某轿车动力装置参数的匹配设计英文翻译毕业论文.doc

某轿车动力装置参数的匹配设计英文翻译毕业论文AbstractThe availability of pressure information of a hydraulic actuator makes it possible to improve the quality of vehicle power transmission via precise feedback control and to realize on-board fault diagnosis. However, the high cost of a pressure sensor has not allowed its widespread deployment despite such apparent advantages. This paper presents an observer-based algorithm to estimate the pressure output of a hydraulic actuator in a vehicle power transmission control system. The proposed algorithm builds on more readily available slip velocity and the models of a hydraulic actuator and a mechanical subsystem. The former is obtained empirically via system identification due to the complexity of the hydraulic actuator, while the latter is derived physically. The resulting robust observer is guaranteed to be stable against possible parametric variations and torque estimation errors. The hardware in-the-loop studies demonstrate the viability of the proposed algorithm in the field of advanced vehicle power transmission control and fault diagnosis. C 2002 Elsevier Science Ltd. All rights reserved. Received 1 March2001; accepted 27 August 2001Keywords: Robust observer; System identification; Hydraulic actuator; Vehicle power transmission control system; Hardware-in-the-loop simulation1.IntroductionAutomatic and continuously variable transmission systems have been expanding their presence in passenger vehicles in recent years,which has naturally prompted active research on vehicle power transmission control systems. The main topics include shift control algorithm (Shin, Hahn, Yi, & Lee, 2000a; Zheng, Srinivasan, & Rizzoni, 1999; Shin, Hahn, & Lee, 2000b), feedback control of torque converter clutch slip systems (Jauch, 1999; Hibino, Osawa, Yamada, Kono, & Tanaka, 1996; Hahn & Lee, 2000), new hydraulic circuits for control performance enhancement (Jung, Cho, & Lee, 2000), etc. Despite the extensive research effort on control algorithms, it appears that the pressure information of a hydraulic actuator has not been fully utilized in vehicle power transmission control, largely due to the high cost of a pressure sensor. As a result, most practical controllers have been largely built upon the mechanical subsystem only, while neglecting the dynamics of a hydraulic actuator.Instead of directly measuring the pressure output of a hydraulic actuator, this paper proposes an indirect alternative to estimate the pressure output: an observer- based approach. The main thrust of this paper is that the pressure output of a hydraulic actuator is observable with the slip velocity measurement of the mechanical subsystem in a vehicle power transmission control system. In addition to the readily available slip velocity measurement, the observer design requires the models of hydraulic and mechanical subsystems whose accuracy directly impacts the observer performance. The mechanical subsystem is physically modeled with relative ease. The complexity of the hydraulic actuator dynamics does not allow a physical model amenable to observer design. Instead, system identification yields a simplified empirical model of the hydraulic actuator. Actual observer design focuses on guaranteeing robust stability against parametric variations and torque estimation errors that are bound to occur in a mechanical power transmission control system. Hardware- in-the-loop simulation studies are conducted to examine the performance of the robust observer-based estimator for the hydraulic actuator pressure, which shows the viability of the proposed approach. The outcome is a robust pressure estimator that relies on the readily available slip velocity measurement only and thus has a potential to be widely employed in vehicle power transmission control and fault diagnosis.This paper is organized as follows. Section 2 derives a physical model for the mechanical subsystem. Simplified empirical models are developed for a hydraulic actuator in Section 3. Section 4 deals with the observer design. The performance of the designed observer is examined in Section 5.2. Overview of a vehicle power transmission control systemA vehicle power transmission control system typically consists of two subsystems, a mechanical subsystem and a hydraulic actuator. The input and output of the system under consideration are the voltage signal to the hydraulic actuator and the slip velocity between the friction elements in the mechanical subsystem, respectively. The hydraulic actuator drives the friction elements and generates the slip velocity of the mechanical subsystem according to its pressure output. Fig. 1 shows a vehicle power transmission control system considered in this paper, a torque converter clutch slip control system. The mechanical subsystem consists of an engine, a torque converter, an automatic transmission with planetary gear sets, and wheels with a final reduction gear. The torque converter clutch generates friction torque acting upon the engine according to the hydraulic actuator pressure, which in turn determines the slip velocity between the engine and the turbine of the torque converter at a desired target value.In order to derive a physical model of the mechanical subsystem, the power transmission at each stage is examined. At the very first stage, the engine torque is transmitted to the impeller and is balanced by the reaction torque of the impeller and the friction torque from the torque converter clutch. The torque converter amplifies and transmits the impeller torque to the turbine. The turbine torque drives the automatic transmission system together with the friction torque of the torque converter clutch, while the driving load torque of the vehicle provides additional resistive force. Denoting the slip velocity between the engine and the turbine as the output of interest (y) results in Hahn & Lee (2000)where Ie is the equivalent rotational