TY - JOUR
T1 - Generalizing negative imaginary systems theory to include free body dynamics
T2 - Control of highly resonant structures with free body motion
AU - Mabrok, Mohamed A.
AU - Kallapur, Abhijit G.
AU - Petersen, Ian R.
AU - Lanzon, Alexander
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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 - 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
UR - http://www.scopus.com/inward/record.url?scp=84907482599&partnerID=8YFLogxK
U2 - 10.1109/TAC.2014.2325692
DO - 10.1109/TAC.2014.2325692
M3 - Article
SN - 0018-9286
VL - 59
SP - 2692
EP - 2707
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 10
M1 - 6819061
ER -