Time-Varying LQG Control for Vibration of Coupled Vehicle-Bridge System

2013 ◽  
Vol 347-350 ◽  
pp. 541-547 ◽  
Author(s):  
Gang Song
Keyword(s):  
Ride Comfort ◽  
Time History ◽  
Vehicle Body ◽  
Time Varying ◽  
Mass Model ◽  
Riccati Differential Equation ◽  
Active Suspensions ◽  
Precise Integration ◽  
Lqg Control ◽  
Bridge System

Time-varying linear quadratic Gaussian (LQG) control for vibration of coupled vehicle-bridge system is studied. The vehicle is modeled as a moving mass model with three degrees of freedom, which consists of vehicle body, bogie and wheel. Active suspensions are adopted for the primary and secondary ones, and the control forces are produced by two actuators placed between the bogie and wheel, and between the vehicle body and the bogie, respectively. Vehicle-bridge coupling systems are time-dependent, which lead to the time-varying Riccati differential equation and the time-varying Kalman-Bucy filter equation in the LQG controller design. However, both of them are solved precisely via precise integration method and symplectic conservative perturbation method. In the example, the time history responses of the bridge and the vehicle were calculated respectively for the vehicle with passive suspensions or with active suspensions. Numerical results show that with active suspensions adopted, ride comfort can be improved when the vehicles passing through the bridge.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Application of Practical Observer to Semi-Active Suspensions

1998 ◽  
Vol 122 (2) ◽  
pp. 284-289 ◽  
Author(s):  
H. Nakai ◽  
S. Oosaku ◽  
Y. Motozono
Keyword(s):  
Ride Comfort ◽  
Difficult Problem ◽  
Nonlinear Observer ◽  
Vertical Acceleration ◽  
Acceleration Sensor ◽  
Active Suspensions ◽  
Linear Observer ◽  
Gain Scheduled

This paper presents the development of gain-scheduled observers for semi-active suspensions. The states of the semi-active suspensions must be accurately obtained because the accuracy directly affects system performances such as ride comfort. Nonlinearity in the absorber of the semi-active suspensions is a difficult problem for estimating the accurate states using conventional linear observer theories. To solve this problem, we have designed a new gain-scheduled observer by introducing two improvements. The validity of this nonlinear observer was confirmed by simulations and experiments. The results indicate that the present observer can accurately estimate the suspension stroke velocity using the vertical acceleration sensor on the sprung mass. [S0022-0434(00)02302-9]

Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kun-Yung Chen ◽  
Te-Wen Tu
Keyword(s):  
Heat Transfer ◽  
Particle Swarm Optimization ◽  
Objective Function ◽  
Hollow Cylinder ◽  
General Type ◽  
Particle Swarm ◽  
Time History ◽  
Time Varying ◽  
Swarm Optimization ◽  
Self Learning

Abstract An inverse methodology is proposed to estimate a time-varying heat transfer coefficient (HTC) for a hollow cylinder with time-dependent boundary conditions of different kinds on inner and outer surfaces. The temperatures at both the inner surface and the interior domain are measured for the hollow cylinder, while the time history of HTC of the outer surface will be inversely determined. This work first expressed the unknown function of HTC in a general form with unknown coefficients, and then regarded these unknown coefficients as the estimated parameters which can be randomly searched and found by the self-learning particle swarm optimization (SLPSO) method. The objective function which wants to be minimized was found with the absolute errors between the measured and estimated temperatures at several measurement times. If the objective function converges toward the null, the inverse solution of the estimated HTC will be found eventually. From numerical experiments, when the function of HTC with exponential type is performed, the unknown coefficients of the HTC function can be accurately estimated. On the contrary, when the function of HTC with a general type is conducted, the unknown coefficients of HTC are poorly estimated. However, the estimated coefficients of an HTC function with the general type can be regarded as the equivalent coefficients for the real function of HTC.

The Time Domain Simulation of Non-Stationary Road Roughness

2013 ◽  
Vol 423-426 ◽  
pp. 1238-1242
Author(s):  
Hao Wang ◽  
Xiao Mei Shi
Keyword(s):  
Power Spectrum ◽  
Time Domain ◽  
Ride Comfort ◽  
Time History ◽  
Random Excitation ◽  
Power Spectrum Density ◽  
The Road ◽  
Road Roughness ◽  
Spectrum Density ◽  
History Of

