Research PaperLuenberger-sliding mode observer based fuzzy double loop integral sliding mode controller for electronic throttle valve
Introduction
With the rapid development of automotive industry, studies on vehicle active safe control have attracted much attention in the research community. As the core part of vehicle active safe control, electronic throttle (ET) control plays an important role in vehicle speed control and modern traffic flow control due to the vehicle speed is the function of throttle opening angle [1], [2]. In addition, from the perspective of traditional vehicle technology, ET is essentially a DC motor-driven valve that regulates air inflow into the vehicle’s combustion system. By using electronic throttle, the engine control unit can correct the throttle position reference value for specific engine operating modes, thus improving drivability, fuel economy, and emissions [3], [4]. While from the autonomous vehicle’s point of view, under intelligent transportation systems (ITS), V2V communications plays an important role in the coordination between individual vehicles as well as between the vehicles and the roadside infrastructure. For example, to avoid collisions in vehicular traffic flow, a wide variety of information is desirable from preceding vehicles and roadside equipment by leveraging V2V communications. In this context, the V2V-based communication of information on the opening angle of the electronic throttle (ET) of the preceding vehicles in a lane enables a following vehicle in that platoon to react autonomously to avoid a collision by adjusting adaptively its ET. This is because the electronic throttle control (ETC) is the core of the vehicle control and past studies illustrate that the vehicle speed is related to the opening angle of the ET.
Moreover, with respect to the response time of the controller, studies [5], [6], [7] on vehicle platoon control suggest that it is desirable for all vehicles in the platoon to move with a safe space headway and a safe speed from a stability perspective. However, under a stimulus such as an accident just in front of a platoon, the lead vehicle in the platoon must brake immediately as an emergency response maneuver to avoid the accident. The following vehicles in the platoon will then respond accordingly. In addition, some other studies also concluded that the throttle control plays a significant role in platoon control. Montanaro et al. [8] proposed a novel approach, named as extended cooperative adaptive cruise control (CACC), to control a platoon of vehicles. Especially, this control strategy exploits the possibility to use more generic network topologies with respect to the classical predecessor-following architecture used for CACC strategies. Moreover, the network protocol takes into account heterogeneous and time varying delays for each communication link as well as heterogeneous time headway for the spacing policy. Finally, a Hardware In the Loop (HIL) system is used to experimental validation. Subsequently, Montanaro et al. [9] applied vehicle-to-vehicle (V2V) wireless technology to address the problem of proving stability for Cooperative Adaptive Cruise Control, where the proof of exponential stability is provided in the presence of time-varying delays and communication structures beyond the classical predecessor-follower architecture. More importantly, based on Ref. [9], Montanaro et al. [10] analyzed the closed-loop performance of the extended CACC algorithm through considering the effects of the throttle and braking system. Numerical results show the effectiveness of the extended CACC strategy and its robustness to communication delays, failures and sudden changing in the communication topology, uncertain and unmodeled vehicles dynamics. Hence, a quick response time is desirable for the ET controller to enhance platoon stability. Therefore, this study focuses on developing a more accurate and responsive ET controller.
Considering there exist many nonlinear uncertainties such as stick-slip friction, nonlinear spring and gear backlash, etc. [2], [11] in the electronic throttle, the problem of controlling electronic throttle valve is regarded as one of the most challenging topics in the automotive industry field. During the past decades, there have been a surge of studies into the control of electronic throttle system owing to the wide-ranging applications of such systems [2], [3], [4], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], and abundant constructive approaches are extensively reported in the literatures [11], [14], including adaptive control [3], [4], [15], [16], [17], [18], nonlinear control [19], [20], [21], optimal control techniques [11], [22], [23], intelligent control [14], [24], [25], [26], [27], and so on. From the viewpoint of adaptive control, Deur et al. [3], [4] investigated the optimized PID controller for ET, where the feedback compensator was used to compensate the effects of nonlinear limp-home and friction. And then the PID parameters were optimized with respect to the damping optimum criterion. However, it is difficult to choose reasonable compensator parameters to guarantee stability. Bernardo et al. [15] presented the linear quadratic new extended minimal control synthesis with integral action (LQ-NEMCSI) to control the ET, which mainly depends on minimal knowledge of the plant and can be implemented easily without requiring time consuming experiments for the precise characterization of the system nonlinear dynamics. In addition, the robustness is guaranteed based on the adaptive gains of the LQ-NEMCSI strategy. Finally, the tracking performance is verified through the experimental based on a Dspace control station. Subsequently, Bernardo et al. [16] put forward the Minimal Control Synthesis (MCS) algorithm based discrete-time model reference adaptive strategy for ET. Then the stability proof for the algorithm is conducted. Experimental results show that the proposed approach can guarantee the robustness to unmodeled nonlinear dynamics over a range of test maneuvers. Additionally, Montanaro et al. [17] put forward a novel discrete time model reference adaptive control (MRAC) method to deal with the nonlinear and discontinuous dynamics of ET. In particular, the minimal control synthesis algorithms for discrete-time system is extended through adding an explicit discrete-time adaptive integral action and an adaptive robust term. Finally, the experimental investigation is carried out on an ET device mounted on a 2-L gasoline engine. Furthermore, based on previous work [15], [16], Gaeta et al. [18] carried out an adaptive control algorithm based robust model reference strategy to control ET, the experimental results guarantee the effectiveness of the method to deal with unmodeled nonlinear terms and unknown parameters. Compared with classical model-based control approaches, the proposed method shows a better control performance. On the contrary, Hu et al. [19], [20] proposed the nonlinear Backstepping based method for ET. But this method requires exact information of the controlled object, and it is difficult to realize in practice. Lately, Bai et al. [21] carried out an adaptive Backstepping sliding mode controller for electronic throttle, which combined the Backstepping with sliding mode control to acquire good performance. However, the unmeasurable character of ET state, which has a great significant effect on controller design, is ignored.
