A parametric approach to finite-dimensional control of linear distributed-parameter systems

• Published in: International journal of control Vol. 83; no. 8; pp. 1674 - 1685
• Main Authors: Deutscher, J., Harkort, Ch
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01-08-2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; compensator design; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; distributed-parameter systems; eigenvalue assignment; Exact sciences and technology; Industrial metrology. Testing; linear systems; Mechanical engineering. Machine design; Modelling and identification; parameter optimisation; static output feedback; Studies; Feedback regulation; Control synthesis; Separation principle; Linear control; Modeling; Pole assignment; Closed feedback; Dimensioning; Dimensional control; Observer; Distributed control; Eigenvalue problem; Asymptotic approximation; System identification; Distributed parameter system; Output feedback
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2010.487545

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.