Research Papers: Gas Turbines: Controls, Diagnostics, and Instrumentation

Optimal Transient Control Trajectories in Diesel–Electric Systems—Part I: Modeling, Problem Formulation, and Engine Properties

[+] Author and Article Information
Martin Sivertsson

Division of Vehicular Systems,
Department of Electrical Engineering,
Linköping University,
Linköping SE-581 83, Sweden
e-mail: marsi@isy.liu.se

Lars Eriksson

Division of Vehicular Systems,
Department of Electrical Engineering,
Linköping University,
Linköping SE-581 83, Sweden
e-mail: larer@isy.liu.se

1Corresponding author.

Contributed by the Controls, Diagnostics and Instrumentation Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received May 15, 2014; final manuscript received June 3, 2014; published online September 16, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(2), 021601 (Sep 16, 2014) (11 pages) Paper No: GTP-14-1238; doi: 10.1115/1.4028359 History: Received May 15, 2014; Revised June 03, 2014

A nonlinear four state-three input mean value engine model (MVEM), incorporating the important turbocharger dynamics, is used to study optimal control of a diesel–electric powertrain during transients. The optimization is conducted for the two criteria, minimum time and fuel, where both engine speed and engine power are considered free variables in the optimization. First, steps from idle to a target power are studied and for steps to higher powers the controls for both criteria follow a similar structure, dictated by the maximum torque line and the smoke-limiter. The end operating point, and how it is approached is, however, different. Then, the power transients are extended to driving missions, defined as, that a certain power has to be met as well as a certain energy has to be produced. This is done both with fixed output profiles and with the output power being a free variable. The time optimal control follows the fixed output profile even when the output power is free. These solutions are found to be almost fuel optimal despite being substantially faster than the minimum fuel solution with variable output power. The discussed control strategies are also seen to hold for sequences of power and energy steps.

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Fig. 1

BAE systems TorqE diesel–electric powertrain

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Fig. 2

Structure of the MVEM. The modeled components as well as the connection between them.

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Fig. 3

Cardan power for a step from idle measured on one of the considered applications

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Fig. 5

Time and fuel optimal solutions to different load transients. The time and fuel optimal transients have similar structures but differ in how they meet the end constraints. Since several trajectories are plotted, the smoke-limit for unloaded engine acceleration is clearly visible.

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Fig. 6

Time and fuel optimal solutions to a load transient from idle to 170 kW

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Fig. 7

Top: kinetic energy in the engine as well as the total kinetic energy in the system at time T. Bottom: kinetic energy in the turbocharger at time T.

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Fig. 8

Change in time and consumption as a function of Preq

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Fig. 9

Comparison between fuel optimal transients and transients to the fuel optimal operating point. * denotes the fuel optimal operating point.

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Fig. 10

Two trajectories that are both time optimal, but the fuel consumptions differ by 10.6%. For higher Ereq, the minimum time solution is not unique.

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Fig. 4

Generator actuation for different criteria. Circles mark the end points.

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Fig. 11

Minimum time transients from idle to Preq = [100 150 200] kW for different Ereq. The characteristics of the solution are independent of both Ereq and Preq.

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Fig. 12

State and control trajectories for minT,Preq = 170 kW for different Ereq

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Fig. 13

Minimum fuel transients from idle to Preq = [100 150 200] kW for different Ereq

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Fig. 14

State and control trajectories for min mf,Preq = 170 kW for different Ereq

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Fig. 15

Torque versus engine speed for minmf/T one and two-phase solutions as well as for a step in power without requirements on produced energy

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Fig. 16

Engine speed and torque trajectories for minT4-phase and minmf4-phase. The solutions are similar despite different criteria.

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Fig. 17

State and control trajectories for min T4-phase and min mf4-phase



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