Nonlinear approach for the control of mechanical coupling effects and smart structures of limited power

Smart structures are often limited in terms of voltage and power. Moreover, when subjected to rigid body displacements, mechanical couplings cause vibrations. The aim of this work is, on the one hand, to describe a control design that reduces vibrations in flexible structures caused by rigid body modes and, on the other hand, to optimize the mechanical work of actuators controlling flexible modes. The nonlinear method proposed improves the control of linear or linearized structures. A nonlinear control for actuators controlling flexible modes is developed to improve their efficiency. It is based on a modal development of mechanical power that separates stiffness and damping effects. These two effects are adapted to each modal variable value and the powers capabilities of the actuators, in order to obtain optimal mechanical work. This part of the study demonstrates the improvement of the controlled behavior of any linear smart structure. When the structure is subjected to rigid body displacement, the coupling between flexible and rigid body modes can be controlled by another independent nonlinear controller. Time varying gains are used to tune the power managed by the rigid body mode controller to minimize the strain of the flexible structure, without decreasing tracking efficiency. The fuzzy design implemented to carry out these two independent nonlinear approaches is described after which the method is used to control a mono-articulated smart structure. Simulation results show successive improvements of these controls, with or without tracking, for several types of disturbances