Parametric state feedback design of linear distributed-parameter systems

• Published in: International journal of control Vol. 82; no. 6; pp. 1060 - 1069
• Main Authors: Deutscher, J., Harkort, Ch
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.06.2009; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; decoupling control; eigenvalue assignment; Exact sciences and technology; linear multi-input distributed-parameter systems; parametric approach; Riesz-spectral operators; MIMO system; State feedback; Decoupling; Eigenfunction; Distributed control; Feedback regulation; Control synthesis; Lumped parameter system; Eigenvalue problem; Distributed parameter system; Pole assignment
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170802434383

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.