To improve the ride comfort of the offroad vibratory roller, the cab’s hydraulic mounts were analyzed to prevent vibration sources transmitting to the cab. However, the cab’s lowfrequency shaking in the vertical direction and the direction of forward motion is still great. This study proposes an optimal fuzzyPID control method for semiactive cab’s hydraulic mounts based on an offroad vehicle roller dynamic model to analyze the lowfrequency performance of semiactive cab’s hydraulic mounts under the different operating conditions. In order to evaluate the ride comfort of the offroad vibratory roller with semiactive cab’s hydraulic mounts, the power spectral density (PSD) and the weighted root mean square (RMS) of acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations in the lowfrequency range are chosen as objective functions. Contrastive analysis of lowfrequency vibration characteristics of the offroad vibratory roller with passive cab’s hydraulic mounts, semiactive cab’s hydraulic mounts without optimization, and semiactive cab’s hydraulic mounts with optimization is, respectively, carried out. The research results show that the semiactive cab’s hydraulic mounts with optimization have an obvious effect on mitigating the cab shaking and improving the ride comfort in comparison with passive cab’s hydraulic mounts and semiactive cab’s hydraulic mounts without optimization.
The vibratory roller plays an important in the field of the construction project on roads, railways, airports, and so on. There is a combination of the static force of the vehicle self and the dynamic force of the vibratory drum yielded by an eccentric mass rotating around the drum axis to compact soil, asphalt, and other materials in its work process. Thus, the vehicle’s vibration dynamics were mainly generated by the wheelsdeformable terrain interaction in the condition of the vehicle traveling and the drum/tyreselastoplastic terrain interactions in the condition of the vehicle working [
Consequently, the vibratory roller’s ride comfort was researched via the interaction model between wheels and offroad terrain. The influence of design parameters of passive cab’s rubber mounts (PRMs) on the ride dynamics of a soil compactor was studied via experiment and simulation [
The vibratory roller cab’s isolation system is one of the most important factors to improve the driver’s ride comfort. A 3D nonlinear dynamic model of an offroad vibratory roller equipped with three different cab’s isolation mounts including the PRM, the passive hydraulic mounts (PHMs), and the pneumatic mounts was studied via the simulation and experimental investigations to investigate the vehicle’s ride comfort in a lowfrequency region [
Nowadays, the combined control methods, such as the neuralPID control, fuzzyPID control, and integrated fuzzywheelbase preview control [
In this study, based on a threedimensional nonlinear dynamic model of the offroad vibratory roller equipped with PHM [
The innovation in this paper is that an 11DOF vehicle dynamics model which can fully reflect the pitch and roll of the cab is concerned under the various operating conditions. A new optimal method of the fuzzy control rules based on the genetic algorithm, which is known as a multiobjective optimal algorithm with wide search range and short search time, is successfully developed and applied for the optimal fuzzyPID controller. The two evaluation methods including the evaluation method of the vibration effect to the driver’s ride comfort via the weighted RMS acceleration response in the time region and the evaluation method of the vibration effect to the health and safety of the driver via the PSD acceleration responses in the lowfrequency region are carried out. The vibration responses of the vibratory roller under lowfrequency excitation of the offroad terrain ground, especially the pitch and roll vibration response of the cab with PHM, SHM without optimization, and SHM with optimization are, respectively, simulated and analyzed. The results show that the lowfrequency and highstiffness characteristics of SHM with optimization have a good effect on isolating lowfrequency vibration transmitted and controlling the cab shaking of the vibratory roller.