The input of road roughness, which affects the ride comfort and the handling stability of vehicle, is the main excitation for the running vehicle. The time history of the road roughness was researched with the random phases, based on the stationary power spectrum density of the road roughness determined by the standards. Through the inverse Fourier transform, the random phases can be used to get the road roughness in time domain, together with the amplitude. Then, the time domain simulation of the non-stationary random excitation when the vehicle ran at the changing speed, would also be studied based on the random phases. It is proved that the random road excitation for the vehicle with the changing speed is stationary modulated evolution random excitation, and its power spectrum density is the stationary modulated evolutionary power spectrum density. And the numerical results for the time history of the non-stationary random inputs were also provided. The time history of the non-stationary random road can be used to evaluate the ride comfort of the vehicle which is running at the changing speed.

scholarly journals Mathematical Modelling of Two-Wheeler Suspension system in a wavy road

2019 ◽  
Vol 8 (11) ◽  
pp. 3630-3635
Keyword(s):  
Ride Comfort ◽  
Health Hazard ◽  
Suspension System ◽  
Vehicle Body ◽  
Continuous Exposure ◽  
Potential Health ◽  
Suspension Spring ◽  
The Road ◽  
Potential Health Hazard ◽  
Two Wheeler

Two wheelers like motorbikes and scooters are one of the major transports in India. In major cities and towns, it is most common private transport as it is fast and easy approach to the destination. But the prolonged drive in the two-wheeler leads to the potential health hazard and musco-skeletal disorder due to continuous exposure to the vibration caused during the ride and force transmitted to the vehicle body due to road irregularities. It is a challenge of automobile engineers to design a promising suspension system to overcome the risk of ride comfort during continuous driving. In this research, two-wheeler suspension system is modelled with a condition of bump and valley in a wavy road. The road surface is assumed to be wavy and the response of new suspension spring with different materials (stainless steel, tungsten and polymeric) along with viscous damper is analyzed and compared. By this analysis, it will be proposed to industry to modify the suspension system to improve its efficiency and reduce force transmitted to the human body to improve the ride comfort

Existence of Solutions of Riccati Differential Equations

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Sinan Kilicaslan ◽  
Stephen P. Banks
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Time Varying ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
Time Varying Systems

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

scholarly journals Ride Blending Control for Electric Vehicles

2019 ◽  
Vol 10 (2) ◽  
pp. 36 ◽  
Author(s):  
Vincenzo Ricciardi ◽  
Valentin Ivanov ◽  
Miguel Dhaens ◽  
Bert Vandersmissen ◽  
Marc Geraerts ◽  
...  
Keyword(s):  
Electric Vehicles ◽  
Ride Comfort ◽  
Simulation Analysis ◽  
Superior Performance ◽  
Ride Quality ◽  
Active Suspensions ◽  
Control Functions ◽  
Performance Indexes ◽  
Advanced Control ◽  
Passive Suspension System

Vehicles equipped with in-wheel motors (IWMs) feature advanced control functions that allow for enhanced vehicle dynamics and stability. However, these improvements occur to the detriment of ride comfort due to the increased unsprung mass. This study investigates the driving comfort enhancement in electric vehicles that can be achieved through blended control of IWMs and active suspensions (ASs). The term “ride blending”, coined in a previous authors’ work and herein retained, is proposed by analogy with the brake blending to identify the blended action of IWMs and ASs. In the present work, the superior performance of the ride blending control is demonstrated against several driving manoeuvres typically used for the evaluation of the ride quality. The effectiveness of the proposed ride blending control is confirmed by the improved key performance indexes associated with driving comfort and active safety. The simulation results refer to the comparison of the conventional sport utility vehicle (SUV) equipped with a passive suspension system and its electric version provided with ride blending control. The simulation analysis is conducted with an experimentally validated vehicle model in CarMaker® and MATLAB/Simulink co-simulation environment including high-fidelity vehicle subsystems models.

Golden Section Search Based Optimization of Road Vehicle Suspension System

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Prasad Bali ◽  
C.V. Chandrashekara
Keyword(s):  
Ride Comfort ◽  
Golden Section ◽  
Optimization Technique ◽  
Relative Displacement ◽  
Suspension System ◽  
Vehicle Body ◽  
Vehicle Handling ◽  
Golden Section Search ◽  
Design Requirements ◽  
Quarter Car

Suspension system is an important part of a vehicle which connects the road wheels and vehicle body. The major function of suspension is to isolate vehicle body from road disturbances. The design of suspension system is generally a compromise between many design requirements that aim to provide a comfortable ride and good vehicle handling. An optimization technique is used to choose the suspension parameters that meet these design requirements. In this present work a two degree of freedom quarter car vehicle vibration model is considered for optimization. Sprung mass acceleration and relative displacement of quarter car are considered as the measure of ride comfort and vehicle handling respectively. Golden section search optimization technique is used for single objective optimization of quarter car considering sprung mass acceleration as objective function and relative displacement as constraint. It is noticed that the accuracy level in getting the optimized value using this approach is comparatively high and reliable..

Sign in / Sign up

Export Citation Format

Share Document