基于预测控制的汽油发动机怠速控制方法研究
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摘要
一直以来,怠速工况是发动机工作的重要工况之一,对于提高汽油发动机的燃油经济性、降低排放具有十分重要的意义。这主要是由于车辆在交通密集度大的道路上行驶时,约有30%的燃油消耗在怠速工况中,并且怠速排放CO和HC量占总排放量的70%左右。因而,怠速控制问题成为发动机控制技术中的一项最重要最基本的内容。
本文根据发动机怠速控制系统的特点,归纳总结了发动机怠速工况下的各种建模方法和控制方法,在平均值模型的基础上建立发动机怠速工况下的非线性混杂系统模型。考虑到发动机怠速工况下模型的特点,以及在整个控制过程中不可避免地存在输入约束和状态约束的特点,文中采用预测控制策略设计了发动机怠速控制器。首先是根据发动机怠速工况的简化模型,采用二次型目标函数设计了基于预测控制策略的怠速控制器,同时给出了闭环系统的稳定性条件；然后利用∞-范数形式的目标函数,将发动机怠速控制问题转换成了带有约束条件的线性规划(LP)问题,并采用终端等式约束的方法来保证系统的稳定性；最后采用准无限时域非线性预测控制策略设计了非线性怠速控制器,在终端域的基础上引入了终端惩罚项,并通过离线求解一个Lyapunov方程来获得该终端惩罚矩阵,利用有限时域控制令系统进入平衡点附近的不变集(终端域),从而保证了该非线性系统的渐近稳定性。
文中对所提的各种控制算法进行了明确的论证,并对基于不同控制算法的发动机怠速控制器进行了大量的仿真实验,实验结果显示设计的控制器具有较好的控制性能,对不确定干扰具有良好的鲁棒性。
Idle Speed Control (ISC) represents one of the most important and basic automo-tive control problems, it has relation with often-conflicting requirements of improved fuel economy and reduced emissions. On the average, about fuel consumption 30% and emis-sion 70% of CO and HC come from engine idle speed condition, when vehicles run on heavy traffic load road. In general, the engine idle speed should be as low as as possible for improved fuel economy; however, the low vehicle speeds will increase the emission; and meanwhile, the unpredictable load variations coming from the intermittent use of devices powered by engine, such as the air conditioning system and the steering wheel servo-mechanism, result in stalling. So, the idle speed control objective is maintaining the engine speed as close as possible to desired value in order to minimize fuel consumption, reduce the emission, and reject the load.
There inevitably exist input constraints (the spark advance angle is bounded to avoid knock and misfire) and state constraints (avoid manifold pressure rising too much and to limit the control range for safety reasons) in the idle speed mode; meanwhile, engine idle model has nonlinear and hybrid nature of combination of time-domain and event-based behaviors, so we focus on the model predictive control for gasoline engine idle speed control in this paper.
Firstly, a reasonable mathematics model of a SI four-cylinder four-stroke engine idle speed is built in order to effectively control engine idle speed system. Considering the good combustion quality of SI gasoline engine, assume that the air-fuel ratio A is 1, and ignore the modeling of fuel loop. While the air control path can provide large control authority, its disadvantage is that it is relatively slow,due to the intake manifold dynamics and subsequent intake-to-power-related delays. A much faster actuation path is provided through spark control, so the spark advance become another input variable for reducing delay. According to engine idle speed feature, based on the mean value models, present nonlinear hybrid model of engine in which both continuous and discrete time-domain as well as event-based phenomena are modeled in a separate but integrated manner in this paper. The following simulations show that the model is effective.
Secondly, in the case of the ISC, the system variables changes should be relatively small by intention, a simple PWA version of the above nonlinear hybrid model in idle speed mode can be easily obtained by linearizing method. using PWA model, this chapter designs model predictive controller in which the quadratic cost function is minimized in order to obtained an optimal control sequence subject to input and state constraints. The first element of the optimal sequence is applied to system. At next time, the procedure is repeated by new measurement value. Furthermore, we discuss guaranteeing stability conditions of closed-loop system under terminal cost and terminal equality constraint, respectively. We can obtain the terminal weight matrix guaranteeing stability by solving a linear matrix inequality(LMI) transformed from nonlinear matrix inequality. And the controller design problem is discussed in the case of terminal equality constraints.
