Study of the Characteristics of Linear Flexible Object Control System

The paper solves a flexible object control problem. The issues of constructing a mathematical model of an inhomogeneous flexible link based on the Euler-Bernoulli equation are considered. The simple design model was chosen, which, for example, can describe the vibrations of a single-link manipulator, load bending during aerial transportation, or a helicopter blade. A universal algorithm for determining the parameters of an elastic system is presented. A convenient method is used to analytically determine mode shapes of an inhomogeneous structure. Vibrations model was built by the method of initial parameters with discretization of distributions of mass and bending rigidity. The system dynamics equations are obtained by integrating the Euler-Bernoulli equation, which makes mathematical formulation universal. The resulting mathematical model describes with sufficiently high accuracy the dynamics of objects, which are characterized by a constant or stepwise distribution of mass and stiffness along their length. The control system, providing high speed with minimal fluctuations, is developed using LQR and LMI methods. It is shown that the LMI method allows one to directly limit the control action and more intuitively set the required characteristics of the system, however, it is less resistant to changes in the parameters of the control object. Control system needs to be done more robust, and thus further research is necessary.