A new approach for minimum phase output definition

ABSTRACT

This paper presents a novel method for output redefinition for linear systems. The approach also determines possible relative degrees for the systems corresponding to any new output vector. To guarantee the minimum phase property with a prescribed relative degree, a set of new conditions is introduced. A key feature of these conditions is that there is no need to any form of transformations which make the scheme suitable for optimisation problems in control to ensure the minimum phase property. Moreover, the results are useful for sensor placement problems and for obtaining minimum phase approximations of non-minimum phase systems. Numerical examples including an example of unmanned aerial vehicle systems are given to demonstrate the effectiveness of the methodology.

KEYWORDS:

• Zero dynamics
• relative degree
• state feedback gain
• output definition

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Fatemeh Jahangiri

Fatemeh Jahangiri received her BSc degree in Control Engineering from Ferdowsi University, Mashhad, Iran in 2006 and her MSc degree in Control Engineering from Amirkabir University of Technology, Tehran, Iran in 2009. She is currently doing PhD in Amirkabir University of Technology from 2010. She was also a visitor at IST institute, Stuttgart University, Germany for one year from 2013. Her research interests include non-minimum phase systems, adaptive control and nonlinear control.

Heidar Ali Talebi

Heidar Ali Talebi received his BS degree in Electronics from Ferdowsi University, Mashhad, Iran, in 1988, MSc degree in Electronics (with first class honours) from Tarbiat Modarres University, Tehran, Iran, in 1991, and his PhD degree in Electrical and Computer Engineering from Concordia University, Montreal, QC, Canada, in 1997. He held several postdoctoral and research positions at Concordia University and University of Western Ontario, before joining Amirkabir University of Technology in 1999 where he is currently a professor. From 2002 to 2004, he also served as the Head of Control Systems Group in Amirkabir University. His research interests include control, robotics, fault diagnosis and recovery, intelligent systems, adaptive control, nonlinear control and real-time systems.

Mohammad Bagher Menhaj

Mohammad Bagher Menhaj received his PhD degree from Electrical and Computer Engineering at OSU in 1992. After one year, he received postdoctoral degree from OSU, in 1993. He is author and co-author of more than 300 technical papers, and four books: Fundamentals of Neural Networks, 1998, Application of Computational Intelligence in Control, 1998, Neural Networks, 2000 and Fuzzy Computations, 2007, all in Persian. His main research interests are theory of computational intelligence, learning automata, adaptive filtering and their applications in control, power systems, image processing, pattern recognition and communications. Other areas of interests are theory of rough set and knowledge discovery. Prof. Menhaj, joined the Amirkabir University of Technology, Tehran, Iran, in 1993. In December 2000 to August 2003, he was with School of Electrical and Computer Engineering and Department of Computer Science at OSU as visiting faculty member and research scholar.

Christian Ebenbauer

Christian Ebenbauer received his MS (Dipl.-Ing.) in Telematics (Electrical Engineering and Computer Science) from Graz University of Technology, Austria, in 2000 and his PhD (Dr.-Ing.) in Mechanical Engineering from the University of Stuttgart, Germany, in 2005. After having completed his PhD, he was a postdoctoral associate and an Erwin Schrödinger Fellow at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, USA. Since April 2009, he is a full professor of Computations in Control at the Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany. His research interests lie in the areas of control, optimisation and system-theoretic inspired computation. He was awarded the Prize of the Vereinigung von Freunden der Universität Stuttgart for doctoral thesis 2006, DFG Emmy Noether Programme 2008.