Model and Controller Order Reduction for Infinite Dimensional Systems

Fatmawati^1,[1], R. Saragih¹, B. Riyanto³ & Y. Soeharyadi²

¹Industrial and Financial Mathematics Group

 email: fatma47@students.itb.ac.id; roberd@math.itb.ac.id

 ²Analysis and Geometry Group

 email: yudish@math.itb.ac.id

³School of Electrical Engineering and Informatics

 email: briyanto@lskk.ee.itb.ac.id

  Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia.

[1]Permanent address: Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Kampus C Mulyorejo Surabaya, Indonesia.

This paper presents a reduced order model problem using  reciprocal transformation and balanced truncation followed by low order controller design of infinite dimensional systems. The class of systems considered is that of an exponentially stable state linear systems (A, B, C), where operator A has a bounded inverse, and the operator B and C are of finite-rank and bounded. We can connect the system (A, B, C) with its reciprocal system via the solutions of the Lyapunov equations. The realization of the reciprocal system is reduced by balanced truncation. This result is further translated using reciprocal transformation as the reduced-order model for the systems (A, B, C). Then the low order controller is designed based on the reduced order model. The numerical examples are studied using simulations of Euler-Bernoulli beam to show the closed-loop performance.

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