Suboptimal State Tracking Control Applied to a Nonlinear Fractional-Order Slewing Motion Flexible Structure

Abstract

The control of slewing motion flexible structures is important to a number of systems found in engineering and physical sciences applications, such as aerospace, automotive, robotics, and atomic force microscopy. In this kind of system, the controller must provide a stable and well-damped behavior for the flexible structure vibrations, with admissible control signal amplitudes. Recently, many works have used fractional-order derivatives to model complex and nonlinear dynamical behavior present in the mentioned systems. In order to perform digital computer-based control of fractional-order dynamical systems, a time discretization of the equations is necessary. In many cases, the Grunwald-Letnikov method is used, resulting in an implicit integration method. In this work, a nonlinear slewing motion flexible structure is modeled considering a fractional-order viscous damping in the flexible beam motion. To obtain an explicit integration method, based on the Grunwald-Letnikov definition, the discretization of the dynamical equations is performed considering the existence of sample and hold circuits. In addition, real-time suboptimal infinite horizon tracking control system strategies, namely, the linear quadratic tracking and the state-dependent Riccati equation tracking controller, are designed and implemented to control the fractional-order slewing motion flexible system. The general behavior and performance of the control systems are tested for parameter uncertainties related to the order of the fractional derivatives.