Matlab Code an Automobile Traveling on a Rough Road Can Be Modeled for Pitch and Bounce Motions

Abstract.

The physiological and psychological issue of vehicle vibrations on passengers is still a challenging problem. Therefore, the passenger ride comfort, which depends on a combination of vehicle displacement (boost) and angular deportation (pitch), has been i of the major problems of vehicle design. This newspaper proposes a fuzzy logic control (FLC) strategy for agile vehicle suspension system which is utilized to generate counter-force to isolate vibration from the rough ground. A iv caste-of-liberty (DOF) half motorcar mathematical model is firstly presented. And a "decoupling transformation" is practical to the translation and pitch motility. The hydraulic actuator is then introduced as well. Concluding the ADMAS control module is used to return co-simulation between ADAMS and MATLAB to verify efficiency of FLC and decoupling transformation. Compared with passive break system, it is indicated that the proposed agile suspension system is very constructive in reducing peak values of vehicle trunk accelerations, specially within the most sensitive frequency range of human response. The root mean square of vehicle vertical and pitch angle accelerations is reduced. Therefore, the ride condolement is improved.

Keywords: active interruption, ADAMS/Auto, fuzzy logic, co-simulation, ISO2631.

1. Introduction

Long-term exposure to whole trunk vibration especially at low frequencies may cause long-term wellness disorders in the internal organs, muscles or bone structure. Rasmussen [one] reported some symptoms and the corresponding frequency levels. For example, vibrations between four and ix Hz cause discomfort feeling and muscle contractions due to chronic musculoskeletal stress. Abdominal pains are placed at 4-ten Hz. Breathing movements are influenced at 4-8 Hz. Chest pains and low jaw symptoms are happened at 5-vii Hz and 6-10 Hz, respectively. Nonetheless, for the urge to urinate are at 10-eighteen Hz, and head symptoms, influence on speech and increased muscle tone prevarication at 13-20 Hz. In improver, the vibration with stiff acceleration may cause serious spinal cavalcade affliction and other complaints [two]. Therefore, improving the ride operation is indispensable.

Vibration and acoustic serve as an incredible part of vehicle design, which in general are determined in large calibration by variety of sources. In item, roadway roughness or aerodynamics forces are external factors while the engine, power train, or suspension mechanisms [3, 4] are the master internal sources.

The main source of vibration, the quality of road surface which is widely described by roughness and slopes, is investigated in this paper. The roughness represents small cavities or projections on the surface which causes random and high frequent bumps of the vehicle, and meanwhile, the slopes means climbing or descending of the road and causes long-term influence on vehicle performance.

The vehicle vibration is closely related with ride comfort quality, which evaluates the passenger's response in the condition of crude terrain. International standards were widely recognized on drive comfort in terms of human being body vibration frequency in ISO2631 [5]. The rider comfort depends largely on a combination of vertical heave movement and pitch rotation motion. In other words, the acceleration of heave and pitch move play an important role. Therefore, the loftier ride comfort of active suspension organisation renders one of passive suspension system which is impossible.

In order to reduce vibration, the suspension system is connected betwixt vehicle body and wheels. Such a organisation contributes to the car'due south handling, braking for skillful active safety and driving pleasure. Moreover, the random vibration and road dissonance due to surface bumps and cavities are isolated to a large extent confronting the driver.

