0
Research Papers

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

[+] Author and Article Information
Mohammad Reza Amini

Mechanical Engineering-Engineering
Mechanics Department,
Michigan Technological University,
Houghton, MI 49931
e-mail: mamini@mtu.edu

Mahdi Shahbakhti

Mechanical Engineering-Engineering
Mechanics Department,
Michigan Technological University,
Houghton, MI 49931
e-mail: mahdish@mtu.edu

Selina Pan

Department of Mechanical Engineering,
University of California, Berkeley,
Berkeley, CA 94720
e-mail: slpan@berkeley.edu

1Corresponding author.

2Present address: College of Engineering at the University of Michigan, Ann Arbor, MI 48109.

3Present address: Toyota Research Institute, Los Altos, CA 94022.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received October 9, 2017; final manuscript received April 30, 2018; published online July 23, 2018. Assoc. Editor: Ardalan Vahidi.

J. Dyn. Sys., Meas., Control 140(12), 121010 (Jul 23, 2018) (12 pages) Paper No: DS-17-1510; doi: 10.1115/1.4040208 History: Received October 09, 2017; Revised April 30, 2018

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 controller (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 (SI) 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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Slotine, J.-J. , and Li, W. , 1991, Applied Nonlinear Control, Prentice-hall, Englewood Cliffs, NJ, Chaps. 7 and 8.
Utkin, V. I. , 1992, Sliding Modes in Control and Optimization, Springer, Berlin, Chap. 4. [CrossRef]
Shahbakhti, M. , Amini, M. , Li, J. , Asami, S. , and Hedrick, J. , 2015, “ Early Model-Based Design and Verification of Automotive Control System Software Implementations,” ASME J. Dyn. Syst., Meas., Control, 137(2), p. 021006. [CrossRef]
Amini, M. R. , Shahbakhti, M. , and Hedrick, J. K. , 2016, “ Easily Verifiable Adaptive Sliding Mode Controller Design With Application to Automotive Engines,” SAE Paper No. 2016-01-0629.
Nollet, F. , Floquet, T. , and Perruquetti, W. , 2008, “ Observer-Based Second Order Sliding Mode Control Laws for Stepper Motors,” Control Eng. Pract., 16(4), pp. 429–443. [CrossRef]
Acary, V. , and Brogliato, B. , 2010, “ Implicit Euler Numerical Scheme and Chattering-Free Implementation of Sliding Mode Systems,” Syst. Control Lett., 59(5), pp. 284–293. [CrossRef]
Huber, O. , Acary, V. , Brogliato, B. , and Plestan, F. , 2016, “ Implicit Discrete-Time Twisting Controller Without Numerical Chattering: Analysis and Experimental Results,” Control Eng. Pract., 46, pp. 129–141. [CrossRef]
Mihoub, M. , Nouri, A. , and Abdennour, R. , 2009, “ Real-Time Application of Discrete Second Order Sliding Mode Control to a Chemical Reactor,” Control Eng. Pract., 17(9), pp. 1089–1095. [CrossRef]
Amini, M. , Shahbakhti, M. , Pan, S. , and Hedrick, J. , 2017, “ Bridging the Gap Between Designed and Implemented Controllers Via Adaptive Robust Discrete Sliding Mode Control,” Control Eng. Pract., 59, pp. 1–15. [CrossRef]
Edelberg, K. , Shahbakhti, M. , and Hedrick, J. K. , 2013, “ Incorporation of Implementation Impercision in Automotive Control Design,” American Control Conference (ACC), Washington, DC, June 17–19, pp. 2854–2859.
Edelberg, K. , Pan, S. , and Hedrick, J. K. , 2013, “ Design of Automotive Control Systems Robust to Hardware Imprecision,” ASME Paper No. DSCC2013-3900.
Amini, M. R. , Shahbakhti, M. , and Hedrick, J. K. , 2016, “ Discrete Sliding Controller Design With Robustness to Implementation Imprecisions Via Online Uncertainty Prediction,” American Control Conference (ACC), Boston, MA, July 6–8, pp. 6537–6542.
Amini, M. R. , Shahbakhti, M. , Pan, S. , and Hedrick, J. K. , 2016, “ Handling Model and Implementation Uncertainties Via an Adaptive Discrete Sliding Controller Design,” ASME Paper No. DSCC2016-9732.
Misawa, E. , 1997, “ Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector,” ASME J. Dyn. Syst., Meas., Control, 119(3), pp. 503–512. [CrossRef]
