Resonant and Antiresonant control of Multiple-Input SecondOrder Systems with Time Delay using Receptance
A variety of problems in control engineering field deal with mathematical models with systems of second-order differential equations, resulting from first-principles analysis using discretization (i.e., finite element method) to obtain finite-dimensional models. These models require, in general, a...
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| Formato: | doctoralThesis |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/56765 |
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| Resumo: | A variety of problems in control engineering field deal with mathematical models with
systems of second-order differential equations, resulting from first-principles analysis using discretization (i.e., finite element method) to obtain finite-dimensional models. These
models require, in general, an accurate knowledge of the parameters involved, such as, for
example, masses, damping and stiffness coefficients in mechanical systems, for the design
of controllers with high performance. The need to consider delays in measuring variables
or actuation in these types of systems makes the problem more challenging, in view of
the transcendent nature of the resulting transfer functions. In this context, the receptance
concept emerges as an alternative, enabling the modeling of these systems entirely from
experimental data, dispensing with the use of simplifying hypotheses and approximations, as is recurrently done in mathematical models with discrete parameters. Another
virtue is highlighted in the waiver of approximations for the exponential term of the delay, which can result in undesirable solutions or very high order transfer functions. Since
their introduction, receptance-based models have gained prominence in several works,
with emphasis on the active control of vibrations by allocating zeros (anti-resonant frequency) and/or poles (resonant frequency). This work proposes a method for controlling
second-order systems with multiple inputs and delays using receptance. The structure of
the controllers uses state feedback, and the control objectives include partial placement of
zeros and poles with guaranteed stability and robustness, based on the maximum peak of
the sensitivity function. Stability is guaranteed from the extended concept of the Nyquist
criterion for systems with multiple inputs. The synthesis of the controller is conducted
from an optimization problem and the solutions are obtained using an algorithm based
on evolutionary theory, where population evaluations are defined according to functions
related to the frequency response of the systems. Numerical examples are presented to
illustrate and discuss the performance of the solutions using the proposed method. |
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