Based on a threedimensional nonlinear dynamic model of the offroad vibratory roller [
Schematic of vibratory roller with different cab’s isolation mounts. (a) Single drum vibratory roller. (b) Passive rubber mount. (c) Passive hydraulic mount. (d) Semiactive hydraulic mount.
A threedimensional nonlinear dynamic model with elevenDOF of a single drum vibratory roller and the cab’s isolation mount models are built as in Figures
Lumped parameter model of the vibratory roller and different cab’s isolation mounts. (a) Vibratory roller dynamic model. (b) Cab’s isolation mount model.
In Figure
Based on the dynamic model of the vibratory roller and offroad terrains interaction, as shown in Figure
Both the PRM and the PHM, as plotted in Figures
In addition, a new model of SHM for the vibratory roller based on the PHM is proposed in this study. The basic structure of an SHM includes a main rubber, a damping plate driven by the bolt, and a closed chamber filled with the fluid. However, the fluid used in the closed chamber is a magnetorheological (MR) fluid with adjustable damping [
The corresponding dynamic force at mount
In actual operating conditions, the excitation forces of the vibratory roller are strongly affected by the rough terrain surfaces apart from wheelsdeformable terrain interactions. The terrain behaviour under wheelsoil contact is nonlinear. Thus, the offroad vibratory rollers must be studied in the frequency domain apart from the traditional time domain to analyze the influence of excitation on the ride response. Offroad terrain surface in the frequency domain is calculated via the PSD value [
More specifically, assuming the vehicle moves with a constant speed
In order to develop an offroad terrain roughness input closing to the actual terrain condition, the simulation parameters used for generating the time domain of a rough terrain surface, as shown in Figure
Generation of the offroad terrain roughness according to unpaved offroad classification. (a) Offroad terrain profile. (b) Spectral densities.
In order to validate the accuracy of the mathematical model of the offroad vibratory roller, experiments and simulations were carried out with cab’s isolation systems when the vehicle moved and compacted at a speed
The experimental and simulation results under an excitation frequency 28 Hz of the drum [
In addition, simulation results with PHM showed that both PSD acceleration responses and the weighted RMS values of the vertical driver’s seat, cab’s pitch, and roll vibrations are greatly reduced, and the PHM has almost no effect on the resonance frequencies in comparison with PRM under the various operating conditions. Therefore, the model of the offroad vibratory roller using PHM not only enhances the vehicle’s ride comfort but also provides the accurate and feasible model for lowfrequency performance analysis of the semiactive cab’s hydraulic mounts (SHMs).
The PID control is one of the controllers with not only a simple structure but also robust performance, and it is generally used in industrial process control. However, the performance of PID control depends on the appropriate selection of the PID’s parameters. The wellknown ZieglerNichols technique has been used to choose the PID’s parameters. However, it is only efficient when the system works at the designed operating condition. Contrariwise, the fuzzy logic control (FLC) does not depend on the designed operating condition; it only depends on the appropriate selection of the fuzzy inference system (FIS). However, the shortcomings of FLC are low precision and stability. In order to avoid shortcomings of both FLC and PID control, fuzzyPID control had been developed [
In the cab’s isolation mounts, there are four SHMs which should be separately controlled; thus, four optimal fuzzyPID controls should be designed. However, the design process of these controls is the same. Therefore, a specific of the optimal FPC is designed to control the active damping force of MR fluid. The model of the optimal FPC for SHM is depicted in Figure
Structure of the vehicle model with SHM. (a) Optimal fuzzyPID control model. (b) FLC control.
