1,721,142 research outputs found
Iterative-interpolation algorithms for L(2) model reduction
No full textThis paper is concerned with the construction of reduced–order models for high–order linear systems in such a way
that the L2 norm of the impulse–response error is minimized. Two convergent algorithms that draw on previous procedures presented by the same authors, are suggested: one refers to s–domain representations, the other to time–domain state–space representations. The algorithms are based on an iterative scheme that, at any step, satisfies certain interpolation constraints deriving from the optimality
conditions. To make the algorithms suitable to the reduction
of very large–scale systems, resort is made to Krylov subspaces and Arnoldi’s method. The performance of the reduction algorithms is tested on two benchmark examples
Fractional order PI controllers for TCP packet flow ensuring given modulus margins
No full textAn Active Queue Management (AQM) robust control strategy for Traffic Control Protocol (TCP) data transfer is proposed. To this purpose, the TCP behaviour is first approximated by a second-order model with delayed input obtained from the linearization of an efficient and commonly used nonlinear fluid-based model. The adopted feedback control structure uses a fractional-order PI controller. To ensure the desired robustness, the parameter regions where such a controller guarantees a given modulus margin (inverse of the H∞ norm of the sensitivity function) are derived. An example commonly used in the literature is worked out to show that the suggested graphically-based design technique is simple to apply while it limits the effects of disturbances and of the unmodelled dynamics
On MIMO model reduction by the weighted equation-error approach
No full textThe paper deals with the problem of approximating a stable continuous-time multivariable system
by minimizing the L 2-norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures for generating approximants that retain different numbers of Markov parameters and time moments are suggested and applied to benchmark examples. The results show that both the transient and the steady-state behaviour of the original systems are reproduced satisfactorily
Locating the equilibrium points of a predator-prey model by means of affine state feedback
No full textA predator–prey model with prey-dependent functional response is considered. The set of all points in the positive quadrant of the state plane that can be made equilibrium points by means of an affine state-feedback control law is determined, and the values of the control parameters ensuring the desired equilibria are provided. It is shown how the asymptotic stability of the equilibrium points depends on simple geometric conditions. The problem of stabilizing unstable equilibrium points is also briefly discussed
A new method for the integer order approximation of fractional order models
No full textThis paper is concerned with the finite–dimensional approximation of a fractional–order system represented in state–space form. To this purpose, resort is made to the Oustaloup method for approximating a fractional–order integrator by a rational filter. The dimension of the resulting integer–order model can be reduced using an efficient algorithm for the minimization of the L2 norm of a weighted equation error. Two numerical examples are worked out to show how the desired approximation accuracy can be ensured
The Lepschy stability test and its application to fractional-order systems
Full text linkIt is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students
Variable-structure control of casting processes
No full textThe paper is concerned with the problem of regulating the molten metal level in the mold of a continuous casting plant despite the continual perturbations caused by mold shaking and the occasional perturbations due to the sudden uncloggings of the nozzle through which the liquid is poured into the mold. To deal with both kinds of perturbations, two distinct controllers are used and suitably activated depending on the operating conditions. It is demonstrated that a controller realization obtained from any time-varying convex combination of two switching-stable controller realizations ensures stability, too. Numerical simulations show that the adopted stability-preserving control policies compare favourably with alternative techniques suggested in the literature to the same purpose
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