Order Reduction and Control of Parametrically Excited Dynamical Systems

Abstract

This paper provides methodology for designing reduced-order controllers for large-scale, linear systems represented by differential equations having time-periodic coefficients. The linear time-periodic sys tem is first converted into a form in which the system stability matrix is time invariant. This is achieved by the application of Lyapunov-Floquet transformation. Then a completely time-invariant auxiliary system is constructed and order reduction algorithms are applied to this system to obtain a reduced-order system. The control laws are calculated for the reduced-order system by minimizing the least square error between the auxiliary and the transformed system. These control laws are then transformed to obtain the desired control action in the original domain. The schemes formulated arc illustrated by designing full-state feedback and output feedback controllers for a five-mass inverted pendulum exhibiting parametric instability

Keywords

Order reduction control parametric excitations Lyapunov-Floquet transformation

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