Sliding Mode Control for Diesel Engine Using
Extended State Observer
Haoping WANG, Wei ZHANG, Yang TIAN*, Qiankun QU
Nanjing University of Science & Technology, School of Automation,
Sino-French International Joint Laboratory of Automatic Control and Signal Processing (LaFCAS),
Nanjing 210094, China
* Corresponding author
Abstract: This paper does a research on turbocharged diesel engines both of air-path or speed-path alone, and proposes a cooperative control strategy of air and speed-path two loop TDE system. For modern diesel engines, accurate air/fuel ratio (AFR) and exhaust gas recirculation (EGR) rates design are very important to meet the requirements of emission standards of NOx and PM. For the EGR and AFR rates are controlled by the EGR and the variable geometry turbine (VGT) actuators, we propose a fourth-order simplified nonlinear model which takes into account the crankshaft speed dynamics and the air-path dynamics for the turbocharged diesel engine. The controller for the speed-path we designed which is based on Lyapunov function is used to track the desired engine speed. For the air-path, a sliding mode controller based on exponential reaching law which uses the concept of total disturbances to control the EGR and VGT valve is designed. In order to estimate the disturbances in the system, we proposed a 2nd-order extended space observer (ESO). The simulation results show that the sliding mode controller which utilizes observer and reaching law can alleviate the chattering problem obviously and the proposed two-loop structure dynamic model exhibits excellent performances in tracking desired signals and overcoming the system disturbances. In the presence of disturbances, the system can still observe the total disturbances, including the unmodeled dynamics and actuator faults, accurately and timely.
Keywords: Turbocharged diesel engine; sliding mode control; ESO; chattering; tracking; disturbances.
CITE THIS PAPER AS:
Haoping WANG, Wei ZHANG, Yang TIAN, Qiankun QU, Sliding Mode Control for Diesel Engine UsingExtended State Observer, Studies in Informatics and Control, ISSN 1220-1766, vol. 24 (4), pp. 439-448, 2015. https://doi.org/10.24846/v24i4y201508
With the rapid development of vehicles in transportation, the exhaust emissions increase seriously the pollution of our environment. The energy efficiency and the environment protection become the prominent concerns in transportation, and make people pay more and more attention to them. How to improve vehicle fuel economy and exhaust emissions standards in order to save energy and reduce pollution is now an extremely urgent problem. Therefore, energy-saving technology of a car engine is one of the trends in the automotive future.
Comparing to gasoline engines, diesel engines have the advantage of providing larger torque under a compromise between fuel consumption and given exhaust emission level. However, diesel engines also have some problems to be resolved and one prominent question is exhaust emissions. Although the emissions of diesel engines in CO, hydrocarbons (HC) and CO2 is lower than gasoline engines, but the emissions of particulate matter (PM) and nitrogen oxides (NOx) are difficult to control.
In order to meet the requirements of emission standards EURO V and VI, especially for PM and NOx emissions, the engine needs to be controlled in each cycles.
Earlier reduction mechanism suggest that NOx emissions can be reduced by increasing the exhaust gas recirculation (EGR) intake manifold fraction and smoke can be reduced by increasing the air/fuel ratio (AFR) . The EGR and AFR ratio is controlled by a variable geometry turbine (VGT) actuator. So, how to design the controller to control the VGT position for the purpose of reducing emissions of NOx and the smoke has become the continuous studies of researchers in recent years.
At present, many foreign researchers have done a lot of work on diesel engine control strategy and has made some progress. However, the EGR and AFR actuators are strongly coupled so that the traditional PI regulator face difficult in providing satisfactory results in the terms of torque response, transient response and engine-out emissions even with time- consuming and detailed calibrations.
In the past decade, many diesel engine (TDE) air and speed-path model are in constant development. In , the authors proposed a full-seven-order TDE air-path model. The model describes the dynamics of several variables such as the pressure and the oxygen mass fractions in the intake and exhaust manifolds, the turbocharger speed, and the two states of the control signals which describe the dynamics of the EGR and VGT actuator. To simplify the control design, the full-seven-order TDE model was simplified into a third-order one. But this simplification resulted in neglecting the unmodeled dynamics, system disturbances or the engine faults affecting the air-path.
With the development of digital processing technology, many sophisticated control strategies are introduced in controlling modern diesel engines. For speed engine regulation, some prior efforts already exist, such as optimal gain scheduling , H∞ control based on linear parameter varying (LPV) approach , adaptive methods , sliding mode control , Lyapunov function based control , or PID control .
And for the air-path, several controllers were proposed in the literature, for example, Lyapunov control design , robust gain-scheduled controller
based on a LPV model for turbocharged diesel engine , indirect passivation , and feedback linearization .
However, most of these algorithms are oriented model, that is, the designed control laws are based on the model of diesel engines. In fact, actuator failure in the input control, can be regarded as external disturbances; modeling uncertainties which act on the system from different channels can be regarded as internal disturbances. Meantime, the total disturbances of the system are difficult to measure, thus, a disturbance observer is needed to estimate them. So one of the main purpose of this paper is to design a control strategy which is robust when facing the disturbances which affects the diesel engine air and speed-path. Here, a sliding mode controller based on extended space observer (ESO) is chosen for the control design [12-14]. In addition, the existing studies are made for air-path or speed-path respectively [12-15]. For the reason that the two paths influence each other deeply, we desire to establish a two loop cooperative control system.
