Technical Brief

Proportional–Integral Controller Design for Combustion-Timing Feedback, From n-Heptane to Iso-Octane in Compression–Ignition Engines

[+] Author and Article Information
Gabriel Ingesson

Department of Automatic Control,
Lund University,
Lund 22363, Sweden
e-mail: gabriel.ingesson@control.lth.se

Lianhao Yin, Per Tunestål

Department of Energy Sciences,
Lund University,
Lund 22363, Sweden

Rolf Johansson

Department of Automatic Control,
Lund University,
Lund 22363, Sweden

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 30, 2016; final manuscript received August 16, 2017; published online December 19, 2017. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 140(5), 054502 (Dec 19, 2017) (8 pages) Paper No: DS-16-1578; doi: 10.1115/1.4037834 History: Received November 30, 2016; Revised August 16, 2017

The problem of designing robust and noise-insensitive proportional–integral (PI) controllers for pressure-sensor-based combustion-timing control was studied through simulation. Different primary reference fuels (PRF) and operating conditions were studied. The simulations were done using a physics-based, control-oriented model with an empirical ignition-delay correlation. It was found that the controllable region in between the zero-gain region for early injection timings and the misfire region for late injection timings is strongly PRF dependent. As a result, it was necessary to adjust intake temperature to compensate for the difference in fuel reactivity prior to the controller design. With adjusted intake temperature, PRF-dependent negative-temperature coefficient (NTC) behavior gave different system characteristics for the different fuels. The PI controller design was accomplished by solving the optimization problem of maximizing disturbance rejection and tracking performance subject to constraints on robustness and measurement-noise sensitivity. Optimal controller gains were found to be limited by the high system gain at late combustion timings and high-load conditions; furthermore, the measurement-noise sensitivity was found to be higher at the low-load operating points where the ignition delay is more sensitive to variations in load and intake conditions. The controller-gain restrictions were found to vary for the different PRFs; the optimal gains for higher PRFs were lower due to a higher system gain, whereas the measurement-noise sensitivity was found to be higher for lower PRFs.

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Grahic Jump Location
Fig. 1

Steady-state θ50/θSOI relation for PRF20 and PRF80 with fuel energies from 2000 to 6000 J. The Qc sweep generates a band of θ50/θSOI relations. For late θSOI, θ50 is excessively delayed, which means that ignition never occurs. For earlier injection timings, the controllability from θSOI to θ50 decreases.

Grahic Jump Location
Fig. 2

Steady-state θ50/θSOI relation with adjusted Tin are presented as layered bands. The lower band corresponds to PRF0 and the upper to PRF 100. As we go from the lower to the upper band, the PRF value is increased from 0 to 100.

Grahic Jump Location
Fig. 3

Ignition delay, τ, used in the auto-ignition criterion in Eq. (6) as a function of injection timing with adjusted Tin according to Table 2. The lower PRFs exhibit a clear NTC behavior for earlier injection timings. Note that both temperature and PRF value are varied for the different curves and that the NTC behavior is dependent on both parameters. It was decided to study the NTC behavior after adjusting the intake temperature since this would be necessary prior to engine operation in order to get satisfactorily operation for the high PRF fuels.

Grahic Jump Location
Fig. 4

The region where 0.1<∂θ50/∂θSOI<∞ (shaded area) for PRF0 and PRF100. In order for the feedback controller to perform satisfactorily, θSOI should be limited within this region. Note that the region is narrower for low load and high PRF100.

Grahic Jump Location
Fig. 5

Combustion-timing feedback loop, θ50 is obtained from the measured in-cylinder pressure p and heat-release analysis. The controller takes action in order to counteract the error, e=rθ50−θ50, caused by, e.g., fuel amount or intake condition changes.

Grahic Jump Location
Fig. 6

Optimal θ50, θSOI trajectories from PRF0 to PRF100. The difference in θ50 is not as significant as the difference in θSOI for the different PRFs. It can be seen that pIMEP variations give greater variations for lower PRF, and that the θSOI response is comparable for Tin and rθ50 variations. During the experiment, Tin changes were applied at cycles 50, 100, 200, 250, 400, 450, 550, and 600; pIMEP changes are applied at cycles 350 (increase) and 700 (decrease); and rθ50 was varied at cycles 150, 300, 350, 500, 650, and 750. During the rpIMEP steps, rθ50 was also changed in order to increase θSOI variation. The markers indicate the points of linearization where Ms and Mt were computed, see Table 3 for more details.

Grahic Jump Location
Fig. 7

Optimal steady-state performance for PRF0 to PRF100. The θSOI standard deviation, σθSOI, is higher for the low pIMEP points (cycles 1–500), σθSOI is also higher for the lower PRFs, as indicated in the figure for the different operating points. The figure data come from a shorter version of the steady-state experiment consisting of 8000 cycles.

Grahic Jump Location
Fig. 8

Optimal controller gains as a function of PRF, the gains decrease as PRF increases. The limiting constraint was always Ms<1.4, at the “◻”-point in Fig. 6; here, the system gain ∂θ50/∂θSOI was the highest among the linearization points; it also increased with PRF.

Grahic Jump Location
Fig. 9

IAE (black), Ms=1.4 (solid) and Mt=1.4 (dashed) level curves as a function of controller parameters kp and kI, for PRF0 and PRF100. IAE decreases as kp and kI increase. The allowed parameters for which Ms, Mt<1.4 are encircled by the solid lines.

Grahic Jump Location
Fig. 10

IAE (solid, black) and σSOI=0.25 for PRF0 and PRF100 as a function of kp and kI. The allowed parameters for which σSOI=0.25 are within the solid lines. The most restrictive σSOI=0.25 constraints for both fuels were found at the late θ50 at the low-load operating points, see Fig. 7.

Grahic Jump Location
Fig. 11

For given controller gains, the noise sensitivity depends on the θ50 partial derivatives with respect to Tin, pin, Qc, and the Sc norm. These quantities are plotted for PRF0, PRF100 with pIMEP=5.15.

Grahic Jump Location
Fig. 12

Injection-timing standard deviation as a function of θ50, computed using Eq. (21). σθSOI decreases with load and also increases when θ50 is delayed.




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