Frequency domain analysis and robust control design for an ideal flexible beam
Copyright policy )Frequency domain analysis and robust control design for an ideal flexible beam
This paper deals with the problem of designing a feedback controller for a highly flexible Euler-Bernoulli beam system by means of an \(H^ \infty\)-control design approach. Using skew Toeplitz theory, a distributed-parameter \(H^ \infty\)-optimal controller with a weighted mixed sensitivity can be designed for the beam. Based on the structure of the optimal controller so designed, suboptimal finite-dimensional linear time-invariant (FDLTI) controllers can be further obtained. The optimal weighted closed-loop system offers a precise measure of achievable performance for judging the suboptimality of the FDLTI controllers to be constructed. An infinite product representation for the distributed beam transfer function is also derived, which facilitates the inner/outer factorization of the system. It has been found that when the output is measured at the opposite end of the beam from the control input the beam transfer function possesses infinitely large number of zeros in the right half plane. These zeros can be factored out of the product representation for the beam as an infinite Blaschke product. Even so, this beam an still be dealt with directly using the distributed \(H^ \infty\)-method. The weights used here do not require a substantial trade-off between optimal sensitivity and optimal complementary sensitivity in the crossover region. This fact is intuitively associated with ``easy'' design problem --- those for which the performance requirements are well within the frequency range where the design model is accurately represented and actuator bandwith is generous. In fact, these weights leads to a reduction of the two-block general distance problem to a one- block problem. Moreover, with this approach it is possible to include the added difficulties due to nonminimum phase systems (caused by a pure time-delay or a non-collocated actuator/sensor pair) directly into the design process. It is also possible to use the weighting function in a two-block problem for robust design with respect to variations of the damping parameter.
- University of Minnesota United States
- Worcester Polytechnic Institute United States
- University of Minnesota System United States
- Control Group United States
- University of Rhode Island United States
Design techniques (robust design, computer-aided design, etc.), feedback controller, robust design, \(H^\infty\)-control, Sensitivity (robustness), Existence theories for optimal control problems involving partial differential equations, Sensitivity, stability, well-posedness, Euler-Bernoulli beam system
Design techniques (robust design, computer-aided design, etc.), feedback controller, robust design, \(H^\infty\)-control, Sensitivity (robustness), Existence theories for optimal control problems involving partial differential equations, Sensitivity, stability, well-posedness, Euler-Bernoulli beam system
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