Nonlinear Attitude Dynamics of Twin Cycle with Feedback Control

Abstract

The nonlinear attitude dynamics of a twin cycle under output feedback control is studied through bifurcation analysis. Two cases are considered. One assumes no slip and the other assumes small slip. The double zero bifurcation is found to occur in both cases but with different bifurcation sets. Among them heteroclinic orbits are found in both cases and a limit cycle in the second case. The region of feedback gains for stability is obtained. Large negative feedback gains are found necessary to assure stability of the twin cycle. Finally, the tire effect is studied and it causes the distortion of the bifurcation sets.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

主动汽车悬架的非线性控制

本文采用１／４车模型对天棚阻尼器和主动悬架的动力学性能进行分析，针对执行器的非线性特性，探讨了微分几何法和反馈法线必互法在主动悬架控制中的应用，在系统控制设计中采用了离散滑模法，仿真结果显示非线性控制律能有效地改善主动悬架的隔振特性。     

Semi-Active Attitude and Vibration Control

The paper discusses the attitude and vibration control of a passenger car on the basis of a full vehicle model. The analysis presented consists of two parts: (I) The introduction of a newly developed semi-active anti-roll/pitch system, (ii) An example of an actively suspended full vehicle model using a simple control strategy to improve ride comfort. The attitude control using semi-actively generated compensation forces prevents the car from rolling in curves and pitching during braking or accelerating. The strength of the system is the small energy consumption. The performance of the combination of both attitude and vibration control can compete with a fully active suspension system.     

考虑塑性变形的振动压路机非线性动力学仿真

借助于土壤变形的一种塑性模式，提出了一种振动压路机压实过程的非线性动力学模型。在此基础上，借助计算机技术，探讨了振动压实中机架与振动轮的运动规律，并对激振力减少、土壤刚度变大和塑性变形增大等情况进行了仿真研究，发现了一些对压路机设计有参考价值的新现象     

On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined, and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice of the numerical solvers. When the equilibrium states are known certain linearizations around one chosen state may be applied carefully in order to facilitate or speed up the numerical solution of the dynamical problem. It is argued, however, that certain problems cannot be linearized. The applications of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

SUMMARY

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

悬索桥的非线性动力行为及其大振幅扭转振动

悬索桥是一种非对称动力系统，有丰富的动力学内容，本文通过几个数值试验，以Tacoma桥为例，给出了有别于颤振理论的失稳解释。     

董家山隧道小净距段爆破控制研究

结合都汶高速公路董家山隧道小净距段的实际情况,应用数值模拟方法,对小净距段在爆破荷载作用下的相互影响问题进行了研究。结果表明：在隧道爆破施工中,应对迎爆侧进行重点监控,采用合理的开挖和加固方式可有效降低爆破施工对先建隧道的不利影响。研究结论为该隧道小净距段的爆破设计、施工及现场监控量测提供指导,同时,为类似小净距段隧道提供参考。     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

SUMMARY

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

An Active Pantograph with Shaped Frequency Response Employing Linear Output Feedback Control

In pantographs used for current collection on high speed electric trains it is desirable to minimise the fluctuations in the contact force between the collector head and the catenary. A simple two-mass linear model is employed for the pantograph and the design of the proposed control system is based on the input admittance at low frequencies. Frequency shaping is incorporated in the performance index, and a simple dynamic controller is employed to achieve optimality in an equivalent transformed system, while minimising the number of feedback quantities to be measured. A significant reduction in the average contact force appears possible.     

计及行驶工况影响的混合动力汽车控制策略

为减小行驶工况波动对汽车性能的影响,引入行驶工况比例系数。应用遗传优化算法,以汽车燃油经济性和排放性为优化目标,在不同比例系数的行驶工况下对控制策略参数进行优化,分析并总结了行驶工况比例系数与控制策略参数之间的关系。通过采用模糊神经网络对行驶工况的比例系数进行识别,建立了一个计及行驶工况影响的混合动力汽车智能控制策略。实车验证结果表明,所建立的控制策略减小了行驶工况波动对电动汽车性能的影响,使其在不同的行驶工况下都具有较好的燃油经济性和排放性。     

Comparison of Feedforward and Feedback Control for 4WS

SUMMARY

A system incorporating feedforward plus feedback control was configured such that it would follow the target yaw rate found by calculation. Selection of optimum values for the control system constants made it possible to separate control of the steering input response characteristic from control of vehicle stability against external disturbances. The former is controlled by the feedforward control function and the latter by the feedback control function; the values of the two functions can be set independently.     

On Lateral Dynamics of Vehicles Based on Nonlinear Characteristics of Tires

The problems of vehicle lateral dynamics based on nonlinear characteristics of tires are discussed in this paper. A new nonlinear perturbation model on the cornering behavior of the tire is constructed. The nonlinear influences of tires on the steady-state steering behavior, dynamic response and handling stability of vehicle are discussed, applying the approximate analytical methods for nonlinear vibration. An analytical criterion of stability is obtained. Some numerical examples are given.     

On Lateral Dynamics of Vehicles Based on Nonlinear Characteristics of Tires

The problems of vehicle lateral dynamics based on nonlinear characteristics of tires are discussed in this paper. A new nonlinear perturbation model on the cornering behavior of the tire is constructed. The nonlinear influences of tires on the steady-state steering behavior, dynamic response and handling stability of vehicle are discussed, applying the approximate analytical methods for nonlinear vibration. An analytical criterion of stability is obtained. Some numerical examples are given.