Citation for published version (APA): Cervera, J., Schaft, A. J. V. D., & Baños, A. (2007). Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica, 43(2), 212-225. DOI: 10.1016/j.automatica.2006 Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractPort-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. PortHamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of portHamiltonian systems results in another port-Hamiltonian system with Dirac structure defined by the composition of the Dirac structures of the subsystems. In this paper the composition of Dirac structures is being studied, both in power variables and in wave variables (scattering) representation. This latter case is shown to correspond to the Redheffer star product of unitary mappings. An equational representation of the composed Dirac structure is derived. Furthermore, the regularity of the composition is being studied. Necessary and sufficient conditions are given for the achievability of a Dirac structure arising from the standard feedback interconnection of a plant port-Hamiltonian system and a controller port-Hamiltonian system, and an explicit description of the class of achievable Casimir functions is derived. ᭧

This work focuses on the problem of automatic loop shaping in quantitative feedback theory (QFT), where the search for an optimum design (a non-convex and nonlinear optimization problem) is traditionally simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator. In relation to previous work, the main idea consists in the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function by using a minimum set of parameters. CRONE controllers, in particular CRONE 2 and CRONE 3, are considered as possible candidate structures, being original structures modified for a better approach to the QFT theoretical optimum. CRONE 3 non-minimum-phase zeros are avoided by constraints on the structure parameters.

No abstract

Ideal Bode Characteristics give a classical answer to optimal loop design for LTI feedback control systems, in the frequency domain. This work recovers 4-parameters and 8-parameters Bode optimal loop gains, providing a useful and simple theoretical reference for the best possible loop shaping from a practical point of view. The main result of the paper is to use CRONE compensators to make a good approximation to the Bode optimal loop. For that purpose, a special loop structure based on second and third generation CRONE compensators is used. As a result, simple design relationships will be obtained for tuning the proposed CRONE compensator.

No abstract