Ebrahim Esmailzadeh

Optimal yaw moment control law for improved vehicle handling

A new optimal control law for direct yaw moment control, to improve the vehicle handling, is developed. Although, this can be considered as part of a multi-layer system, for the traction control of a motorized wheels electric vehicle, but the results of this study are quite general and can be applied to other types of vehicles. The dynamic model of the vehicle system is initially developed and, using the well-known optimal control theory, an optimal controller is designed. Two different versions of control laws are considered here and the performance of each version of the control law is compared with the other one. The numerical simulation of the vehicle handling with and without the use of the optimal yaw moment controller, and assuming a comprehensive non-linear vehicle dynamic model, has been carried out. Simulation results obtained indicate that considerable improvements in the vehicle handling can be achieved whenever the vehicle is governed by the optimal yaw moment control.

Design of a VDC System for All-Wheel Independent Drive Vehicles

It is shown that the vehicle dynamic control (VDC) system can improve the vehicle handling and active safety of driver and passengers considerably. The control of vehicle yaw moment through differential braking, based on the vehicle dynamic state feedbacks, is a traditional way of VDC. In this study, a new VDC system for a four motorized-wheels electric vehicle has been developed, for which the traction of each wheel can be controlled individually. Using this feature, the new VDC system provides the desired tractive force of vehicle and the desired external yaw moment through the integrated control of wheel motors. The structure of the control system is a multilayer type, which has been developed by using independent controllers, designed in accordance with the appropriate theories.

Automobile Passenger Comfort Assured Through LQG/LQR Active Suspension

An analytical investigation of a half-car model including passenger dynamics, subjected to random road disturbances is performed, and the advantage of active over conventional passive suspension systems are examined. Two different performance indices for optimal controller design are proposed. The performance index is a quantification of both ride comfort and road handling. Due to practical limitations, all the states required for the state-feedback controller are not measurable, and thus must be estimated with an observer. Stochastic inputs are applied to simulate realistic road surface conditions, and statistical comparisons between passive system and the two controllers, with and without state estimator, are carried out to gain a clearer insight into the performance of the controllers.The simulation results demonstrate that an optimal observer- based controller, when including passenger acceleration in the performance index, retains both excellent ride comfort and road handling characteristics.

Dynamic Modeling and Analysis of a Four Motorized Wheels Electric Vehicle

A comprehensive dynamic model of a four motorized wheels electric vehicle has been developed and different types of motor control laws were addressed. The first part of this study deals with the full description of the model scope in which the structure of the model, including the sub-models, has been expressed. Subsequently, the sub-models including the tire sub-model, the body motion, and the motor dynamics are fully investigated, and with the use of simulink software, the computer model of the vehicle is simulated. Finally, the motor control laws are presented and the vehicle dynamic behavior studied under different driving conditions. Detailed analyses and comparison of the simulation results are carried out.

Active vehicle suspensions with optimal state-feedback control

This paper examines the potential benefits of incorporating active controllers in order to remedy the drawbacks associated with conventional passive suspensions. A methodology to define the performance index, together with the weighting matrices being assigned, are presented in order to achieve optimum ride comfort and the road handling requirements. Nondeterministic inputs are applied to simulate the road surface conditions more realistically. Stochastical comparisons between the two controllers and passive system are carried out to gain insight into the performance of the controllers. The results demonstrate that an optimal state-feedback controller, when it indudes passenger acceleration in the performance index, retains excellent ride comfort and road-handling characteristics.

Periodic behavior of a cantilever beam with end mass subjected to harmonic base excitation

A massless cantilever beam with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Greens function and employing Schauders fixed point theorem.

Vehicle–passenger–structure interaction of uniform bridges traversed by moving vehicles

Abstract An investigation into the dynamics of vehicle–occupant–structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler–Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of the dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span, while the maximum bending moment occurs at ±20% of the mid-span point. It is shown that one can find a critical speed at which the maximum values of the bridge dynamic deflection and the bending moment attain their global maxima.

