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

[+] Author Affiliations
Mohammad Reza Amini, Mahdi Shahbakhti

Michigan Technological University, Houghton, MI

Selina Pan

Ford Motor Company, Palo Alto, CA

Paper No. DSCC2017-5010, pp. V001T09A001; 10 pages
  • ASME 2017 Dynamic Systems and Control Conference
  • Volume 1: Aerospace Applications; Advances in Control Design Methods; Bio Engineering Applications; Advances in Non-Linear Control; Adaptive and Intelligent Systems Control; Advances in Wind Energy Systems; Advances in Robotics; Assistive and Rehabilitation Robotics; Biomedical and Neural Systems Modeling, Diagnostics, and Control; Bio-Mechatronics and Physical Human Robot; Advanced Driver Assistance Systems and Autonomous Vehicles; Automotive Systems
  • Tysons, Virginia, USA, October 11–13, 2017
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5827-1
  • Copyright © 2017 by ASME


The performance of a conventional model-based controller significantly depends on the accuracy of the modeled dynamics. The model of a plant’s dynamics is subjected to errors in estimating the numerical values of the physical parameters, and variations over operating environment conditions and time. These errors and variations in the parameters of a model are the major sources of uncertainty within the controller structure. Digital implementation of controller software on an actual electronic control unit (ECU) introduces another layer of uncertainty at the controller inputs/outputs. The implementation uncertainties are mostly due to data sampling and quantization via the analog-to-digital conversion (ADC) unit. The failure to address the model and ADC uncertainties during the early stages of a controller design cycle results in a costly and time consuming verification and validation (V&V) process. In this paper, new formulations of the first and second order discrete sliding mode controllers (DSMC) are presented for a general class of uncertain linear systems. The knowledge of the ADC imprecisions is incorporated into the proposed DSMCs via an online ADC uncertainty prediction mechanism to improve the controller robustness characteristics. Moreover, the DSMCs are equipped with 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 problem in real-time using a processor-in-the-loop (PIL) setup with an actual ECU. The results show that the proposed SISO and MIMO second order DSMCs improve the conventional SISO first order DSMC tracking performance by 69% and 84%, respectively. Moreover, the proposed adaptation mechanism is able to remove the uncertainties in the model by up to 90%.

Copyright © 2017 by ASME
Topics: Linear systems



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