In Figure
The force output of the PID control is given by
The initial values of proportionality factors in equation (5) determined by the ZieglerNichols method via the subsystem model are
The next is a design of the FLC. The basic fuzzy control consists of the following major parts: fuzzification interface, FIS, and defuzzification interface. First, the crisp values in fuzzification are transformed into linguistic variables, FIS is then used by control rules in accordance with inference rules, and finally, the linguistic variables are transformed back to crisp values through defuzzification for use by the physical plant [
Choosing the fuzzy control inputoutput: two input variables E and EC belong to [−0.25, 0.25]. Besides, three output variables
The linguistic variables of two inputs are defined by the positive big (PB), positive small (PS), zero (ZO), negative small (NS), and negative big (NB). Besides, the linguistic variables of three outputs are also defined as small (
Membership function: the shape of membership functions of inputoutput variables is used by the triangular function, and its degree of membership is between 0 and 1, as shown in Figure
The FIS’s rules: the initial control rules are given by the designer’s knowledge and experience as follows:
If
If
If
where FIS is selected by the minimum function and the centroid method of Mamdani and Assilian [
GA is an optimization method based on principles of natural selection. It seeks the maximum or the minimum values of one or more objective functions using computational techniques motivated by biological reproduction. Therefore, GA is defined as finding a vector of decisive variables that satisfies constraints to give acceptable values to all objective functions [
Find the vector
GA is structured into the following steps: encoding, population initialization, fitness evaluation, parent selection, genetic operations (crossover and mutate), and termination criterion. The flow chart of the GA program for SHM is built in Figure
The flow chart of the GA program for SHM.
The goal main of GA is to seek the optimal control rules in FIS to get the minimum values of the weighted RMS acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations via the subsystem model in Figure
Encoding mechanism and initial population: in “(iii) The FIS’s rules,” there are 25 control rules that contain a total of 75 elements. The 75 elements are then connected into a string of numbers as a chromosome which is regarded as a vector. Encoding mechanism can shorten the chromosome length of the individuals in population space to enhance the running speed and to reduce the searching space of the algorithm program. Thus, the linguistic variables of two inputs (
Objective function and fitness value: the minimum values of the weighted RMS acceleration responses (
where subscript
The individuals with the higher fitness value
Genetic operations: after establishing the initial population and selecting the parents. Genetic operations (including crossover and mutation) are then performed. Herein, crossover probability of 0.95 and mutation probability of 0.05 have been used in 200 generations. Therefore, the arithmetic crossover is performed on 95% of the selected parents, whereby two children are created from the weighted sum of two parents, and children of the remaining 5% of selected parents are exact copies of the parents. Crossover operation is performed until the population number is doubled. Then, each individual undergoes the mutation operation which is the process of randomly changing the values of genes in a chromosome with a probability of 0.05. The mutation can create new genetic material into an existing individual and add diversity to the genetic characteristics of the population. Finally, through the fitness value
In order to seek the optimal control rules for the FPC, we assume that the vibratory roller travels on the deformable terrain at a constant speed
The weighted RMS acceleration responses on a deformable terrain.
Performance  PHM  SHM without optimization  SHM with optimization  SHM with optimization versus PHM (%) 


