Handling Model and Implementation Uncertainties via an Adaptive Discrete Sliding Mode Controller Design

Abstract

Analog-to-digital conversion (ADC) and uncertainties in modeling the plant dynamics are the main sources of imprecisions in the design cycle of model-based controllers. These implementation and model uncertainties should be addressed in the early stages of the controller design, otherwise they could lead to failure in the controller performance and consequently increase the time and cost required for completing the controller verification and validation (V&V) with more iterative loops. In this paper, a new control approach is developed based on a nonlinear discrete sliding mode controller (DSMC) formulation to mitigate the ADC imprecisions and model uncertainties. To this end, a DSMC design is developed against implementation imprecisions by incorporating the knowledge of ADC uncertainties on control inputs via an online uncertainty prediction and propagation mechanism. Next, a generic online adaptive law will be derived to compensate for the impact of an unknown parameter in the controller equations that is assumed to represent the model uncertainty. The final proposed controller is an integrated adaptive DSMC with robustness to implementation and model uncertainties that includes (i) an online ADC uncertainty mechanism, and (ii) an online adaptation law. The proposed adaptive control approach is evaluated on a nonlinear automotive engine control problem in real-time using a processor-in-the-loop (PIL) setup with an actual electronic control unit (ECU). The results reveal that the proposed adaptive control technique removes the uncertainty in the model fast, and significantly improves the robustness of the controllers to ADC imprecisions. This provides up to 60% improvement in the performance of the controller under implementation and model uncertainties compared to a baseline DSMC, in which there are no incorporated ADC imprecisions.