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

Abstract

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%.

Application of switched-dynamics friction models in feedback control

“…The controller with feedback GMS compensation from Remark 2 and the alternative with feedforward GMS compensation have been tested on the experimental setup. In addition, these results are then compared with those from the controller implemented in Villegas et al, 22 which includes feedforward friction compensation based on the simpler Stribeck-tanh model. 25 First, a jerk-limited positioning reference has been considered.…”

“…As a particular case, Corollary 1 allows to prove stability for controllers with feedback compensation of friction based on the GMS model. In fact, this is done in the next section when adding feedback friction compensation to the controller in Villegas et al 22 Thus, in the following section, the details of the proposed controller and the corresponding stability results are given as well as a comparison of the experimental results between feedback and feedforward GMS friction compensation.…”

“…The parameters of the model can be obtained as shown in the work by Villegas et al, 24 where the model was developed. Also, more detail about the determination of the bounds can be seen in Villegas et al 22…”

“…Now, considering the stability results in the previous sections for the use of the GMS model in feedback control, the controller in Villegas et al 22 is modified next in order to include the capability of feedback GMS friction compensation.…”

“…0. Here, s = mc 0 e 0 + mc 1 e 1 + me 2 , the state e 0 is defined as _ e 0 = e 1 À k e 0 (t)e 0 for k e 0 (t) satisfying Assumption 1 of Villegas et al, 22 d m (t, x m ) is a function related to disturbances and model uncertainties as defined in the work by Villegas et al, 23 and x gc is the state vector of the GMS model used for friction compensation. The constants c i are such that the polynomial p(n) = c 0 + c 1 n + n 2 is Hurwitz.…”