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

Abstract

Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation. arXiv:1805.06800v1 [math.OC]

Disturbance-observer-based finite time sliding mode controller with unmatched uncertainties utilizing improved cubature Kalman filter

“…Several works on hybrid combination of various SMC and disturbance observer have been addressed for effective robustness, reduce chattering and finite time stability with the mismatched disturbances (Charfeddine and Lassaad, 2015). These SMC with disturbance observer or GS with sliding mode disturbance observer or by adaptive and fuzzy based have been implemented to varied electrical processes like permanent magnet linear model, semi-automated hand-held ear surgical device and attitude control for the dual arm of a humanoid robot (Amini et al, 2018; Charfeddine and Lassaad, 2015; Sinha and Mishra, 2018). But not much concentration was given to noise and matched disturbances.…”

“…Sinha and Mishra (2018) presented event-driven SMC which ensures closed-loop stability to control temperature and concentration. Amini et al (2018) explained an adaptive second-order discrete SMC (DSMC), and it shows that the tracking performance can be improved up to 90% while comparing with first-order DSMC. However, most of the above techniques show undesirable non-minimum phase and overshoot.…”

A discrete output feedback 2-SMC using Linear Matrix Inequalities and adaptive switching gain approaches: Real application on a chemical reactor

“…Salgado et al (2016) suggested a super-twisting-like discrete SMC and demonstrated its convergence to an ultimate finite bound. A discrete adaptive 2SMC based on Lyapunov stability for an uncertain non-linear combustion engine is studied by Amini et al (2018). Sharma and Janardhanan (2018) developed a higher order SMC with a disturbance forecast strategy for discrete linear uncertain system.…”

Temperature control of real‐time identified fixed bed reactor by adaptive sliding mode control equipped with Arduino in Matlab

“…This approach reduces the computational load in comparison to traditional SMC. Amini et al proposed an adaptive second order Discrete Sliding Mode Control (DSMC), and results showed that the tracking performance can be improved up to 90% in comparison to first order DSMC. However, the overall improvement is 25% when shifted from single‐input single‐output to multi‐input multi‐output system.…”