And then, different norm presents different physical meaning in physic. The quadratic performance index which is used widely in model predictive control means power; and inf-norm describes the maximum amplitude conception, different cost function shows different performance. So, this paper presents the model predictive control strategy based on inf-norm cost function into engine idle speed control. The performance index amounts to the sum of a weighted inf-norm of the input and the state deviation from the origin. Therefore, the engine idle speed control problem comes down to linear programming problem with input and state constraints. We design the controller with terminal equality constraints for guaranteeing stability. Comparing the simulation results, it is found that quadratic MPC cost and MPC cost based on∞-norms have different effect to engine system.
Finally, a quasi-infinite horizon nonlinear model predictive controller is designed for engine idle speed system. For the strong nonlinear engine system, it can not satisfy high performance requirement that linearizing model of engine is applied for controller design. In this chapter, nonlinear control is applied to design a engine idle speed controller. The terminal region and terminal penalty matrix can be calculated off-line so that reducing on-line computational burden and guaranteeing the asymptotic stability of closed-loop system. In order to validate the efficiencies of the proposed approaches, we give simulation results for each approach, which is discussed in detail from modeling, controller parameter choosing, disturbance attenuation testing. The simulation results indicate that the control effects with the proposed approaches are satisfactory.
The formulation processes and the proof of mentioned approaches are presented in detail in this thesis. Moreover, we give simulation results for each approach, which is discussed in detail from modelling, controller parameter choosing, disturbance testing. The simulation results indicate that the control effects with the proposed approaches are satisfactory.
Due to the limit of experiment equipment, we just give the theoretical analysis, numerical and hardware-in-loop simulation results. If the experiments are performed, we believe that more valuable conclusion can be obtained. Deeper research work needs to be done since some problems are still remain to be solved, such as how to reduce the the rank of the output feedback controller, or how to speed up the online calculation etc.
本文根据发动机怠速控制系统的特点,归纳总结了发动机怠速工况下的各种建模方法和控制方法,在平均值模型的基础上建立发动机怠速工况下的非线性混杂系统模型。考虑到发动机怠速工况下模型的特点,以及在整个控制过程中不可避免地存在输入约束和状态约束的特点,文中采用预测控制策略设计了发动机怠速控制器。首先是根据发动机怠速工况的简化模型,采用二次型目标函数设计了基于预测控制策略的怠速控制器,同时给出了闭环系统的稳定性条件；然后利用∞-范数形式的目标函数,将发动机怠速控制问题转换成了带有约束条件的线性规划(LP)问题,并采用终端等式约束的方法来保证系统的稳定性；最后采用准无限时域非线性预测控制策略设计了非线性怠速控制器,在终端域的基础上引入了终端惩罚项,并通过离线求解一个Lyapunov方程来获得该终端惩罚矩阵,利用有限时域控制令系统进入平衡点附近的不变集(终端域),从而保证了该非线性系统的渐近稳定性。
文中对所提的各种控制算法进行了明确的论证,并对基于不同控制算法的发动机怠速控制器进行了大量的仿真实验,实验结果显示设计的控制器具有较好的控制性能,对不确定干扰具有良好的鲁棒性。
Idle Speed Control (ISC) represents one of the most important and basic automo-tive control problems, it has relation with often-conflicting requirements of improved fuel economy and reduced emissions. On the average, about fuel consumption 30% and emis-sion 70% of CO and HC come from engine idle speed condition, when vehicles run on heavy traffic load road. In general, the engine idle speed should be as low as as possible for improved fuel economy; however, the low vehicle speeds will increase the emission; and meanwhile, the unpredictable load variations coming from the intermittent use of devices powered by engine, such as the air conditioning system and the steering wheel servo-mechanism, result in stalling. So, the idle speed control objective is maintaining the engine speed as close as possible to desired value in order to minimize fuel consumption, reduce the emission, and reject the load.
