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Research Papers

A Model-Based Control Design Approach for Linear Free-Piston Engines

[+] Author and Article Information
T. N. Kigezi

Department of Engineering and Design,
The School of Engineering and Informatics,
The University of Sussex,
Falmer, Brighton BN1 9QT, UK
e-mail: T.Nsabwa-Kigezi@sussex.ac.uk

J. F. Dunne

Department of Engineering and Design,
The School of Engineering and Informatics,
The University of Sussex,
Falmer, Brighton BN1 9QT, UK
e-mail: j.f.dunne@sussex.ac.uk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 11, 2016; final manuscript received May 17, 2017; published online August 8, 2017. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 139(11), 111010 (Aug 08, 2017) (10 pages) Paper No: DS-16-1550; doi: 10.1115/1.4036886 History: Received November 11, 2016; Revised May 17, 2017

A general design approach is presented for model-based control of piston position in a free-piston engine (FPE). The proposed approach controls either “bottom-dead-center” (BDC) or “top-dead-center” (TDC) position. The key advantage of the approach is that it facilitates controller parameter selection, by the way of deriving parameter combinations that yield both stable BDC and stable TDC. Driving the piston motion toward a target compression ratio is, therefore, achieved with sound engineering insight, consequently allowing repeatable engine cycles for steady power output. The adopted control design approach is based on linear control-oriented models derived from exploitation of energy conservation principles in a two-stroke engine cycle. Two controllers are developed: A proportional integral (PI) controller with an associated stability condition expressed in terms of controller parameters, and a linear quadratic regulator (LQR) to demonstrate a framework for advanced control design where needed. A detailed analysis is undertaken on two FPE case studies differing only by rebound device type, reporting simulation results for both PI and LQR control. The applicability of the proposed methodology to other common FPE configurations is examined to demonstrate its generality.

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References

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Figures

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Fig. 1

Generic FPE schematic. The piston, translator, and generator permanent magnet (for this illustration of an FPE generator) constitute the moving mass. The rebound device may be a mechanical spring, an air bounce chamber or another cylinder. 1—Cylinder, 2—piston, 3—translator rod, 4—piston load (generator), and 5—rebound device.

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Fig. 2

Visualization of piston motion over time annotated withnotation used in analysis. One complete cycle is from b to b+. The lines xT and xB are the nominal piston endpoints. The arrows represent inputs to the engine as fuel addition or rebound device stiffness adjustment.

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Fig. 3

Visualization of piston motion over time annotated with notation used in analysis. One complete cycle is from t to t+. The lines xT and xB are the nominal piston endpoints. The arrows represent inputs to the engine as fuel addition or rebound device stiffness adjustment.

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Fig. 4

Parameter combinations kp, ki and associated regions of stability or instability, where a=1.05 in system (24)

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Fig. 5

BDC/TDC error and input fuel response for PI and LQR controllers with a mechanical spring as rebound device. Controller parameters were chosen within their stability bounds. LQR response transient is slower than the PI response transient owing to a minimization of input objective.

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Fig. 6

Output power and engine speed responses with a mechanical spring as rebound device. The same power and speed are achieved at steady-state regardless of controller type.

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Fig. 7

BDC/TDC error and input fuel response for PI and LQR controllers with a bounce chamber as rebound device. Controller parameters were chosen within their stability bounds. LQR response transient is slower than the PI response transient owing to a minimization of input objective.

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Fig. 8

Output power and engine speed responses with a bounce chamber as rebound device. The same power and speed are achieved at steady-state regardless of controller type.

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Fig. 9

BDC/TDC error response for PI and LQR controllers with a combustion chamber as rebound device. Controller parameters were chosen within their stability bounds. LQR response transient is slower than the PI response transient owing to a minimization of input objective.

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Fig. 10

An opposed piston FPE. Two pistons sharing a combustion volume oppose each other about the centerline.

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