Design of Dynamic Sliding Mode Controller in the Presence of both Matched and Mismatched Uncertainty without Chattering for Nonlinear Second Order Systems

The most important property of sliding mode control (SMC) is invariant against matched uncertainties، which is due to the using of Sign function and this Sign function produces chattering. Moreover، SMC is not invariant with respect to the mismatched uncertainties، which is its other problem. In this paper to solve these two problems، using of multiple surface dynamic sliding mode control (DSMC) is proposed. In DSMC the chattering is removed due to the integrator where is placed before the input control signal of the plant. However، in DSMC the augmented system (the system plus the integrator) is one dimension bigger than the actual system and then، the plant model should be completely known. To solve this problem، an observer is proposed called integral-chain observer or ICO. To counteract with mismatched uncertainty، any system dynamics are considered as a distinct nonlinear system and multiple sliding surfaces is defined. One of the advantages of the proposed approach is the upper bound of the uncertainty not used in DSMC and ICO، which is important in practical implementation. Then، a design procedure is described and simulation result is presented to demonstrate the approach.