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Sliding mode control (SMC) is a robust and computationally efficientmodel-based controller design technique for highly nonlinear systems, in thepresence of model and external uncertainties. However, the implementation ofthe conventional continuous-time SMC on digital computers is limited, due tothe imprecisions caused by data sampling and quantization, and the chatteringphenomena, which results in high frequency oscillations. One effective solutionto minimize the effects of data sampling and quantization imprecisions is theuse of higher order sliding modes. To this end, in this paper, a newformulation of an adaptive second order discrete sliding mode control (DSMC) ispresented for a general class of multi-input multi-output (MIMO) uncertainnonlinear systems. Based on a Lyapunov stability argument and by invoking thenew Invariance Principle, not only the asymptotic stability of the controlleris guaranteed, but also the adaptation law is derived to remove theuncertainties within the nonlinear plant dynamics. The proposed adaptivetracking controller is designed and tested in real-time for a highly nonlinearcontrol problem in spark ignition combustion engine during transient operatingconditions. The simulation and real-time processor-in-the-loop (PIL) testresults show that the second order single-input single-output (SISO) DSMC canimprove the tracking performances up to 90%, compared to a first order SISODSMC under sampling and quantization imprecisions, in the presence of modelinguncertainties. Moreover, it is observed that by converting the engine SISOcontrollers to a MIMO structure, the overall controller performance can beenhanced by 25%, compared to the SISO second order DSMC, because of thedynamics coupling consideration within the MIMO DSMC formulation.

Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems