Improved backstepping-based adaptive PID control

In this paper, an adaptive PID controller for second-order models based on the backstepping approach is presented. The integral action is obtained by adding the integral of the tracking error to the error considered in the first step of the backstepping procedure. In the non adaptive case, a new method is proposed to select the backstepping tuning parameters in order to place the regulation without having to change the time scale. In the adaptive version, a switching-sigma modification is implemented to avoid parameter drift. To make possible switching off the adaptation when desired, nonlinear damping terms are added to the command. A simulation example illustrates the performance of the proposed adaptive PID controller.