TY - GEN
T1 - Stability analysis and controller designs for linear time periodic systems using normal forms
AU - Subramanian, Susheelkumar C.
AU - Redkar, Sangram
N1 - Publisher Copyright:
Copyright © 2020 ASME.
PY - 2020
Y1 - 2020
N2 - The investigation of stability bounds for linear time periodic systems have been performed using various methods in the past. The Normal Forms technique has been predominantly used for analysis of nonlinear equations. In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique for a linear system with time periodic coefficients. Moreover, the authors utilize the Normal Forms technique to transform a linear time periodic system to a time-invariant system by using near identity transformation, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to enable the application of time independent Normal Forms directly without the use of detuning or book-keeping parameter. This method provides a closed form analytical expression for the state transition matrix with the elements as a function of time. Additionally, stability analysis is performed on the transformed system and the resulting transitions curves are compared with that of numerical simulation results. Furthermore, a linear feedback controller design is discussed based on the stability bounds and the implementation of an effective feedback controller for an unstable case is discussed. The theory is validated and verified using numerical simulations of temporal variation of a simple linear Mathieu equation.
AB - The investigation of stability bounds for linear time periodic systems have been performed using various methods in the past. The Normal Forms technique has been predominantly used for analysis of nonlinear equations. In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique for a linear system with time periodic coefficients. Moreover, the authors utilize the Normal Forms technique to transform a linear time periodic system to a time-invariant system by using near identity transformation, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to enable the application of time independent Normal Forms directly without the use of detuning or book-keeping parameter. This method provides a closed form analytical expression for the state transition matrix with the elements as a function of time. Additionally, stability analysis is performed on the transformed system and the resulting transitions curves are compared with that of numerical simulation results. Furthermore, a linear feedback controller design is discussed based on the stability bounds and the implementation of an effective feedback controller for an unstable case is discussed. The theory is validated and verified using numerical simulations of temporal variation of a simple linear Mathieu equation.
KW - Control system
KW - Linear time periodic systems
KW - Normal forms
KW - Stability analysis
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U2 - 10.1115/DSCC2020-3132
DO - 10.1115/DSCC2020-3132
M3 - Conference contribution
AN - SCOPUS:85100933175
T3 - ASME 2020 Dynamic Systems and Control Conference, DSCC 2020
BT - Intelligent Transportation/Vehicles; Manufacturing; Mechatronics; Engine/After-Treatment Systems; Soft Actuators/Manipulators; Modeling/Validation; Motion/Vibration Control Applications; Multi-Agent/Networked Systems; Path Planning/Motion Control; Renewable/Smart Energy Systems; Security/Privacy of Cyber-Physical Systems; Sensors/Actuators; Tracking Control Systems; Unmanned Ground/Aerial Vehicles; Vehicle Dynamics, Estimation, Control; Vibration/Control Systems; Vibrations
PB - American Society of Mechanical Engineers
T2 - ASME 2020 Dynamic Systems and Control Conference, DSCC 2020
Y2 - 5 October 2020 through 7 October 2020
ER -