Optimal Velocity Function Research Articles

2P1-B35 クーロン摩擦をもつ位置制御系の散逸エネルギーを最小にする最適な速度関数と減速比

This paper discusses an optimal velocity function and an optimal reduction gear ratio which minimize the dissipated energy in a mechanical servo system. Coulomb friction of gears is represented by the efficiency and proposed to be proportional to the absolute value of the output torque of a motor with Coulomb friction. The optimal current and velocity functions can be obtained from an optimal control theory by introducing a zero cross time t_c, when the output torque of a motor is changed from positive to negative. As the dissipated energy can be expressed by a function of t_c, an optimal cross time t_c* minimizing the energy can be represented by a simple function of efficiency of the gears. An optimal number of stages of gear trains is determined from the minimized energy which is a function of the reduction ratio. The theory minimizing the energy is verified by experiments using planetary gear trains driven with a DC motor.

Minimization of Dissipated Energy in Position Control System Considering the Friction of Gears

This paper discusses on optimal current and velocity functions which minimize the dissipated energy of a servo system with a reduction gear train. Coulomb friction of the gears is represented by the efficiency of the gears and assumed to be proportional to the absolute value of the current of a motor. The optimal functions can be obtained from an optimal control theory by introducing a zero cross time tc, when the current is changed from positive to negative. As the dissipated energy can be given as a function of tc, the optimal zero cross time tc* minimizing the energy can be represented by a simple function of the efficiency of the gears. This method is expanded into the case including the viscous friction in addition to the Coulomb friction. The influence of the viscous frictional coefficient upon the optimal zero cross time tc* is examined by simulations. The expression of the Coulomb and the viscous frictions is verified by experiments using planetary gears with a DC motor.

THE EFFECT OF DELAY TIMES ON THE OPTIMAL VELOCITY TRAFFIC FLOW BEHAVIOR

We have numerically investigated the effect of the delay times τf and τs of a mixture of fast and slow vehicles on the fundamental diagram (the current-density relation) of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time τs, the current profile displays qualitatively five different forms, depending on τf, τs and the fractions df and ds of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τs. Furthermore, there exist a critical value of τf above which the metastability and hysteresis appear. The spatial-temporal traffic patterns near the congested-jamming first-order transition is also presented.

Phase diagram in multi-phase traffic model

A multi-phase traffic model is presented to take into account the complex motion of vehicles. The multi-phase model is one of the extended optimal velocity model. The optimal velocity (OV) function is modified to have multi turning points. The original OV model with a single turning point exhibits two-phase traffic, while the model with n ( n ⩾ 2 ) turning points displays n + 1 phase traffic. The multiple phase transitions occur by varying the density. The phase transitions depend highly on the sensitivity (the inverse of delay time). The neutral stability line is obtained by using the linear stability analysis and is consistent with the jamming transition points. The phase diagrams are presented for the multiple jamming transitions.

Numerical bifurcation analysis of a ‘car‐following’ model

AbstractWe study a system of ordinary differential equations describing a car‐following model for the motion of N car around a circular highway. All cars behave in the same way. The acceleration of each car is determined as a function of the headway (optimal velocity function). This model is known to have a solution with constant velocities and headways which, in a certain parameter regime, is stable and, varying the density of the cars, the loss of stability is generally due to a super‐ or subcritical Hopf bifurcation. Guided by analytical results, we numerically investigate the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of the model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Many-neighbour interaction and non-locality in traffic models

The optimal-velocity model, as proposed by Bando et al. [1], shows unrealistic values of the acceleration for various optimal-velocity functions [2,3]. We discuss different approaches of how to correct this problem. Multiple look-ahead (many-neighbour interaction) models are the most promising candidates in reducing accelerations and decelerations to realistic values. We focus on two such models and, in particular, their linear stability and how these affect the vehicle dynamics and wave solutions. As found earlier [4], multiple look-ahead models reproduce many real flow features, and our results further support the necessity of this ansatz. However, the problem of non-locality arises when they are transformed into the corresponding continuum model. We discuss three methods of how to interpret many-neighbour interaction in macroscopic models.

One-Dimensional Traffic Flow by Compressible Flow Model Including Several Types of Optimal Velocity Functions

In this paper, we considered a model which describes the one-dimensional traffic flow observed in a highway. Optimal velocity model which has been introduced in the microscopic model was applied to the macroscopic compressible fluid equations. Numerical simulations were performed by applying the finite difference method to this model. Effect of sensitivity which depend on the stability of asymptotic numerical solutions is discussed. Furthermore, we adopted several types of optimal velocity functions, the well-known optimal velocity function proposed by Bando et al., the linear one and the non-smooth one. Different non-trivial asymptotic structure of clusters of congestion are observed between the cases using two types of optimal velocity functions except the linear one.

GENERALIZED OPTIMAL VELOCITY MODEL FOR TRAFFIC FLOW

A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by considering a small perturbation around the homogeneous flow solution. The effect of the generalized optimal velocity function is also confirmed with numerical simulations, by examining the hysteresis loop in the headway-velocity phase space, and the relation between the flow and density of cars. In the model with a specific parameter choice, it is found that an intermediate state appears for the movement of cars, where the car keeps a certain velocity whether the headway is short or long. This phenomenon is different from the ordinary stop-and-go state.

Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow

We analyse the Newell-Whitham-type car-following model described by a differential-difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one. Linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car. From the nonlinear analysis, the propagating kink solution for traffic jams is obtained. The fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation. We find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation.

Effect of looking at the car that follows in an optimal velocity model of traffic flow

An extension of an optimal velocity model is proposed. In the new model, a driver looks at the following car as well as the preceding car. We introduce an additional optimal velocity function that depends on the headway of the following car. We investigate the effect of looking back at the car that follows and show that this extension effectively stabilizes the traffic flow.

Congested Flow Induced by Noise in Headway Measurements

The coupled map traffic flow model based on optimal velocity functions, which is one of car-following models, enables us to introduce various types of noise. We introduce a noise term in a headway measurement process. Qualitative effects of noise are the same as those in the case with noise in a velocity update process. Because the noise in the current case is imposed to the headway measurement, the effect of the noise directly appears as vibrations with high frequencies in time-sequences. The average density increases with the noise. This behavior comes from the shape of the optimal velocity function.

Multiple jamming transitions in traffic flow

The effect of accelerating stepwise on the jamming transition is investigated in the extended car-following model. The optimal velocity function is modified to take into account accelerating stepwise vehicles. It is shown that the multiple phase transitions occur on varying the car density. The multiple transitions change with the delay time. The flow-density curves and the velocity-headway curves are presented for various delay times. It is also shown that the multiple jamming transition lines are consistent with the neutral stability curves. The jamming transitions are closely related with the turning points of the optimal velocity function.

Three-component OBS-data processing for lithology and fluid prediction in the mid-Norway margin, NE Atlantic

In 1992, acomprehensive three-component ocean bottom seismic survey was performed in the central and northern area of the Voring Basin, offshore mid-Norway, NE Atlantic. An important part of the data acquisition program consisted of a local survey with 20 Ocean Bottom Seismographs (OBS) dropped at approximately 200 m interval in 1300 m water depth. The main purpose of the local survey was to acquire densely sampled P- and S-wave reflection data above a seismic flatspot anomaly observed earlier, in order to more accurately predict if hydrocarbons could be related to it. The conventional reflection data processing methods applied to the vertical components included predictive deconvolution in order to attenuate low frequency ringing, near offset mute and a series of constant velocity stacks in order to obtain the optimal velocity function. The final result is a “trouser” shaped, high resolution VZ stacked section with minor influence of water multiples. The inline (Vx ) component contains no strong multiples, and extensive near trace muting was hence not necessary to apply for this component. Velocity analysis together with ray-tracing modelling indicate that P-S-converted shear waves (reflections) represent the dominant mode. The results of the interpretation and modelling indicated a Vp/Vs-ratio of approximately 2.6 in the overburden, which suggests domination of partly unconsolidated shale, while the Vp/Vs-ratio in the assumed reservoir was approximately 1.8, which indicates a more sand dominated facies. Outside the flatspot area a higher Vp/Vs-ratio ratio (approximately 2.0) was estimated, indicating that hydrocarbons could be present in the assumed reservoir.

Multibunch solutions of the differential-difference equation for traffic flow

The Newell-Whitham type of car-following model, with a hyperbolic tangent as the optimal velocity function, has a finite number of exact steady traveling wave solutions that can be expressed in terms of elliptic theta functions. Each such solution describes a density wave with a definite number of car bunches on a circuit. In our numerical simulations, we observe a transition process from uniform flow to congested flow described by a one-bunch analytic solution, which appears to be an attractor of the system. In this process, the system exhibits a series of transitions through which it comes to assume configurations closely approximating multibunch solutions with successively fewer bunches.

Coupled map car-following model and its delayed-feedback control.

This paper proposes a coupled map car-following traffic model, which describes a dynamical behavior of a group of road vehicles running in a single lane without overtaking. This model consists of a lead vehicle and following vehicles, which have a piecewise linear optimal velocity function. When the lead-vehicle speed is varied, we can observe a traffic jam in the group of the vehicles. We derive a condition under which the traffic jam never occurs in our model. Furthermore, in order to suppress the traffic jam, for each vehicle we use a dynamic version of decentralized delayed-feedback control proposed in [Konishi, Hirai, and Kokame, Phys. Rev. E 58, 3055 (1998)], and provide a systematic procedure for designing the controller.

Coupled Map Traffic Flow Simulator Based on Optimal Velocity Functions

A coupled map traffic flow model is introduced, based on optimal velocity functions. The model is simulated under open boundary conditions. Effects of noises in velocity are investigated. The average car density increases with the noise level. The high throughput flow is realized when the noise level is sufficiently large, and power law behavior appears in temporal spectra of density fluctuations at the same time. By introducing traffic bottlenecks, a hysteresis loop, which indicates the emergence of traffic jams, is observed in the headway-velocity plane. Temporal spectra of density fluctuations also obey a power law in this case, whose exponent is independent of the noise level.