Based on piecewise quadratic Lyapunov function techniques, this paper first provides a stability condition for the uncertain piecewise discrete-time linear system, which is a feasibility problem of linear matrix inequalities. Then the control methods for uncertain piecewise discrete-time linear systems via state feedback and output feedback controllers are proposed. It is shown that both the state feedback and output feedback controllers can be obtained by solving a set of bilinear matrix inequalities. A numerical example is given to illustrate the effectiveness of the developed methods
Ride comfort is a long-standing research topic and has been deeply investigated due to its great influence on evaluating the performances of railway vehicles. Many standards have been proposed to evaluate the ride comfort of the railway vehicles. However, the carbody hunting instability was rarely considered during the evaluation of ride comfort. To face this problem, this paper performs the comparison of various evaluation methods for ride comfort in the case of carbody hunting instability. The Sperling method, Mean Comfort standard method and Continuous Comfort method are introduced and compared focusing on the specific experimental data. The benefits and limitations of these methods are analyzed and the most appropriate evaluation method for the condition of carbody hunting instability is determined. Moreover, making full use of the peak value information, an original evaluation method of ride comfort specifically to the carbody hunting instability is proposed. The critical parameters of the method are compared and discussed to investigate their influences on the evaluation results.
The coil spring is an important element in the suspension system of railway vehicles, and its structural vibration caused by the mass distribution can deteriorate the dynamic performance of the vehicle. However, the coil spring is usually modelled as a simple linear force element without considering the dynamic characteristics in multibody dynamic simulations of railway vehicles. To integrate the dynamic characteristics of the coil spring into the simulation, three equivalent dynamic models of the coil spring are established by treating the coil spring as multimass spring series, Timoshenko beam, and flexible spring, respectively. The frequency-sweep method is applied to obtain the dynamic response of the proposed models of coil spring, and the accuracy of the models’ results has been compared and verified by the laboratory test. Results show that all of these three equivalent models can reflect the influence of the spring mass distribution on its dynamic responses. Compared with the mass-spring series and beam element equivalent models, the flexible spring model can better reflect the dynamic stiffness and stress of the coil spring changing with the exciting frequency. Thus, the flexible spring model proposed in this paper is more applicable to railway vehicle system dynamics and the fatigue analysis.
e objective of this paper is to establish an accurate nonlinear mathematical model of the hydraulic damper during the orificeworking stage. A new mathematical model including the submodels of the orifices, hydraulic fluids, pressure chambers, and reservoir chambers is established based on theories of the fluid mechanics, hydropneumatics, and mechanics. Subsequently, a force element based on the established model of the hydraulic damper which contains 56 inputs, 6 force states, and 47 outputs is developed with the FORTRAN language in the secondary development environment of the multibody dynamics software SIMPACK. Using the force element, the damping characteristics of the modified yaw damper with different diameters of the base orifice are calculated under different amplitudes and frequencies of the sine excitation, and then the simulation results are compared with the experimental results which are obtained under the same conditions. Results show that during the orificeworking stage, the new established mathematical model can accurately reproduce the nonlinear static and dynamic characteristics of hydraulic dampers such as the force-displacement characteristic, force-velocity characteristic, fluid shortage, hysteresis effect, and pressure limited effect. Furthermore, it also shows that the nonlinear characteristics of the orifice, air release, cavitation, leakage for high frequencies, and dynamic characteristics of fluid (i.e., the density, bulk modulus, and air/gas content) should be taken seriously during the modelling of the hydraulic damper at the orifice-working stage. e mathematical model proposed in this paper is more applicable to the railway vehicle system dynamics and individual system description of the hydraulic damper.
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