Interconnection structure preservation design for a type of port‐controlled hamiltonian systems—A parametric approach

• Published in: IET control theory & applications Vol. 15; no. 3; pp. 338 - 347
• Main Authors: Zhao, Tianyi, Duan, Guangren
• Format: Journal Article
• Language: English
• Published: Wiley 01.02.2021
• Subjects: Algebra; Control system analysis and synthesis methods; Multivariable control systems; Nonlinear control systems; Optimisation techniques; Stability in control theory
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/cth2.12046

It is a very important issue to minimise the change of the interconnect structure matrix when stabilising a port‐controlled Hamiltonian (PCH) system. Toward this problem, a parametric design method is proposed in this paper for a type of PCH systems. First, concepts of H‐damping‐assignable and H‐damping‐assigning controller are introduced, and the stability of the closed‐loop system resulting from this type of controller is discussed. Secondly, a necessary and sufficient condition for the system to be H‐damping‐assignable is given, and, when this condition is met, a parametric general expression of all the H‐damping‐assigning controllers is obtained. Thirdly, the free parameters are optimised to minimize the change of the interconnect structure matrix and also the norm of the control gain matrix. The parameter optimisation is formulated as a standard quadratic programming problem, to which analytical solutions are obtained. Finally, comparative simulations are carried out for a numerical example to verify the effect and the superiority of the proposed method.