inertia of the engine, Iv the equivalent rotational inertia of the vehicle, We the angular velocity of the engine, Wt the angular velocity the turbine, Te the engine torque, Tp the impeller torque, Tt the turbine torque, Tc the friction torque of the torque converter clutch, Tl the driving load torque, c the equivalent damping constant of the torque converter clutch, rt the gear ratio of the automatic transmission, rf the gear ratio of the final reduction, m the friction coefficient of the torque converter clutch, Ro the outer radius of the torque converter clutch, Ri the inner radius of the torque converter clut chand Pc the pressure output of the hydraulic actuator, It is worth noting that the quantities inEq. (1) are subject to errors; the damping constant is not exactly known; absence of torque sensors in a commercial vehicle entails torque estimation errors; the equivalent rotational inertia of the vehicle varies as the number of passengers changes, and only a rough bound on the friction coefficient is available.3. Identification of a hydraulic actuator3.1. Motivation for empirical modelingFig. 2 shows the hydraulic actuator considered in this paper. It basically consists of three elements: a PWM type solenoid valve, a pressure modulator valve and a pressure control valve. The first and second regulating valves, not shown in Fig.2, regulates the main pressure of the entire hydraulic circuit. The pressure modulator valve further decreases the output pressure of the first regulating valve (channel #7) to a lower pressure level.The output pressure of the pressure modulator valve at channel #9 is always regulated around 4.0 bar in the steady-state by means of the feedback chamber #10 (Hahn, 1999). The voltage signal from the transmission control unit (TCU) drives the PWM-type solenoid valve so that the pressure at channel #11 assumes values between 0 bar and 4 bar. The pressure at channel #11 acts on the spool of the pressure control valve, which in turn generates engage/disengage pressures for the friction element in the mechanical subsystem. Since the engage/disengage pressures are applied to the same friction element from the opposite sides, the difference between engage and disengage pressures may be regarded as the output of the hydraulic actuator. A nonlinear mathematical model of the hydraulic actuator has been obtained in Hahn (1999) using the Newtons second law of motion. Although the nonlinear model in Hahn (1999) matches the experimental results to a certain extent, it has some drawbacks when applied to the observer design problem considered in this paper:1. The model order is too high (E10).2. The governing differential equations are too stiff to numerically solve in real-time.3. There exist numerous unknown parameters that need to be estimated or tuned in order to obtain reasonable match between experimental results and model predictions.A possible alternative is to capture the dynamics essential to the design of a nonlinear observer and to obtain a lower-order control-oriented empirical model. In this paper, two empirical models are proposed based on the system identification (Ljung, 1999).1. Nonlinear.2. Mostly smooth, although its behavior is qualitatively different at a couple of points, i.e. nearly discontinuous.3. Not one-to-one when the duty cycle is around 60%. 4. Not even symmetric with respect to origin; 60% duty cycle approximately corresponds to 0 bar pressure output.These observations raise an immediate concern that the brute-force application of system identification (Ljung, 1999) may utterly fail to give a high-fidelity model if a conventional model structure, e.g., ARX (auto-regressive with exogenou s input) is adopted. In the steady-state, an ARX model approximates the nonlinear mapping in Fig. 3 by a straight line passing through the origin, by virtue of its linearity. A better approach would be to shift the origin to a point around which the inputoutput mapping is approximately symmetric. The new origin becomes 60% duty cycle and 0 bar pressure output. Such a shift of the origin amounts to subtracting the input duty cycle by 60%. The relatively high signal-to-noise ratio leads to the choice of the ARX model structure as a model set, due primarily to its simplicity:where uoffset is the aforementioned offset value for input data and na=nb are the orders of the model, which are determined later. Then, the step response of the hydraulic actuator is obtained in order to help to design the identification input. The natural frequency (in an approximate sense) turns out to be around 5 Hz. A safety factor of 2results in the excitation frequency band of 10 Hz. 50 sinusoids with various combinations of amplitudes and phases are generated within the 10Hz band. The length of data is chosen to be 1024 considering the frequency content of the model to be identified, and the sample rate of 100 Hz is used, which corresponds to the sampling rate of TCU in commercial vehicles. MATLAB System Identification Toolbox (Ljung, 1995) is used to process the data and to obtain an ARX model.The orders of the ARX model are initially set to be equal to those of the nonlinear model developed in Hahn (1999): na=nb=10.The resulting tenth-order model has mean square prediction residual of 0.2376, which appears to be sufficiently small for observer design application considering that the pressure of the hydraulic actuator usually fluctuates about 0.2 bar (refer to Fig. 5). However, the relatively high order of the ARX model does not render itself amenable to efficient design of a nonlinear observer. In order to reduce the model order without compromising the fidelity to a great extent, the identified ARX model is transformed into a balanced realization, where most controllable and observable states may be determined for model reduction (Skogestard & Postlethwaite, 1996). Based on Hankel singular values, the tenth-order model is reduced to a