1.063  0.875  0.691  34.99 

0.982  0.810  0.564  42.56 

0.139  0.100  0.081  41.72 
The result in Figure
The curve of fitness value.
Result of the optimal control rules.
EC  E  



 
NB  NS  ZO  PS  PB  NB  NS  ZO  PS  PB  NB  NS  ZO  PS  PB  
NB  M  MB  B  MS  S  S  S  M  MB  S  S  M  B  MB  B 
NS  MB  M  MS  M  MS  S  B  MB  MS  M  MS  S  M  M  S 
ZO  M  S  S  S  M  MS  MS  S  M  MB  M  B  S  S  MS 
PS  MS  M  MS  M  B  MS  S  M  MB  S  MB  MS  S  MS  MS 
PB  S  MS  M  MB  MB  M  M  MS  S  S  MS  B  S  S  M 
The performance of the vehicle suspension system is evaluated by three main indices in the time domain, including the ride comfort, working space, and road holding characteristics.
Among these three indices, the ride comfort performance evaluated via the weighted RMS acceleration response is considered to be the most important index [
In this study, the vehicle is assumed to be traveling on a terrain type of Grenville loam given by Wong [
A good cab’s isolation system should be able to minimize its deflection and acceleration to enhance the driver’s ride comfort. In addition, the driver’s mental and physical health is affected not only by the acceleration responses in the time region but also by the PSD acceleration responses in the lowfrequency region [
The simulation results of the PSD acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations are plotted in Figures
Results of the PSD acceleration responses on the deformable terrain. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
The maximum resonance peaks of the PSD acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM without optimization are smaller than PHM. Meanwhile, the maximum resonance peaks of the PSD acceleration responses of SHM with optimization are the smallest. Especially in lowfrequency below 4 Hz, the maximum PSD values of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM with optimization are greatly reduced by 32.97%, 29.08%, and 64.40% in comparison with PHM, respectively. This is due to the main impact of the semiactive damping force of hydraulic mount
The simulation results of the acceleration responses are also shown in Figures
Results of the acceleration responses on the deformable terrain. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
In the working condition of the vibratory roller, the effect of the elastoplastic soil grounds on the performance of the compaction process was studied under the excitation frequencies of the drum in a range of 0.1–70 Hz [
The comparison results of the PSD acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations with the cab’s isolation systems at a low/high excitation frequency, 28/35 Hz, of the vibratory drum are seen in Figures
Results of the PSD acceleration responses under a low excitation frequency, 28 Hz, of the drum. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
Results of the PSD acceleration responses under a high excitation frequency, 35 Hz, of the drum. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
Besides, at a lowfrequency range below 4 Hz, the maximum resonance peaks of the PSD acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM with optimization are strongly reduced in comparison with PHM by 24.46%, 31.47%, and 59.37% at a low excitation frequency, 28 Hz, of the drum and by 17.76%, 33.52%, and 53.85% at a high excitation frequency, 35 Hz, of the drum, respectively. This is also due to the main impact of the semiactive damping force of hydraulic mount
The simulation results in Figures
Results of the acceleration responses under a low excitation frequency, 28 Hz, of the drum. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
Results of the acceleration responses under a high excitation frequency, 35 Hz, of the drum. (a) Vertical driver’s seat. (b) Cab’s pitch angle. (c) Cab’s roll angle.
The weighted RMS values under a low excitation frequency, 28 Hz, of the drum.
Performance  PHM  SHM without optimization  SHM with optimization  SHM with optimization versus PHM (%) 


0.657  0.501  0.426  35.16 

0.323  0.184  0.167  48.29 

0.085  0.056  0.053  37.65 
The weighted RMS values under a high excitation frequency, 35 Hz, of the drum.
Performance  PHM  SHM without optimization  SHM with optimization  SHM with optimization versus PHM (%) 


0.512  0.453  0.385  24.80 

0.241  0.162  0.137  43.15 

0.061  0.040  0.039  36.06 
Modeling and lowfrequency performance analysis of semiactive cab’s hydraulic mounts of the offroad vibratory roller are addressed in this work. The comparison between the simulation and test results of passive cab’s isolation mounts is also carried out. The lowfrequency performance of SHM using the optimal fuzzyPID controller is then evaluated through the PSD acceleration and weighted RMS values of the vertical driver’s seat, cab’s pitch, and roll vibrations in both the frequency and time domains. The results are summarized as follows:
In the condition of the vehicle traveling, the weighted RMS acceleration responses and the PSD acceleration responses of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM with optimization are lower than both PHM and SHM without optimization. Particularly, the weighted RMS values of SHM with optimization are strongly reduced in comparison with PHM by 34.99%, 42.56%, and 41.72%, respectively.
In condition of the vehicle working, both PSD acceleration responses and the weighted RMS values of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM using the optimal fuzzyPID controller are clearly smaller comparable with both PHM and SHM without optimization under both low/high excitation frequency, 28/35 Hz, of the drum on the high elastoplastic soil ground. Especially, the maximum PSD values of the vertical driver’s seat, cab’s pitch, and roll vibrations of SHM with optimization are strongly reduced by 24.46%, 31.47%, and 59.37% in comparison with PHM when the vehicle compacts at a low excitation frequency, 28 Hz, of the drum.
The above analysis results indicate that the lowfrequency and highstiffness characteristics of SHM using the optimal fuzzyPID controller have the best effect on isolating lowfrequency vibration transmitted and controlling the cab shaking under various operating conditions of the offroad vibratory roller.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.