Quasioptimal sliding mode controller for a flexible structure

In this paper, we describe the combined design of a time-optimal and a sliding mode controller for a single-axis, N-mode model of a flexible slewing structure, where the main goal is the implementation of a fast controller. A model consisting of an aluminum flexible link with torque actuation provided by a DC motor at its hub is constructed in modal coordinates and a recently introduced time-optimal torque law for a one-mode model of this system that can be implemented in real time is used. The sliding-mode controller is designed so that the torque generated by a DC motor converges to the desired time-optimal torque law. After the time-optimal control law has been tracked within a neighborhood of the origin, a full-state feedback controller is used to drive the system´s elastic modes exactly to the origin in finite time. The optimal gain vector for this terminal controller is the solution to an LQR problem. An observer is designed to estimate the unknown system states from actual measurements of tip-position, angle, and speed of the flexible structure, where its gain is obtained by the pole placement technique. Computer simulations of the proposed controller are shown in this work to illustrate the design idea. In the simulations, a one mode model system of the flexible slewing structure is considered first, then the controller is applied to a model of the system that includes higher-order flexible modes