LMI-Based Approach for Non-Rigid System Control

The paper solves the problem of controlling a cargo UAV with a flexible elongated cargo. Construction of inhomogeneous flexible link mathematical model based on Euler-Bernoulli equation issues are considered. A universal algorithm for determining the parameters of an elastic system and compiling its mathematical model is presented. A convenient method for the analytical determination of eigenmodes of vibrations of an inhomogeneous structure is used. Vibrations model was built using the method of initial parameters, which discretizes the diagrams of mass distribution and bending stiffness. The equations of system dynamics are obtained using the Euler-Lagrange equations. The control system, which provides fast response with minimal link fluctuations, is designed using LQR and LMI methods. It is shown that the LMI method allows you to directly limit the control action and set the required characteristics of the system in a more intuitive way. The results are confirmed by computer simulation. It is proposed to use an observer to obtain strain coordinates without measurement.