MATLAB CONTROL SYSTEM TOOLBOX 9 Podręcznik Użytkownika Pobierz pdf (Strona 386)

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10 Reliable Computations

10-14

• The pole locations are very sensitive to the coefficients of the denominator

polynomial.

• The balanced companion form produced by

ss, while better than the

standard companion form, often results in ill-conditioned eigenproblems,

especially with higher-order systems.

The above statements hold even for systems with distinct poles, but are

particularly relevant when poles are multiple.

Zero-Pole-Gain Models

The third major representation used for LTI models in MATLAB is the

factored, or zero-pole-gain (ZPK) representation. It is sometimes very

convenient to describe a model in this way although most major design

methodologies tend to be oriented towards either transfer functions or

state-space.

In contrast to polynomials, the ZPK representation of systems can be more

reliable. At the very least, the ZPK representation tends to avoid the

extraordinary arithmetic range difficulties of polynomial coefficients, as

illustrated in the “Transfer Function” section. The transformation from state

space to zero-pole-gain is stable, although the handling of infinite zeros can

sometimes be tricky, and repeated roots can cause problems.

If possible, avoid repeated switching between different model representations.

As discussed in the previous sections, when transformations between models

are not numerically stable, roundoff errors are amplified.

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