Gray based Fuzzy Gain-Scheduling PID Controller Design for Air-Fuel System Under Variable Engine Operating Conditions

Abstract

In this study, the problem of regulation of air-fuel ratio (AFR) in gasoline engines under different engine operating conditions is discussed. Firstly, the mean value mathematical model of the AFR system has been created. Then, two different approaches named with classical proportional-integral-derivative (PID) and a fuzzy logic gain scheduling PID controller combined with gray system modelling approach (Gray GS-PID)have been used to improve the performance of the engine to monitor stoichiometric conditions. The parameters of classical PID parameters are determined by the pattern search algorithm. The design procedures for both controllers have been presented in detail. In order to evaluate the performance analysis for both of the proposed controllers, variable conditions were established based on engine speed and throttle opening ratios in the US06 and UDDS driving conditions and validated by simulation results. According to the results, Gray GS_PID is more powerful than optimally adjusted PID in terms of reducing the amount of deviation of AFR from stoichiometric value under variable engine operating conditions. The most important contribution of this study is that, unlike conventional AFR regulation, the prediction of future error value relative to the previous AFR error values ​​using the gray prediction algorithm, and the design of the control algorithm that determines the control action for the next step depending on the predicted error value before the error occurs and sets the gain parameters.

Keywords

• AFR system,GM(1-1) predictive model,Fuzzy logic,GainScheduling PID

References

1. Manzie, C., Palaniswami, M., Ralph, D., Watson, H., Yi, X., (2002). Model Predictive Control of a Fuel Injection System with a Radial Basis Function Network Observer. Journal of Dynamic Systems, Measurement, and Control, Doi: 10.1115/1.1515328.
2. Franceschi, E.M., Muske, K.R., Peyton Jones, J.C., Makki, I., (2007). An Adaptive Delay-Compensated PID Air Fuel Ratio Controller, Doi: https://doi.org/10.4271/2007-01-1342.
3. Pace, S., Zhu, G.G., (2014). Transient air-to-fuel ratio control of an spark ignited engine using linear quadratic tracking. Journal of Dynamic Systems, Measurement, and Control 136(2): 21008.
4. Ebrahimi, B., Tafreshi, R., Masudi, H., Franchek, M., Mohammadpour, J., Grigoriadis, K., (2012). A parameter-varying filtered PID strategy for air-fuel ratio control of spark ignition engines. Control Engineering Practice 20(8): 805–15, Doi: 10.1016/j.conengprac.2012.04.001.
5. Hendricks, E., Chevalier, A., Jensen, M., Sorenson, S.C., Trumpy, D., Asik, J., (1996). Modelling of the Intake Manifold Filling Dynamics, Doi: https://doi.org/10.4271/960037.
6. Jones, V.K., Ault, B.A., Franklin, G.F., Powell, J.D., (1995). Identification and air-fuel ratio control of a spark ignition engine. Control Systems Technology, IEEE Transactions On 3(1): 14–21, Doi: 10.1109/87.370705.
7. Tseng, T.-C., Cheng, W.K., (1999). An Adaptive Air/Fuel Ratio Controller for SI Engine Throttle Transients, Doi: https://doi.org/10.4271/1999-01-0552.
8. Al-Olimat, K.S., Ghandakly, A.A., Jamali, M.M., (2000). Adaptive Air-Fuel Ratio Control of an SI Engine Using Fuzzy Logic Parameters Evaluation, Doi: 10.4271/2000-01-1246.

9. Wang, S.W., Yu, D.L., Gomm, J.B., Page, G.F., Douglas, S.S., (2006). Adaptive neural network model based predictive control for air–fuel ratio of SI engines. Engineering Applications of Artificial Intelligence 19(2): 189–200, Doi: https://doi.org/10.1016/j.engappai.2005.08.005.
10. Suzuki, K., Tielong, S., Kako, J., Yoshida, S., (2009). Individual A/F Estimation and Control With the Fuel–Gas Ratio for Multicylinder IC Engines. Vehicular Technology, IEEE Transactions On 58(9): 4757–68, Doi: 10.1109/TVT.2009.2025862.
11. Ljung, L., (1998). System Identification: Theory for the User. Pearson Education.
12. Han, P., Liu, H.-J., Meng, L.-M., Wang, N., (2005). Research of grey predictive fuzzy controller for large time delay system. 2005 International Conference on Machine Learning and Cybernetics, vol. 2. IEEE p. 829–33.
13. Kayacan, E., Kaynak, O., (2009). An adaptive grey PID-type fuzzy controller design for a non-linear liquid level system. Transactions of the Institute of Measurement and Control 31(1): 33–49.
14. Kudinov, Y.I., Kolesnikov, V.A., Pashchenko, F.F., Pashchenko, A.F., Papic, L., (2017). Optimization of Fuzzy PID Controller’s Parameters. Procedia Computer Science 103: 618–22, Doi: https://doi.org/10.1016/j.procs.2017.01.086.
15. Liu, H., Li, Y., Zhang, Y., Chen, Y., Song, Z., Wang, Z., et al., (2018). Intelligent tuning method of PID parameters based on iterative learning control for atomic force microscopy. Micron 104: 26–36, Doi: https://doi.org/10.1016/j.micron.2017.09.009.
16. K. Ogata., (2002). Modern Control Engineering.
17. Heywood, J., (1988). Internal Combustion Engine Fundamentals. McGraw-Hill Education.
18. Zhao, Z.Y., Tomizuka, M., Isaka, S., (1992). Fuzzy gain scheduling of PID controllers. Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992
19. Mamdani, E.H., Assilian, S., (1975). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies, Doi: 10.1016/S0020-7373(75)80002-2.