Abstract
In this paper, a practical and general adaptive robust nonlinear controller is proposed for positioning control of a nonlinear mechanical system. To overcome the main obstacles that prevent the adaptive control techniques from coming into wide use in the industrial side, our attention is focused on the guaranteed transient performance and theoretical transparency of the control system. The controller is designed in a backstepping manner. At the first step, a PI controller is designed to stabilize the position error. Then at the second step, an adaptive robust nonlinear controller is designed to stabilize the velocity error, where the input-to-state stability (ISS) property which guarantees the transient performance is achieved by the nonlinear damping terms. And the adaptive laws are added to achieve a small ultimate error. It is commented that the complicated looking adaptive robust nonlinear controller can be explained as hierarchical modifications of the coventional PI positioning controller with minor-loop. Therefore it is believed that the proposed controller may gain wide acceptance of the engineers. Finally, numerical and experimental examples are included to verify the theoretical results.