This paper is organized as follows. Section 2 presents the TDE air and speed-path modeling and the faulty system that we will deal with in this paper. Section 3 develops the controller for the two loop TDE system, the Lyaounov based controller for the speed-path and the ESO based sliding mode controller for the air-path. Then we show some numerical simulation results in Section 4. Finally, some concluding remarks and discussions are given in Section 5.
- CABRERA, E., G. CABRERA, B. CRAWFORD, F. PAREDES, J. M. RUBIO, SOTO, A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer Programming Applied to a Large-Scale Capacitated Facility Location Problem, Mathematical Problems in Engineering, vol. 2012, 2012.
- GLOVER, F., M. LAGUNA, Tabu Search, Norwell, MA, USA: Kluwer Academic Publishers, 1997.
- HOOS, H., Automated Algorithm Configuration and Parameter Tuning, in Autonomous Search, Y. Hamadi, E. Monfroy, and F. Saubion, Eds. Springer Berlin Heidelberg, 2012, pp. 37-71.
- GONZÁLEZ-HIDALGO, M., A. JAUME-I-CAPÓ, A. MESEJO-CHIONG, O. L. VERA-PÉREZ, Automatic Parameter Configuration: A Case Study on a Rehabilitation Oriented Human Limb Tracking Algorithm, Studies in Informatics and Control , vol. 23, no. 3, 2014, pp. 313-323.
- KOBAYASHI, R., N. KOMODA, M. MORI, M. SAMEJIMA, Cost-benefit Analysis of Decentralized Ordering on Multitier Supply Chain by Risk Simulator, Studies in Informatics and Control, vol. 21, no. 1, 2012, pp. 75–83.
- CRAWFORD, B., E. MONFROY, F. PAREDES, R. SOTO, C. VALENZUELA, Parameter Tuning of Metaheuristics Using Metaheuristics, Advanced Science Letters, vol. 19(12), 2013, pp. 3556-3559.
- KOZA, J., Genetic Programming as a Means For Programming Computers by Natural Selection. Kluwer Academic Publishers, vol. 4, no. 2, 1994.
- BEASLEY, J., An Algorithm for Solving Large Capacitated Warehouse Location Problems, European Journal of Operational Research, vol. 33, no. 3, 1998, pp. 314-325.
- BÖLTE, A., U. W. THONEMANN, Optimizing Simulated Annealing Schedules with Genetic Programming, European Journal of Operational Research , vol. 92, no. 2, 1996, pp. 402-416.
- KIRKPATRICK, S., Optimization by Simulated Annealing: Quantitative Studies. Journal of Statistical Physics, vol. 34, no. 5-6, 1984, pp. 975-986.
- GELATT, C. D., S. KIRKPATRICK, M. P. VECCHI, Optimization by Simulated Annealing, Science, vol. 220, no. 4598, 1983, pp. 671-680.
- METROPOLIS, N., A. W. ROSENBLUTH, M. N. ROSENBLUTH, A. H. TELLER, E. TELLER, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol. 21(6), 1953, pp. 1087-1092.
- CABRERA, G., C. CUBILLOS, J. P. RIQUELME, S. RONCAGLIOLO, R. SOTO, A Hybrid Particle Swarm Optimization-Simulated Annealing Algorithm for the Probabilistic Travelling Salesman Problem, Studies in Informatics and Control, vol. 21, 2012, pp. 49-58.
- CHENG, Z., C. C. KANG, W. C. LIN, S. LIU, W. H. WU, A Single-Machine Two-Agent Scheduling Problem by a Branch-And-Bound and Three Simulated Annealing Algorithms, Discrete Dynamics in Nature and Society, vol. 2015, 2015, Article ID 681854.
- NI, L., J. QIN, H. XIANG, Y. YE, A Simulated Annealing Methodology to Multiproduct Capacitated Facility Location with Stochastic Demand, The Scientific World Journal, vol. 2015, 2015, Article ID 826363.
- LUNDY, M., A. MESS, Convergence of an Annealing Algorithm. Mathematical Programming, vol. 34, 1986, pp. 111-124.
- WILHELM, M., T. WARD, Solving Quadratic Assignment Problems by Simulated Annealing, IIE Transactions, vol. 19, no. 1, 1987, pp. 107-119.
- FOGEL, L. J., A. J. OWENS, M. J. WALSH, Artificial Intelligence through Simulated Evolution, New York, USA: John Wiley, 1966.
- HOLLAND, J. H., Adaptation in Natural and Artificial Systems, Ann Arbor, MI, USA: University of Michigan Press, 1975.
- RECHENBERG, I., Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution, Ph.D. dissertation, TU Berlin, 1971.
- EGGERMONT, J., Data Mining Using Genetic Programming: Classification and Symbolic Regression, Ph.D. dissertation, Universiteit Leiden, September 2005.
- WALKER, M., Introduction to Genetic Programming, Computer Science Department, Montana State University, Tech. Rep., December 2001.
- BEASLEY, J., OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, vol. 41(11), 1990, pp. 1069-1072.