Modified integral action with time-varying forgetting function for tracking control

While the use of integral action in control is quite common, in part due to its benefits for output regulation, it can also be counterproductive when abrupt changes in disturbance occur during tracking. In order to mitigate its counterproductive effect while at the same time maintaining its advantages for regulation, this work proposes a new type of integral action, including a time-varying forgetting factor suited to the expected behavior of the disturbance during tracking. Also, Lyapunov stability techniques are used to derive general results aiming to reduce the complexity of stability analysis and control design when the proposed integral action is included in a control law. In particular, these results are used for stability analysis when the proposed integral action is implemented in a deterministic robust controller for a linear motor system. Furthermore, the controller is implemented in the corresponding experimental setup, resulting in an improvement on maximum tracking error of up to 32%.