Parametric response of cantilever Timoshenko beams with tip mass under harmonic support motion

Abstract The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial support motion is investigated. The Timoshenko beam theory is used to assess the effects of rotary inertia and shear deformation for the beam. In this regard, different modal amplitudes for transverse displacement and angle of rotation of the cross-section are considered. This yields a more accurate description of the dynamic model. The governing equations of motion are then derived for an arbitrary axial support motion which provide the flexibility of choosing the number of characteristic modes of the beam. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for the existence of periodic oscillatory behavior of the beam are established. Consequently, the phase domains of periodicity and stability for various values of the physical characteristics of the beam-mass system and harmonic base excitation are presented. Depending on the values of the excitation amplitude and frequency in the stable and unstable regions, the solution exhibits many shapes besides the transition periodic shapes. A numerical example assessing the role of slenderness ratio of the beam, is presented to demonstrate the effectiveness of the proposed study. Results indicate that for a given beam system with a known excitation, increasing the tip mass would almost always reduce the stable periodic region. The effect of the beam model assumption on the periodic domain is also studied. Results show that using purely flexural or even the Euler–Bernoulli model rather than Timoshenko, would produce an incorrect periodic region.

Automatic path control based on integrated steering and external yaw-moment control:

Nowadays improving safety is an indispensable part of research issues in the automotive industry. Due to increased travelling time, accident potentials and also traffic congestions, automated vehicles are seen as a way to increase freeway capacity and vehicle speed while reducing accidents resulted from human errors. In order to guide a vehicle automatically, vehicle lateral motion should be controlled, active steering control (ASC) and direct yaw-moment control (DYC) are two common methods to control the vehicle lateral dynamic, automatically. For higher vehicle lateral acceleration, where the tyres will not be capable of producing enough lateral forces (yaw-moment), ASC could not be useful. In such situation, the advantages of DYC can be clearly observed. Indent In this paper, a novel optimal control law is proposed to control the vehicle path, automatically. The control law uses the vehicle dynamic variables such as the yaw and lateral velocities, lateral offset, and the heading error as well as the road-related variables. These are the road curvature and the lateral offset between the desired path and the vehicle as the feedback/feed-forward signals to produce both the front steering angle and the external yaw-moment signals as the control efforts. Simulation results illustrate the dominant power of the front steering/DYC in the control of the vehicle lateral motion.

Optimum design of Vibration Absorbers for structurally damped Timoshenko beams

A procedure in designing optimal Dynamic Vibration Absorbers (DVA) for a structurally damped beam system subjected to an arbitrary distributed harmonic force excitation, is presented. The Timoshenko beam theory is used to assess the effects of rotatory inertia and shear deformation. The method provides flexibility of choosing the number of absorbers depending upon the number of significant modes which are to be suppressed. Uniform cross-sectional area is considered for the beam and each absorber is modeled as a spring-mass-damper system. For each absorber with a selected mass, the optimum stiffness and damping coefficients are determined in order to minimize the beam dynamic response at the resonant frequencies for which they are operated. For this purpose, absorbers each tuned to a different resonance, are used to suppress any arbitrarily number of resonances of the beam. The interaction between absorbers is also accounted for in the analysis. The optimum tuning and damping ratios of the absorbers, each tuned to the mode of concern, are determined numerically by sloving a min-max problem. The Direct Updated Method is used in optimization procedure and the results show that the optimum values of the absorber parameters depend upon various factors, namely: the position of the applied force, the location where the absorbers are attached, the position at which the beam response should be minimized, and also the beam characteristics such as boundary conditions, rotatory inertia, shear deformation, structural damping, and cross sectional geometry. Through the given examples, the feasibility of using proposed study is demonstrated to minimize the beam dynamic response over a broad frequency range. The resulting curves giving the non-dimensional absorber parameters can he used for practical applications, and some interesting conclusions can be drown from the study of them.