基于ADRC的汽油机瞬态空燃比控制：时变延迟处理策略

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本文探讨了汽油发动机在存在时变运输延迟的情况下，采用改进型主动抗扰控制器（Active Disturbance Rejection Control, ADRC）进行瞬态空燃比（Air/Fuel Ratio, AFR）控制的研究。作者Zhijing Wang和Xiaohong Jia合作，他们的研究成果发表在《电气与电子工程学刊》(IEEE Journal on Transactions on Electrical and Electronic Engineering, IEEJTrans2017) 的S1卷第12期上，具体页码为S117至S124，可在 Wiley Online Library 上获取全文，DOI号为10.1002/tee.22444。在汽油机的工作过程中，维持AFR在理论燃烧比是非常关键的，因为这直接影响发动机性能和排放。然而，实际操作中，动态变化的因素如进气歧管压力、发动机转速以及负载扭矩的波动，再加上燃料蒸发过程中的不确定参数和氧传感器老化等问题，都会作为“总扰动”影响AFR的稳定控制。为了克服这些挑战，研究人员设计了一种基于ADRC的控制器，它利用扩展状态观测器（Extended State Observer, ESO）来估计这些扰动。 ADRC算法的核心在于其能够实时跟踪和补偿系统中的不确定性和外部干扰。在设计过程中，作者利用李亚普诺夫-克拉索夫斯基稳定性理论，通过确定控制器和观测器增益矩阵，构建了一个有效的解决方案。这种方法旨在确保在处理时变运输延迟时，控制器能够快速、准确地调整喷油量，使得AFR始终保持在理想值附近，从而优化发动机性能，降低排放，并减少运行中的不稳定性。通过线性矩阵不等式（Linear Matrix Inequalities, LMIs）的求解，本文提供了一种实用的设计方法，使得该控制器能够在复杂的动态环境中实现稳定的AFR控制，这对于提升汽油发动机的整体效率和可靠性具有重要意义。这篇论文不仅深化了我们对ADRC在汽车工程中的应用理解，也为解决汽油机瞬态控制问题提供了新的策略和技术支持。

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING

IEEJ Trans 2017; 12(S1): S117–S124

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.22444

Paper

ADRC-Based Transient Air/Fuel Ratio Control with Time-Varying Transport

Delay Consideration for Gasoline Engines

Zhijing Wang, Non-member

Xiaohong Jiao

, Non-member

This paper presents a fuel injection controller based on the modiﬁed active disturbance rejection control (ADRC) algorithm to

maintain the air/fuel ratio (AFR) at the stoichiometric value in the presence of a transport time delay. The factors affecting the

dynamics of the AFR include the variations of the intake manifold pressure, engine speed, and load torque, as well as uncertain

parameters existing in the fuel ﬁlm evaporation and the oxygen sensor aging, which are viewed as the ’total disturbance’ to the

AFR system and estimated by the extended state observer (ESO). Thus, based on the Lyapunov–Krasovskii functional stability

theory, the ADRC fuel injection controller is designed with the gain matrices of the controller and observer and solved by

employing linear matrix inequalities. Considering the time-varying transport delay, a time delay block is added to the ESO. By

synchronizing the input signals of the ESO, the performance in terms of the timely compensation for the disturbance is improved.

The effectiveness of the proposed control strategy is validated through simulation of a V6 spark ignition engine model developed

by the Society of Instrument and Control Engineers (SICE) Research Committee on Advanced Powertrain Control Theory.

Keywords: spark ignition engine; air/fuel ratio; active disturbance rejection control; time-varying delay; linear matrix inequality

Received 19 May 2016; Revised 19 November 2016

1. Introduction

In consideration of energy saving and environmental protection,

maintaining the air/fuel ratio (AFR) at the stoichiometric value

seems more and more important because of the great inﬂuence

AFR has on the conversion efﬁciency of the three-way catalyst

and fuel economy of a spark ignition (SI) engine. The main

challenges in the precise control of the AFR, especially during the

transient operations of the engine, involve the transport time delay

in the AFR system, which varies with the switching of engine

operations, variations of the intake manifold pressure, engine

speed, and load torque, as well as plant uncertainties due to the

wall-wetting phenomenon and aging of the universal exhaust gas

oxygen (UEGO) sensor.

In view of the impact of the transport time delay on the

dynamics of the AFR, several studies have been made. For

example, in [1] the internal model control and its application

to the AFR control system are presented. This method handles

the time delay in the AFR system under the condition that the

structure of the plant is already known in the absence of any

disturbance to the system. The Smith predictor shown in [2,3]

is widely used for time delay, which can remove the time delay

from the main loop. But the predictor is available only when

the parameters in the model match those in the plant, and the

performance may decrease when modeling errors exist. Moreover,

other challenges in maintaining the AFR at the stoichiometric

value involve the complications in the model construction of the

engine and some physicochemical processes such as the air intake

[4], fuel delivery, and the combustion. Thus, many algorithms

have been proposed to get an appropriate solution, such as the

neural network control algorithm applied in [5–7], which can

identify the engine model for controlling the AFR. However, this

Correspondence to: Xiaohong Jiao. E-mail: jiaoxh@ysu.edu.cn

School of Electrical Engineering, Yanshan University, Hebei 066004,

China

method deﬁnitely requires much training in practice. For reducing

the canister purge disturbance, [8] has derived a sliding-mode

controller. In [9], to reduce the inﬂuence of the uncertainties caused

by the wall-wetting phenomenon and the variations of the intake

manifold and engine speed, an extended state observer (ESO)

was constructed. But the time-varying transport delay in the AFR

system, which leads to the deviation of the fuel command, is

ignored. As for the parameter uncertainties in the AFR control

plant, the adaptive control algorithm is widely employed, typical

examples being given in [10–13]. On the basis of the mean value

engine model, adaptive fuel injection controllers are derived in

[10,11] to remove the inﬂuence of the uncertain parts caused by

the fuel ﬁlm evaporation and the system description. Adaptive

update laws are derived on the Lyapunov design for the uncertain

parameters [12,13]. In [14], to deal with the biofuel parameters,

the adaptive algorithm is applied to estimate the biofuel content for

internal combustion engines. Taking the time-varying parameters

into consideration, [15] applies the switching linear parameter

varying (LPV) controller to the AFR control system for managing

the dynamics of the fuel path.

In this paper, a modiﬁed active disturbance rejection control

(ADRC) algorithm for the accurate regulation of the AFR is

derived, which can deal with the transport time delay generated

from the fuel injection to the AFR measurement and tries to

diminish the inﬂuence caused by the change of the engine

operation and the uncertain parameters in the AFR system. An ESO

is designed to estimate the ’total disturbance’ that is associated

with the unmeasurable air mass ﬂow rate into the cylinder, the

uncertainties in the fuel ﬁlm evaporation process, and the change

of the engine torque for the port-injected SI engine. The modiﬁed

part for the transport delay makes the control signal and the

system output to synchronize and removes the time delay from

the ESO, thus improving the performance of the estimations. The

gain matrices of the ADRC controller and the ESO can be solved

by linear matrix inequalities (LMIs), which ensures the stability of

the augmented error system.

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