Chan, C. , 1997, “ Discrete Adaptive Sliding-Mode Tracking Controller,” Syst. Control Lett., 33(5), pp. 999–1002.
Pan, S. , and Hedrick, J. K. , 2015, “ Tracking Controller Design for MIMO Nonlinear Systems With Application to Automotive Cold Start Emission Reduction,” ASME J. Dyn. Syst., Meas., Control, 137(10), p. 101013. [CrossRef]
Salgado-Jimenez, T. , Spiewak, J. M. , Fraisse, P. , and Jouvencel, B. , 2004, “ A Robust Control Algorithm for AUV: Based on a High Order Sliding Mode,” MTTS/IEEE TECHNO-OCEAN '04 (OCEANS '04), Kobe, Japan, Nov. 9–12, pp. 276–281.
Gao, W. , Wang, Y. , and Homaifa, A. , 1995, “ Discrete-Time Variable Structure Control Systems,” IEEE Trans. Ind. Electron., 42(2), pp. 117–122. [CrossRef]
Xiao, L. , and Zhu, Y. , 2011, “ Higher Order Sliding Mode Prediction Based Discrete-Time Variable Structure Control for Nonlinear Uncertain Systems,” International Conference on Computer Science and Service System (CSSS), Nanjing, China, June 27–29, pp. 446–449.
Pan, S. , 2014, “ Discrete Sliding Control for the Dynamics of Engine Cold Start,” Ph.D. dissertation, University of California, Berkeley, CA. https://escholarship.org/uc/item/20f739kr
Barkana, I. , 2015, “ The New Theorem of Stability-Direct Extension of Lyapunov Theorem,” Math. Eng., Sci. Aerosp., 6(3), pp. 519–550.
Barkana, I. , 2014, “ Defending the Beauty of the Invariance Principle,” Int. J. Control, 87(1), pp. 186–206. [CrossRef]
Khalil, H. , and Grizzle, J. , 1996, Nonlinear Systems, Prentice-hall, Englewood Cliffs, NJ. Chap. 13.
Monsees, G. , 2002, “ Discrete-Time Sliding Mode Control,” Ph.D. dissertation, Delft University of Technology, Delft, The Netherlands. https://www.dcsc.tudelft.nl/Research/PublicationFiles/publication-5390.pdf
Shaw, B. T., II , 2002, “ Modelling and Control of Automotive Coldstart Hydrocarbon Emissions,” Ph.D. dissertation, University of California, Berkeley, CA.
Sanketi, P. R. , 2009, “ Coldstart Modeling and Optimal Control Design for Automotive SI Engines,” Ph.D. dissertation, University of California, Berkeley, CA.
Amini, M. R. , Shahbakhti, M. , and Ghaffari, A. , 2014, “ A Novel Singular Perturbation Technique for Model-Based Control of Cold Start Hydrocarbon Emission,” Int. J. Engines, 7(3), pp. 1290–1301. [CrossRef]
Stefanopoulou, A. G. , Freudenberg, J. S. , and Grizzle, J. W. , 2000, “ Variable Camshaft Timing Engine Control,” IEEE Trans. Control Syst. Technol., 8(1), pp. 23–34. [CrossRef]
Amini, M. R. , Shahbakhti, M. , Pan, S. , and Hedrick, J. K. , 2017, “ Discrete Adaptive Second Order Sliding Mode Controller Design With Application to Automotive Control Systems With Model Uncertainties,” American Control Conference (ACC), Seattle, WA, May 24–26.

Figures

Grahic Jump Location
Fig. 1

Schematic of the second-order adaptive DSMC with ADC uncertainty prediction and propagation mechanism

Grahic Jump Location
Fig. 2

Block diagram of the engine cold start control system

Grahic Jump Location
Fig. 3

Engine tracking results by the first- and second-order SISO DSMCs for (a) T = 20 ms, quantization level = 16-bit and (b) T = 80 ms, quantization level = 10-bit

Grahic Jump Location
Fig. 4

Results of desired trajectories tracking from SISO baseline first- and second-order DSMCs, and MIMO second-order DSMC with predicted ADC uncertainties (T = 200 ms, quantization level = 16-bit)

Grahic Jump Location
Fig. 5

Results of unknown multiplicative parameters convergences (T = 80 ms, quantization level = 16-bit)

Grahic Jump Location
Fig. 6

Results of engine control under model uncertainties: (a) airfuel ratio, (b) exhaust gas temperature, and (c) engine speed (T = 80 ms, quantization level = 16-bit)

Grahic Jump Location
Fig. 7

Performance of the adaptive second-order DSMC in tracking nonsmooth trajectories: (a) engine performance and (b) control inputs (T = 20 ms, quantization level = 16-bit)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In