Abstract
An adaptive backstepping sliding mode controller combined with a nonlinear disturbance observer is designed for trajectory tracking of the electrically driven hybrid conveying mechanism with mismatched disturbances. A nonlinear disturbance observer is constructed for estimation and compensation of the mismatched and matched disturbances. Then, a hybrid control scheme is designed by combining the adaptive backstepping sliding mode controller and the mentioned observer. The Lyapunov candidate functions are utilized to derive the control and adaptive law. According to the simulation and experimental results, superior tracking performance could be obtained through the presented control scheme compared with conventional backstepping sliding mode control. Meanwhile, the presented control scheme can effectively reduce the chattering problem and improve tracking precision.
Highlights
In recent years, nonlinear disturbance observer (NDO) has received more and more attention [22,23,24]
A novel hybrid control scheme consisting of backstepping, SMC, and NDO is constructed for the trajectory tracking problem of HCM with matched and mismatched disturbances
The backstepping method is used to design control laws. en, in order to improve the robustness of the system, the mismatched disturbance estimation is introduced into the virtual control laws to compensate for the mismatched disturbance
Summary
An NDO-based adaptive backstepping SMC is developed for the HCM (7). e schematic diagram of the. According to equations (11) and (12), the time derivative of V0 could be written as follows: V_ 0 dTd − dT1 p2d1 − dT2 p3d2 ≤ 0 It could be concluded from (13) that the NDO system (10) is asymptotically stable. According to the adaptation mechanism (38), the following hybrid control law could be obtained:. Consider the hybrid conveying mechanism (7), if the control law (38) is employed, the tracking error can tend to zero. By differentiating from both sides of (40), we have the following:. Taking the time derivative of V_ 5, yields the following: V€5 −2zT1 c1z_1 − 2zT2 K1 + kz_2 − 2sThs_ − 2dT2 p3d 2. According to the Barbalat theorem. erefore, the tracking error can tend to zero and the closed-loop system is asymptotically stable
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