A Symmetry and Structure Preserving State Derivative Feedback Control Strategy for Second-order Linear Systems
João Batista da Paz Carvalho1; José Mário de Araújo2; Carlos Eduardo Trabuco Dórea3; Luiz Marcos Garcia Gonçalves3
1 UFRGS; 2 IFBA; 3 UFRN
doi:10.20906/CPS/CILAMCE2017-0996
Resumo
Second-order Linear Control Systems are governed by systems of diferential equations that can be cast (state-space approach) into M x'' + C x' + K x = f, where M, C and K are mass, damping and stiffness matrices, all assumed to be symmetric, M symmetric positive definite; x is the state vector, and f the external force vector. In order to drive the system to achieve better performance, control strategies can be accomplished by feeding back into the system the information on its state vectors x and x', using estimators, sensors and actuators. In this work we propose a state derivate control strategy that is capable of preserving the structure of the problem, meaning that the second-order poles that are not intended to changed are assured to not change at all (Second-order Model Updating technique is applied), while the poles that are intended to change are assigned to the controlled system through the solution of a mathematical matrix equation. However, the strategy feeds back into the system the information of state vectors x, x' and also x'', and therefore must be considered as derivative state feedback. Mathematical framework of the associated Model Updating problem and real-life numerical examples are presented.
Palavras-chave: derivative; control; second-order; model updating