Non Linear Active Control of the Dynamic Behavior of Bi-Articulated Flexible Structures

When vibrating structures are subjected to large displacements, coupling may occur between the vibrations and the displacements inducing possibly strongly non-linear behavior. In this case, linear control algorithms and independent control strategy are no longer suitable. This study deals with the nonlinear control of Bi-articulated structures. A model that combines both finite element (FE) discretization, taking into account strains/electric field coupling, and global behavior is carried out. Multivariable control is carried out by electromechanical and piezoelectric actuators. The control strategy developed consists in weighting the output of parallel state controllers, calculated for the p discretized operating points crossed during the progression of the structure’s dynamic behavior. The multivariable control u is obtained by weighting interpolation functions f_i of the linear quadratic control gains K_i of each controller optimized according to large displacements. The first application to Bi-articulated rigid beam systems shows, in comparison with a stable linear control, that non-linear control is by far the better of the two. This is mainly due to increased efficiency of motor torque use. The second application of the proposed nonlinear control algorithm concerns a Bi-articulated flexible beam system modeled by two rigid body modes and five flexible modes. The control obtained is robust regarding both stability and performance. Quasi-steady controlled dynamic behavior is obtained during movement.