Gain margins and root locus asymptotic behaviour in multivariable design Part II. A critical appraisal of frequency response methods from a root locus point of view
作者:
B. KOUVARITAKIS,
期刊:
International Journal of Control
(Taylor Available online 1978)
卷期:
Volume 27,
issue 5
页码: 725-751
ISSN:0020-7179
年代: 1978
DOI:10.1080/00207177808922406
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A prerequisite for a linear multivariable feedback: system to have good gain margins is that the set of finite zeros and the set of infinite zeros lie in the left half of the complex plane. The spatial arrangement of the asymptotes to branches of the root locus vitally depends on the order of the infinite zeros and this in turn depends on the null structure of a set of parameters called the: projected Markov parameters. The study of the geometric structure of these parameters therefore may be employed as the basis of a critical appraisal of frequency response techniques from a root locus point of view; the inverse Nyquist array (INA) and characteristic locus (CL) techniques are considered here. It is shown that attempts to achieve diagonal dominance, a feature necessary for the application of the INA, may on certain occasions lead to infinite zeros of higher order and thus may severely curtail the system gain margins. The alignment of the characteristic directions at high frequencies, used by the CL on the other hand for the reduction of the misalignment angles, is shown to have a beneficial effect on the structure of the projected Markov parameters. Insight gained by such an appraisal reinforces the belief that root locus and frequency response methods used in a complementary manner may lead to a hybrid design philosophy which is more flexible and effective than either of the two approaches applied separately.
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