Research Papers

Modeling and Control of an Automotive All-Wheel Drive Clutch as a Piecewise Affine System

[+] Author and Article Information
Shiming Duan

e-mail: duansm@umich.edu

A. Galip Ulsoy

Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48105

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 16, 2011; final manuscript received August 20, 2013; published online September 26, 2013. Assoc. Editor: Bor-Chin Chang.

J. Dyn. Sys., Meas., Control 136(1), 011008 (Sep 26, 2013) (10 pages) Paper No: DS-11-1257; doi: 10.1115/1.4025275 History: Received August 16, 2011; Revised August 20, 2013

Piecewise affine (PWA) systems belong to a subclass of switched systems and provide good flexibility and traceability for modeling a variety of nonlinear systems. In this paper, application of the PWA system framework to the modeling and control of an automotive all-wheel drive (AWD) clutch system is presented. The open-loop system is first modeled as a PWA system, followed by the design of a piecewise linear (i.e., switched) feedback controller. The stability of the closed-loop system, including model uncertainty and time delays, is examined using linear matrix inequalities based on Lyapunov theory. Finally, the responses of the closed-loop system under step and sine reference signals and temperature disturbance signals are simulated to illustrate the effectiveness of the design.

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Fig. 1

An automatic AWD system

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Fig. 2

Structure of an AWD clutch system

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Fig. 3

An AWD clutch system

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Fig. 4

Existing control design (open-loop observer + feed forward P control)

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Fig. 5

Proposed feedback control design (disturbance observer + feed forward control + piecewise PI feedback control)

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Fig. 6

Test profile for clutch thermal system modeling

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Fig. 7

Mu factor, μ, versus plate temperature, Tp

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Fig. 8

Comparing the nominal output torque, Cq, versus current, ic, with its piecewise affine approximation

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Fig. 9

Simulated temperature fluctuation

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Fig. 10

Step response of the open-loop system

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Fig. 11

Open-loop system responses under a sine input signal

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Fig. 12

Step response of the closed-loop system

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Fig. 13

Closed-loop system responses under a sine input signal

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Fig. 14

Comparison between existing design and proposed design

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Fig. 15

Step responses of closed-loop systems with proposed control design and different delay levels

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Fig. 16

Map of feasible design region showing the trade-off between speed of response, uncertainty and delay



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