Design of a Composite Control in Two-Time Scale Using Nonlinear Disturbance Observer-Based SMC and Backstepping Control of a Two-Link Flexible Manipulator

Abstract Flexible manipulators are used in many fields because of their many advantages. But, such types of manipulators have greater larger complexity as compared to their rigid counterparts. Many control techniques are reported in the literature for handling the complexity in the flexible manipulator and to achieve the desired operation in the presence of matched disturbances. Rarely papers are available on the design of the controller for the flexible manipulator in the presence of unmatched disturbances. In this chapter, the problem of trajectory tracking control in the presence of unmatched disturbances and quick tip deflection suppression for a two-link flexible manipulator is considered. The problems are solved simultaneously by designing a composite control technique using the singular perturbation method. First, the dynamics of a two-link flexible manipulator are obtained using the assumed mode method. Then, a singular perturbation method using the two-time scale property is applied to decompose the dynamics into the slow subsystem and the fast subsystem. The slow subsystem consists of the rigid body dynamics of the flexible manipulator and the fast subsystem consists of the flexible body dynamics of the flexible manipulator. A nonlinear disturbance observer-based sliding mode control (SMC) is designed on the slow subsystem under the presence of unmatched disturbances for the trajectory tracking control. A disturbance observer is used to estimate the unmatched disturbances. A backstepping controller in used on the fast subsystem for the quick suppression of the link deflection. Finally, a composite controller is designed for the two-link flexible manipulator using the nonlinear disturbance observer-based SMC on the slow subsystem and the backstepping controller on the fast subsystem. The simulation results using Matlab validate the effectiveness of the proposed composite controller for a two-link flexible manipulator.