In this paper, an optimal control scheme for reducing the fluctuation of residual gas fraction (RGF) under variational operating condition is developed by combining stochastic logical system approach with statistical learning method. The method estimating RGF from measured in-cylinder pressure is introduced firstly. Then, the stochastic properties of the RGF are analyzed according to statistical data captured by conducting experiments on a test bench equipped with a L4 internal combustion engine. The influences to the probability distribution of the RGF from both control input and environment parameters are also analyzed. Based on the statistical analysis, a stochastic logical transient model is adopted for describing cyclic behavior of the RGF. Optimal control policy maps for different fixed operating conditions are calculated then. Besides, a statistical learning-based method is applied to learn the probability density function (PDF) of RGF in the real-time which is used to adjust the control MAP based on logical optimization. The whole optimal control policy map is obtained based on Gaussian process regression with consideration of statistical information of RGF. Finally, the performance of the proposed method is experimentally validated.
The authors gratefully acknowledge the support and generosity of Toyota Motor Corporation, without which the present study could not have been completed.
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Figure 1
(Color online) Representation of the engine cyclic gas exchange phenomena.
Figure 2
(Color online) Pressure measurement points.
Figure 3
(Color online) Test bench.
Figure 4
(Color online) Stochastic properties of RGF.
Figure 5
(Color online) Influence of environment to RGF probability distribution. (a) ${\rm~VVT}=33$; (b) ${\rm~VVT}=39$.
Figure 6
Block diagram of the control scheme.
Figure 7
(Color online) Conditional probability density for $y_{k+1}$ given $y_k\in~A^i$, $i=1,2,\ldots,9$, under different VVT values. (a) ${\rm~VVT}=27$; (b) ${\rm~VVT}=30$; (c) ${\rm~VVT}=36$; (d) ${\rm~VVT}=39$.
Figure 8
(Color online) Statistical learning for RGF.
Figure 9
(Color online) Optimal feedback control law for VVT. (a) RGF $A^1$; (b) RGF $A^3$; (c) RGF $A^5$; (d) RGF $A^7$.
Figure 10
(Color online) Cycle-to-cycle RGF response with (a) fixed and (b) optimal control VVT input.
Figure 11
(Color online) Comparison of (a) the occupancy frequency distributions and (b) probability density functions of RGF.
Engine specification | Dynamo technical data | ||
Item | Value | Item | Value |
Cylinder type | L-type 4 cylinders | Rated power (Absorbing/Driving) (kW) | 250/225 |
Ignition system | DIS | Rated torque (Absorbing/Driving) (Nm) | 480/442 |
Compression ratio | 13:1 | Rated speed (Absorbing/Driving) (kW) | 4980/4860 |
Displacement | 1797 ml | Maximum speed (rpm) | 10000 |
Maximum torque | 142 N.m | Moment of inertia ($\textrm{kg}\cdot~\textrm{m}^2$) | 0.36 |
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