Abstract
This paper proposed an integral sliding mode control scheme based on repetitive control for uncertain repetitive processes with the presence of matched uncertainties, external disturbances and norm-bounded nonlinearities. A new method based on the combination of repetitive control and sliding mode approach is studied in order to use the robustness sensibility property of the sliding mode control to matched uncertainties and disturbances and to cancel gradually tracking error for periodic processes. A sufficient condition of the existence of sliding mode is studied based on basic repetitive control and a sliding mode controller is synthesized through linear matrix inequalities, which guarantees the stability along the periods of the controlled closed-loop process and the reachability of the sliding surface is ensured. Then, an adaptive integral sliding mode controller is synthesized to improve performances of the proposed control scheme. The effectiveness of the proposed controlled design schemes is proved by the use of a third order uncertain mechanical system and the simulation results using the new approaches give good performances.
Highlights
Repetitive Control (RC) has been applied to many engineering applications, such as robot manipulators, rotary systems, power supply systems, computer disk drives, etc. [1][4]
The main advantage of this work is to design a repetitive controller based on integral sliding mode control of matched uncertain systems with external disturbances by exploiting two major properties; the first is the insensibility to uncertainties satisfying the matching condition and the second is the improving control system performance in a periodic manner by including the learning capacity
In order to prove that the proposed Repetitive Integral Sliding Mode Control (RISMC) law satisfies the reachability condition, substituting the value of (33) into (16) gives
Summary
Repetitive Control (RC) has been applied to many engineering applications, such as robot manipulators, rotary systems, power supply systems, computer disk drives, etc. [1][4]. When the controller is applied to real systems, disturbances and uncertainties must be absolutely considered and examined. Authors in [9]-[14] offer some methods of repetitive control system design for a class of linear system. They are based on two-dimensional (2D) continuous/discrete hybrid model. SMC can offer good transient performance, fast response, and order reduction These advantages make SMC a very practical and effective way in robust control design. The main contribution of this work is to propose a new Repetitive Integral Sliding Mode Control (RISMC) law of matched uncertain linear repetitive processes with external disturbances in order to achieve a zero tracking error.
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