MATLAB CONTROL SYSTEM TOOLBOX 9 Podręcznik Użytkownika Pobierz pdf (Strona 374)

10 Reliable Computations

10-2

When working with low-order SISO models (less than five states), computers

are usually quite forgiving and insensitive to numerical problems. You

generally won't encounter any numerical difficulties and MATLAB will give

you accurate answers regardlessofthe modelorconversion method you choose.

For high order SISO models and MIMO models, however, the finite-precision

arithmetic of a computer is not so forgiving and you must exercise caution.

In general, to get a numerically accurate answer from a computer, you need:

• A well-conditioned problem

• An algorithm that is numerically stable in finite-precision arithmetic

• A good software implementation of the algorithm

A problem is said to be well-conditioned if small changes in the data cause only

small corresponding changes in the solution. If small changes in the data have

the potential to induce large changes in the solution, the problem is said to be

ill-conditioned. An algorithm is numerically stable if it does not introduce any

moresensitivity to perturbation than is already inherent in the problem. Many

numerical linear algebra algorithms can be shown to be backward stable; i.e.,

the computed solution can be shown to be (near) the exact solution of a slightly

perturbed original problem. The solution of a slightly perturbed original

problem will be close to the true solution if the problem is well-conditioned.

Thus, a stable algorithm cannot be expected tosolve an ill-conditioned problem

any more accurately than the data warrant, but an unstable algorithm can

produce poor solutions even to well-conditioned problems. For further details

and references to the literature see [5].

While most of the tools in the Control System Toolbox use reliable algorithms,

some of the tools do not use stable algorithms and some solve ill-conditioned

problems. These unreliable tools work quite well on some problems (low-order

systems) but can encounter numerical difficulties, often severe, when pushed

on higher-order problems. These tools are provided because:

• They are quite useful for low-order systems, which form the bulk of

real-world engineering problems.

• Many control engineers think in terms of these tools.

• A more reliable alternative tool is usually available in this toolbox.

• They are convenient for pedagogical purposes.

1 2 ... 369 370 371 372 373 374 375 376 377 378 379 ... 648 649

Komentarze do niniejszej Instrukcji

Brak uwag

Haga clic en el alfabeto a continuación para desplazarse a la lista completa de modelos que comienzan con esa letra

All
a

Modelos	Tipo de documento
AT-3GSDI-14	Manual de usuario Residential - AVPro Alliance, 96 paginas
AT-DVI-14A	Manual de usuario Atlona AT-DVI-14A User manual, 20 paginas
AT-HD-V112	Manual de usuario Product Catalog, 60 paginas Manual de usuario Atlona AT-HD-V112 User manual, 7 paginas
AT-HD-V116	Manual de usuario AtlonA - BZB Express, 9 paginas
AT-HD-V18	Manual de usuario Atlona AT-HD-V18 User manual, 7 paginas Manual de usuario AtlonA, 9 paginas
AT-HD19SS	Manual de usuario www.AtlonA.com, 2 paginas
AT-HDCAT-8	Manual de usuario atlona-2014-catalog-2 - Genesis Technologies, 86 paginas Manual de usuario Atlona HDMI Distribution Amplifier Family, 6 paginas Manual de usuario Atlona 2 x 8 HDMI to HDBaseTTM Extended Distance Distribution, 1 paginas
AT-HDDA-4	Manual de usuario Summer 2013 Catalog, 96 paginas
AT-HDDA-8	Manual de usuario Atlona HDDA HDMI Distribution Amplifier Collection Atlona 1 x 8, 1 paginas
AT-HDRS	Manual de usuario Atlona AT-HDRS User`s manual, 12 paginas
AT-PA100	Manual de usuario Atlona [en] , 4 paginas
AT-PA100-G2	Manual de usuario Atlona AT-PA100-G2 User manual, 10 paginas Manual de usuario Atlona AT-PA100-G2 User manual, 13 paginas
AT-SDI-14	Manual de usuario Atlona AT-SDI-14 User`s manual, 16 paginas