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Sliding Mode Repetitive Control Based On A Novel Reaching Law

The chattering occurs when the system works under the controller which is based on the traditional reaching law. This paper proposes a novel reaching law to avoid the system chattering by using a mathematical expression to replace the switching function in the traditional reaching law. The discrete time expression of the novel reaching law is given. And the design of discrete time sliding mode repetitive controller which based on the novel reaching law is presented to achieve perfect tracking. The periodic perturbations are rejected completely. The monotone decreasing region, absolute attraction layer and steady state error are derived to characterize the reaching phase of the sliding mode. Numerical simulation demonstrates the effectiveness of the proposed repetitive control strategy.