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

## TL;DR

This paper introduces an adaptive second order discrete sliding mode controller that effectively reduces chattering and handles uncertainties in nonlinear systems, demonstrated on automotive engine control with significant performance improvements.

## Contribution

It presents a novel adaptive second order discrete sliding mode control method with Lyapunov-based stability, addressing sampling imprecisions and uncertainties in nonlinear systems.

## Key findings

- Improves tracking performance by up to 80% over first order DSMC.
- Effectively mitigates chattering and data sampling imprecisions.
- Ensures asymptotic stability through Lyapunov-based adaptation.

## Abstract

Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and sensitivity to data sampling imprecisions limit the digital implementation of conventional first order continuous-time SMC. Higher order discrete SMC is an effective solution to reduce the chattering during the controller software implementation, and also overcome imprecisions due to data sampling. In this paper, a new adaptive second order discrete sliding mode control (DSMC) formulation is presented to mitigate data sampling imprecisions and uncertainties within the modeled plant's dynamics. The adaptation mechanism is derived based on a Lyapunov stability argument which guarantees asymptotic stability of the closed-loop system. The proposed controller is designed and tested on a highly nonlinear combustion engine tracking control problem. The simulation test results show that the second order DSMC can improve the tracking performance up to 80% compared to a first order DSMC under sampling and model uncertainties.