second-order model. Fig. 4 shows the comparison of the two identified ARX models in the frequency domain. The two models exhibit quite similar frequency responses up to 6 Hz. It is worth pointing out that the 6Hz natural frequency of the identified model in Fig. 4 justifies the use of the excitation signal with 10 Hz frequency bandAs discussed earlier in this section, the steady-state characteristic of the identified model bears particular importance. Fig. 5 shows the comparison of the measured and predicted (based on the identified model) steady-state responses. Since the response of a linear system with respect to the input amplitude is nothing but a straight line passing through the origin, the steady state response of the identified model seems to deliver the desired characteristics, that is, the difference between the experimental steady-state response and the straight line (predicted by the identified model) seems to remain relatively small through the range of the duty ratio over which the hydraulic actuator operates. Note that the best brute-force application of ARX model incurs much larger deviations from the experimental response.Although the identified ARX model shows satisfactory prediction residual for the test signal and reasonable steady-state response, it may incur relatively large prediction errors in the steady-state, around 75% and 90% duty ratio. The steady-state response can be improved by approximating the nonlinear steady-state behavior of the hydraulic actuator by an input dependent memory-less nonlinear gain:where () is a polynomial function of the duty cycle. The identification procedure with the model structure (3) results in a second-order model of the hydraulic actuator with mean square prediction residual of 0.1308. The steady-state response of the identified model with the model structure (3) is shown in Fig. 5, which matches the actual response much better over the range of hydraulic actuator operation.In order to further validate the identified models, the Predictions with the second-order identified models are compared with the experimental data (not used in identification). Fig. 6 shows excellent agreements between the predictions and measurements, which reassures that the identified models represent the hydraulic actuator dynamics with high fidelity. The model structure (3) is shown in Fig. 5, which matches the actual response much better over the range of hydraulic actuator operation.In order to further validate the identified models, the predictions with the second-order identified models are compared with the experimental data (not used in identification). Fig. 6 shows excellent agreements between the predictions and measurements, which reassures that the identified models represent the hydraulic actuator dynamics with high fidelity.Equipped with lower-order models of the hydraulic actuator, we proceed to design a state observer for the entire system (mechanical subsystem +hydraulic actuator), which is the topic of the following section. The problem of designing an observer for the combined system turns out to reside in the framework of the linear system theory (Chen, 1984). It should be noted that the nonlinear mathematical model in Hahn (1999) cannot provide such simplification.4. Observer design4.1. Overall system model for observer designThe mechanical subsystem model (1) and the hydraulic actuator model (2) and (3)yield a third model of the entire vehicle power transmission control system. Since the mechanical subsystem generates continuous output measurements, i.e. slip velocity, the observer design for the overall system takes place in the continuous-time domain. The identified hydraulic actuator model is converted into a continuous-time domain transfer function via the bilinear transform (Franklin, Powell, & Workman, 1998):The hydraulic actuator model (4) refers to both the model (2) and the model (3) for simplicity, since the observer design procedure for the two identified actuator models are nearly identical. When the actuator transfer function (4) refers to (3), V(s)= U(s) is implicitly assumed, where V(s) is Laplace transformation of v defined in (3). Denoting the state variables of the hydraulic actuator as x2 and x3 gives an observer canonical form (Chen, 1984): With x1 = y; (1) becomesCombining (5) and (6) results in the following state equation of the overall system:As previously pointed out, there are uncertain terms in damping constant? ,nonlinear portion of the mechanical subsystem dynamics due to torque estimation errors, and input gain related to the friction coefficient uncertainty. It is worth noting that the uncertainties of the hydraulic actuator are not explicitly considered in this paper, since the identified models reproduce the experimental data with reasonable accuracy. In this framework, the estimation accuracy of the resulting observer may be dominated by the fidelity of the identified hydraulic actuator models. In fact, such fact ors as viscosity change due to temperature variation may affect the coefficients of the identified model. However, the uncertainties of the hydraulic actuator model appear to be relatively insignificant, in comparison to the uncertainty caused by the mechanical subsystem which are explicitly taken into account in this paper.Separating the uncertain system dynamics from the nominal system dynamics yields WhereA B and F represent the nominal system dynamics, while W(x,u) denotes the uncertain mechanical subsystem dynamics that depends on both state and input. Note that the uncertain system dynamics are present only in the first row that corresponds to the system output.4.2. Robust observer designIn this paper, the utmost goal of the observer design is to guarantee robust performance against the uncertain dynamics W(x,u).As stated earlier, W(x,u) arises from three qualitatively different sources. Damping constant and friction coefficient are inherently