Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion

Mohamed A. Mabrok; Abhijit G. Kallapur; Ian R. Petersen; Alexander Lanzon

doi:10.1109/TAC.2014.2325692

Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion

Mohamed A. Mabrok, Abhijit G. Kallapur, Ian R. Petersen, Alexander Lanzon

Research output: Contribution to journal › Article › peer-review

Abstract

© 2014 IEEE.Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.

Original language	English
Article number	6819061
Pages (from-to)	2692-2707
Number of pages	15
Journal	IEEE Transactions on Automatic Control
Volume	59
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2014.2325692
Publication status	Published - 1 Oct 2014

Keywords

Flexible structures
free body motion
negative imaginary systems

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10.1109/TAC.2014.2325692

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title = "Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion",

abstract = "{\textcopyright} 2014 IEEE.Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.",

keywords = "Flexible structures, free body motion, negative imaginary systems",

author = "Mabrok, {Mohamed A.} and Kallapur, {Abhijit G.} and Petersen, {Ian R.} and Alexander Lanzon",

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language = "English",

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Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion. / Mabrok, Mohamed A.; Kallapur, Abhijit G.; Petersen, Ian R. et al.
In: IEEE Transactions on Automatic Control, Vol. 59, No. 10, 6819061, 01.10.2014, p. 2692-2707.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion

AU - Mabrok, Mohamed A.

AU - Kallapur, Abhijit G.

AU - Petersen, Ian R.

AU - Lanzon, Alexander

PY - 2014/10/1

Y1 - 2014/10/1

N2 - © 2014 IEEE.Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.

AB - © 2014 IEEE.Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.

KW - Flexible structures

KW - free body motion

KW - negative imaginary systems

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

M1 - 6819061

ER -

Generalizing negative imaginary systems theory to include free body dynamics: Control of highly resonant structures with free body motion

Abstract

Keywords

UN SDGs

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