While from the optimal control techniques perspective, Vašak et al. [22] presented the constrained finite-time optimal control method, which addressed the gearbox friction and limp-home nonlinearity by solving a constrained optimal control problem formulated for the discrete-time piecewise affine model of the throttle. The drawback of this approach is that it relies excessively on the model. Hence it will lead to significant performance deterioration if the model accuracy declines. To address this issue, Vašak et al. [11] proposed a model predictive control based time-optimal control strategy to improve the controller performance. Kim et al. [23] proposed a dynamic programming based optimal controller for the ET valve. However, it can not provide enough power since the maps lack a self-learning capability.
On the basis of intelligent control, Yuan et al. [24], [25] presented the neural-network approaches, where the neural-network was used to ET control and parameters identification. Nevertheless, the back propagation (BP) algorithm used in the neural network can deteriorate the performance of the controller. Recently, Wang et al. [14] investigated an intelligent fuzzy controller with feed-forward closed-loop configuration to deal with the nonlinear hysteretic behavior of electronic throttle, meanwhile, the new closed-loop back-propagation tuning was also proposed for tuning of the fuzzy output membership function to get better tracking performance. Unfortunately, the fuzzy rule about the feed-forward controller is designed too simple to elaborate the condition of the nonlinear hysteresis (NH). Subsequently, Sheng et al. [26] proposed a fractional order fuzzy-PID controller for ET, and the fruit fly optimization algorithm (FOA) was used to search for the optimal values of the controller parameters. Yet, the gear backlash torque is ignored in this control strategy, which plays an important role in the controller design. Moreover, Yadav et al. [27] put the ET control into the uncertain hybrid electric vehicle (HEV) speed control, where a self-tuning fuzzy PID controller and model reference adaptive systems (MRAS) with sliding mode adaptation mechanisms were developed to achieve the robust performance of the ET controlled HEV. However, the use of the sign function in the sliding mode control (SMC) brings about high-frequency chattering which deteriorate the control performance of ET controller.
In response to the above-mentioned practical issues-accuracy and response time of the ET controller and also to increase the transient control performance. Aiming at the shortcoming of literature [21], we proposed a Luenberger-sliding mode observer based fuzzy double loop integral sliding mode controller for electronic throttle valve to achieve both precise ET control performance and compensate the system uncertainties. Specifically, we first use input shaping to filter the reference tracking of the valve plate angle. Then we introduce a Luenberger-sliding mode observer to estimate the angular velocity of ET valve plate since angular velocity is unmeasurable in practice. After that, the fuzzy double loop integral sliding mode strategy, including internal loop and external loop control law, is proposed to further improve the performance of the ETC, where the fuzzy logical system is employed to approximate the unknown behavior of the total uncertainties. To the best of our knowledge, the novelty of this study is to consider both the throttle opening angle errors and throttle angle velocity errors as feedback. Accordingly, in our double closed loop controller, the inner loop controller is designed based on throttle angle velocity errors and the outer loop is put forward based on the throttle opening angle errors. Therefore, the controller can track the throttle opening angle and opening angle velocity simultaneously to enhance the precision of the presented ET controller. Additionally, the convergence and control performance are proven by Lyapunov techniques and Barbalat’s Lemmas. At last, some simulations are performed in the environment of Matlab/Simulink, of which the results indicate that the new control method can achieve superior performance for ET.
The remainder of our paper is outlined in the following fashion. Section 2, describes the mathematical model of the electronic throttle valve system including friction, nonlinear spring, and gear backlash model. Subsequently, the observer based fuzzy double loop integral sliding mode controller is directly derived based on fuzzy control system and sliding mode control in Section 3. In Section 4, several simulations illustrate the performance of the proposed nonlinear controller for ET. Finally, the paper is wrapped up with some concluding remarks in Section 5.
Section snippets
The mathematic model of electronic throttle valve
Fig. 1 shows a schematic of the electronic throttle control system, including an accelerator pedal, an electronic throttle body and an electronic control unit (ECU). The electronic throttle body consists of a dc motor, a reduction gear set, a valve plate, a position sensor and a return spring.
The dynamical character of the throttle is described with the following equations [11]:where u and ia represent the input control
Fuzzy double loop integral sliding model controller design
Fig. 5 illustrates the control strategy of the electronic throttle valve. Firstly, an input shaping, which can eliminate the impact of signal mutation, is designed to filter the desired input signal. Secondly, the electronic throttle valve controller is designed based on double integral sliding mode approach and Lyapunov stability theory. As shown in Fig. 5, is the estimation of the unmeasurable electronic throttle angular velocity. is the estimation of total uncertainties of
Simulations
This section shows the simulations of the proposed control strategy for the electronic throttle. And Table 1 shows the nominal values of parameters of the electronic throttle mathematical model.
For fuzzy control system and input shaping, the parameters are chosen as follows: γ = 0.05, θD(0) = 0.1, kg = p0 = 25,600, and p1 = 320. In addition, the parameters of internal loop and external loop control law are given as: c1 = 1, η1 = 2.5, k1 = 1200, c2 = 0.5 and η2 = 25.
For , we select the following five membership
Conclusions
This paper has presented an explicit Luenberger-sliding mode observer based fuzzy double loop integral sliding mode control development approach for the electronic throttle, which overcomes the drawbacks associated with Ref. [21]. The proposed approach enhances the external disturbance and gear backlash torque compensation and leads to an improvement of control performance. In particular, we first design Input shaping to reduce the noise effect of the input tracking signal. Then, the
Acknowledgment
This work is jointly supported by the INHA UNIVERSITY Research Grant.
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