaptive finite fractional difference (AFFD) is recalled and effectively modified by the introduction of a time-varying forgetting factor. The modified AFFD is shown in simulations to provide an excellent approximation performance, both in terms of the modeling...
This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.
This paper presents (structurally stable) pole-free control designs for (a deterministic version of) generalized minimum variance control and linear quadratic regulation for nonsquare LTI MIMO systems. For both discrete-time control strategies, two alternative approaches are offered, the numerical one related with limiting control solutions as control weighting matrices tend to the zero ones and the...
In the paper a multicontroller-based switchable control system structure is proposed to control nonlinear MIMO plants. The considered structure contains a set of linear feedback controllers operating together with an additional, statically decoupled loop of the control system. The nonlinear model of a drilling vessel in three degrees of freedom (3DOF) on the sea surface is used as a MIMO plant to...
Constrained minimum variance control is offered for nonsquare LTI MIMO systems. A constrained control design takes advantage of the so-called control zeros. The new control strategy is compared with familiar generalized minimum variance control and possible application areas of the two are discussed.
The task schedulability theorem in the celebrated GRMS theory provides a sufficient condition only, specifying the upper bound on CPU utilization by scheduled periodic tasks. This paper presents a simulation study on real-time task scheduling for a specific case when the upper bound on processor utilization can be exceeded. The results are applied in a problem of multiprocessor task scheduling.
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