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Sliding mode control (SMC) is a robust and computationally efficient solutionfor tracking control problems of highly nonlinear systems with a great deal ofuncertainty. High frequency oscillations due to chattering phenomena andsensitivity to data sampling imprecisions limit the digital implementation ofconventional first order continuous-time SMC. Higher order discrete SMC is aneffective solution to reduce the chattering during the controller softwareimplementation, and also overcome imprecisions due to data sampling. In thispaper, a new adaptive second order discrete sliding mode control (DSMC)formulation is presented to mitigate data sampling imprecisions anduncertainties within the modeled plant's dynamics. The adaptation mechanism isderived based on a Lyapunov stability argument which guarantees asymptoticstability of the closed-loop system. The proposed controller is designed andtested on a highly nonlinear combustion engine tracking control problem. Thesimulation test results show that the second order DSMC can improve thetracking performance up to 80% compared to a first order DSMC under samplingand model uncertainties.

Discrete Adaptive Second Order Sliding Mode Controller Design with Application to Automotive Control Systems with Model Uncertainties