Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems
| Autor: | Alberto Trevisani, Roberto Belotti, Dario Richiedei |
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| Rok vydání: | 2020 |
| Předmět: |
Optimal design
Semidefinite embedding 0209 industrial biotechnology Eigenstructure assignment Control and Optimization Optimality criterion Computer science Underactuation Linear system 0211 other engineering and technologies 02 engineering and technology Active control Rank minimization Structural modification Computer Graphics and Computer-Aided Design Computer Science Applications Mechanical system 020901 industrial engineering & automation Control and Systems Engineering Control theory Convex optimization Software Subspace topology 021106 design practice & management |
| Zdroj: | Structural and Multidisciplinary Optimization. 63:499-514 |
| ISSN: | 1615-1488 1615-147X |
| DOI: | 10.1007/s00158-020-02709-x |
| Popis: | The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone. |
| Databáze: | OpenAIRE |
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