Investigation To System Modeling Identifications For Vehicle Lateral Dynamics With Applications

Vehicle lateral dynamics modeling is of importance in the design and analysis of automotive controlability and stability, being related to vehicle active safety technology. Establishment of an accurate modeling for the vehicle is indispensible in evaluation of its dynamics control. The mathematical modeling of the vehicle handling behaviors according to a set of scientific laws would certainly result in incorrect governing equations due to systematic simplifications and lack of the system parameters. By multi-body system dynamics, the multi-degrees- of-freedom model with a refined structure can be built according to real physical and geometrical properties at a price of much computational effort and a lot of field and bench tests for model validation. Thus, data-based system identification which is recognized to be a quick modeling technique may be employed for the purpose of vehicle development cost reduction. With development of system identification theory, the inverse engineering modeling approaches have a significant prospect of engineering applications.The vehicle handling stability modeling is a typical multi-input and multi-output model. The identification algorithm used for the analysis should be suitable to the MIMO system. Among available time-domain methods, the subspace algorithms are known to be a class of identification algorithms for linear state-space multi-variable systems by time-domain data. These algorithms have many advantages of computational robustness, high speed and accuracy because of use of QR factorization and singular value decompositions. Therefore, the subspace algorithms are applied for identification of the vehicle lateral dynamic model.It is confronted frequently in vehicle handling and stability test, however, that the inputs of the steering wheel angle and vehicle speed requirement of persistent excitation is not satified for simutaneously. Therefore, the system identification under incontinuously excitation as partial input is the special case of study. The coupling relationship among the inputs would certainly result in deviated estimates under this condition. For solving such a problem, a subspace algorithm for the model decoupling is adopted. This subspace algorithm is featured to decouple into deterministic and stochastic parts of inputs. As a result, interference between the stochastic subsystem and the deterministic subsystem may be reduced in order to improve the model precision of the deterministic subsystem.Two SISO model identification approaches are proposed according to the theoretical analysis of the vehicle handling and stability models of 10 orders for the system. A cross-validation approach is presented for validation of the identified result and the identification algorithm. In the case that the vehicle drives at low speed, results of steering return-ability test are used for vehicle model system identification, which is validated by a slalom test at similar speed. It is shown that single-input identification model of the vehicle at constant speed has a fairly good accuracy in the system model identification and the present algorithm is reliable and applicable. In the case that the vehicle drives at high speed, a numerical model which is identified according to testing data in a left-turning steering wheel pulse input test is verified by a right-turning steering wheel pulse input test. Among the two model structures, S1 and S2, the former is the linear model and well suitable for identification of the vehicle model at constant speed in test, and the later is nonlinear on and well appropriate to the vehicle model identification at constant steering wheel angle for accurate yaw rate.All constant speed vehicle performance tests according to National Standards are made to identify a set of vehicle models at variable speeds for examination of inherent properties of the test car at high speed by the present algorithm and the valid model. From these identified models, steady gain curves of three outputs are plotted. According to the steady gain of yaw rate, a new approach is also proposed to estimate understeering behaviors, based on Levenberg-Marquardt approach. The estimation results obtained for the vehicle at low speed is in fair agreement with experiments in the steady circle test. This present method may be generalized to cover the range of application for the vehicle understeer analysis from low speed to high speed. A progress has been made in speed limitation of the vehicle in steady circular test. It is demonstrated by the 3 simulation results that existence of residuals of the yaw rate gain generated by the estimation of understeer indicates difference in steering ratio is between design and real overall steering ratios. Thus, the approach for overall steering ratio estimation is validated based on national standard tests. It is found further that the resonant frequency of lateral acceleration is higher than that of yaw rate at same speed in the analysis of resonant frequencies.In fact, however, the vehicle system is such a system with multi-inputs that the multi-input system identification is required in development of the vehicle system identification modeling. Since there exist nonlinearities of the vehicle system, it is difficult for the vehicle model to apply directly the multi-input system identification algorithm. It follows from the linear model identified for the vehicle at constant speed that there exists an approximate linear relationship between the model simulation and experimental results. A new nonlinear model for the multi-input system incorporation with a Wiener structure may be underset by the relationship. The nonlinear model is composed of a linear dynamic model and a nonlinear static function. The steering wheel angle is an input for the linear identification model and the vehicle speed is a parametric vriable of the nonlinear function. Accordingly the 2-stage modeling approach is applied in real situation to construct the vehicle model. By detailed analysis it is shown that the linear model identified from high speed tests is of higher accuracy than other the identification models. Then, the final system model of the vehicle is comprised of a linear model identified from a steering wheel angle pulse input test and a nonlinear function. A random input test is carried for validation the final identification model. By the comparisons between experimental and numerical results it is indicated that the nonlinear identification model may produce computational predictions accurate enough to meet engineering requirements.