There inevitably exist input constraints (the spark advance angle is bounded to avoid knock and misfire) and state constraints (avoid manifold pressure rising too much and to limit the control range for safety reasons) in the idle speed mode; meanwhile, engine idle model has nonlinear and hybrid nature of combination of time-domain and event-based behaviors, so we focus on the model predictive control for gasoline engine idle speed control in this paper.
Firstly, a reasonable mathematics model of a SI four-cylinder four-stroke engine idle speed is built in order to effectively control engine idle speed system. Considering the good combustion quality of SI gasoline engine, assume that the air-fuel ratio A is 1, and ignore the modeling of fuel loop. While the air control path can provide large control authority, its disadvantage is that it is relatively slow,due to the intake manifold dynamics and subsequent intake-to-power-related delays. A much faster actuation path is provided through spark control, so the spark advance become another input variable for reducing delay. According to engine idle speed feature, based on the mean value models, present nonlinear hybrid model of engine in which both continuous and discrete time-domain as well as event-based phenomena are modeled in a separate but integrated manner in this paper. The following simulations show that the model is effective.
Secondly, in the case of the ISC, the system variables changes should be relatively small by intention, a simple PWA version of the above nonlinear hybrid model in idle speed mode can be easily obtained by linearizing method. using PWA model, this chapter designs model predictive controller in which the quadratic cost function is minimized in order to obtained an optimal control sequence subject to input and state constraints. The first element of the optimal sequence is applied to system. At next time, the procedure is repeated by new measurement value. Furthermore, we discuss guaranteeing stability conditions of closed-loop system under terminal cost and terminal equality constraint, respectively. We can obtain the terminal weight matrix guaranteeing stability by solving a linear matrix inequality(LMI) transformed from nonlinear matrix inequality. And the controller design problem is discussed in the case of terminal equality constraints.
And then, different norm presents different physical meaning in physic. The quadratic performance index which is used widely in model predictive control means power; and inf-norm describes the maximum amplitude conception, different cost function shows different performance. So, this paper presents the model predictive control strategy based on inf-norm cost function into engine idle speed control. The performance index amounts to the sum of a weighted inf-norm of the input and the state deviation from the origin. Therefore, the engine idle speed control problem comes down to linear programming problem with input and state constraints. We design the controller with terminal equality constraints for guaranteeing stability. Comparing the simulation results, it is found that quadratic MPC cost and MPC cost based on∞-norms have different effect to engine system.
Finally, a quasi-infinite horizon nonlinear model predictive controller is designed for engine idle speed system. For the strong nonlinear engine system, it can not satisfy high performance requirement that linearizing model of engine is applied for controller design. In this chapter, nonlinear control is applied to design a engine idle speed controller. The terminal region and terminal penalty matrix can be calculated off-line so that reducing on-line computational burden and guaranteeing the asymptotic stability of closed-loop system. In order to validate the efficiencies of the proposed approaches, we give simulation results for each approach, which is discussed in detail from modeling, controller parameter choosing, disturbance attenuation testing. The simulation results indicate that the control effects with the proposed approaches are satisfactory.
The formulation processes and the proof of mentioned approaches are presented in detail in this thesis. Moreover, we give simulation results for each approach, which is discussed in detail from modelling, controller parameter choosing, disturbance testing. The simulation results indicate that the control effects with the proposed approaches are satisfactory.
Due to the limit of experiment equipment, we just give the theoretical analysis, numerical and hardware-in-loop simulation results. If the experiments are performed, we believe that more valuable conclusion can be obtained. Deeper research work needs to be done since some problems are still remain to be solved, such as how to reduce the the rank of the output feedback controller, or how to speed up the online calculation etc.
引文
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