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.

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Fig. 1

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

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Fig. 2

Block diagram of the engine cold start control system

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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

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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)

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Fig. 5

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

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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)

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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)



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