Design of Simple Adaptive Nonlinear Robust Controller

In this paper, we propose an adaptive nonlinear robust controller which estimates the upper bound of uncertain elements. The structure of our controller is much simpler than those of other available controllers. After separating the original nonlinear dynamic system into linear and nonlinear parts, we first determine the virtual input to stabilize the linear part, so that we can obtain a unique solution to the algebraic Lyapunov equation. Next, we determine a min-max (or bang-bang) controller with an estimated upper bound for uncertainties that contain the original unknown nonlinear elements and the virtual input. The controller is applied to control a pantograph-type 2-link manipulator. The effectiveness of the proposed method is illustrated by some computer simulations. Specifically, we examine the relationships among the control perfarmance, the estimation rate of an upper bound, and the magnitude of a boundary layer in the computer simulations.