MIMO First and Second Order Discrete Sliding Mode Controls of Uncertain Linear Systems under Implementation Imprecisions

摘要

The performance of a conventional model-based controller significantlydepends on the accuracy of the modeled dynamics. The model of a plant'sdynamics is subjected to errors in estimating the numerical values of thephysical parameters, and variations over operating environment conditions andtime. These errors and variations in the parameters of a model are the majorsources of uncertainty within the controller structure. Digital implementationof controller software on an actual electronic control unit (ECU) introducesanother layer of uncertainty at the controller inputs/outputs. Theimplementation uncertainties are mostly due to data sampling and quantizationvia the analog-to-digital conversion (ADC) unit. The failure to address themodel and ADC uncertainties during the early stages of a controller designcycle results in a costly and time consuming verification and validation (V&V)process. In this paper, new formulations of the first and second order discretesliding mode controllers (DSMC) are presented for a general class of uncertainlinear systems. The knowledge of the ADC imprecisions is incorporated into theproposed DSMCs via an online ADC uncertainty prediction mechanism to improvethe controller robustness characteristics. Moreover, the DSMCs are equippedwith adaptation laws to remove two different types of modeling uncertainties(multiplicative and additive) from the parameters of the linear system model.The proposed adaptive DSMCs are evaluated on a DC motor speed control problemin real-time using a processor-in-the-loop (PIL) setup with an actual ECU. Theresults show that the proposed SISO and MIMO second order DSMCs improve theconventional SISO first order DSMC tracking performance by 69% and 84%,respectively. Moreover, the proposed adaptation mechanism is able to remove theuncertainties in the model by up to 90%.