Integrated topology and controller optimization using the Nyquist curve

Arnoud Delissen*, Fred van Keulen, Matthijs Langelaar

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
18 Downloads (Pure)


The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation.

Original languageEnglish
Article number80
Number of pages25
JournalStructural and Multidisciplinary Optimization
Issue number4
Publication statusPublished - 2023


  • Closed-loop performance
  • Control co-design
  • Local approximation
  • PID feedback control
  • Robust formulation
  • SISO

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