The controlled suspension arrangement is now widely practical such every bit semi-active suspension [6, 7], and active interruption [8, 9]. Chen [half dozen] proposed a new method on design and stability analysis of semi-active intermission fuzzy control system. Based on the Lyapunov stability theory, each fuzzy subspace's stability of close loop system is analyzed. And and so stable condition of whole fuzzy command system is obtained. The event of experiment and simulation shows that fuzzy control arrangement of semi-active intermission is constructive and stable and improves the ride functioning. Pang [7] studied the trouble of stability analysis and fuzzy-smith compensation control for semi-agile suspension systems with time delay. Based on the Lyapunov stability analysis, the necessary and sufficient condition of the critical fourth dimension delay for the semi-active interruption is derived, and the numerical computation method of solving the asymptotic stability expanse for the pause system is given. Finally, the results show the ride condolement is improved. Although many scholars explored diverse semi-active vehicle suspensions to improve ride functioning, the active break is widely utilized for luxurious vehicle since it can effectively improve the ride condolement also as stability. However, a challenging trouble for active pause design is determined by a control strategy to improve the system performance. During the by two decades, many control strategies take been proposed past many researchers. A half auto model with active suspension was presented by [10]. They utilized a dual loop PID controller strategy to better dynamic performance. A nonlinear optimal control law is developed, and applied on a half-motorcar model for the control of active suspension systems to improve the tradeoff betwixt ride quality and intermission travel compared to the passive suspension system [11]. An effective and robust proportional integral sliding fashion control strategy is proposed in the active break system [12]. Control strategies are investigated for agile suspension systems with control concepts of look-ahead and wheelbase preview. The corresponding controllers were designed and the interruption system operation was improved [13]. A robust fuzzy sliding-mode controller for an active pause organisation was applied in a half-car model. The feasibility was verified [14]. The uncoupled half car model is constructed such as Karnopps' piece of work [fifteen]. He presented a passive and active control of road heave and pitch motions for approximately uncoupled motions. Wong'south work [sixteen] considered a ii DOF vehicle model to report the heave and pitch motions neglecting the vehicle suspension dynamics.

Four DOF mathematical model of one-half car is firstly introduced in this work. And a "decoupling transformation" is applied to the translation and pitch move. The hydraulic actuator is then adopted also. A control scheme FLC is employed to meliorate ride performance in heave and pitch motion compared with passive suspensions. The about advantage of FLC is to provide human logic way instead of accurate mathematical model. The heave and pitch motion dispatch are employed to estimate ride comfort performance. The active vehicle suspension consists of ii loops. The desired force signal is firstly computed at the outer loop. For simplicity, the PID controller is and so utilized to command the forcefulness into the hydraulic actuator in the inner loop and so that the desired force indicate is obtained in a robust manner.

A nonlinear model, implemented with ADAMS/CAR [17], is introduced and co-simulated with MATLAB. The outcome shows that the attractive benefit related to ride comfort performance is achieved for the active suspension system. Moreover, instance studies or sensitivity studies could be easily carried out without additional experimental setup based on ADAMS model.

two. Planar vehicle model

The vehicle model is firstly described in this section to apply for controller analysis. A vehicle body is more often than not a rigid torso with 6-DOF motions presented in Fig. one. Information technology composes of translation motion (surge, sway, and heave) and rotation motion (roll, pitch, and yaw). These motions are constricted past suspension geometries in vehicles and are more or less coupled with another motion. Besides vehicle suspension has a mechanical construction with sprung and unsprung mass, therefore, coupling can also occur between 2 parts. Through neglecting the gyre and yaw motions and taking into account the vehicle'southward symmetry, the reduced-order mathematical model is benefited to design an active suspension system. Therefore, the vehicle's dynamics is represented by a single-runway one-half machine model in the $X$, $Z$ plane. Without loss of generality, the intermission model is valid for the assumption.

Fig. i. Vehicle motion coordinates

Fig. 2. Single-track half car linear model

The general half-car intermission model is displayed in Fig. 2, which is a linear iv-DOF system. It has a single sprung mass (car trunk) connected to ii unsprung masses (front and rear wheels) at each corner. The sprung mass is free to heave and pitch, while the unsprung masses are costless to bounce vertically with respect to the sprung mass. The passive suspensions betwixt the sprung and unsprung mass are modeled as linear viscous dampers and spring elements, while the tires are modeled as simple spring elements. In the active suspension, two hydraulic actuators are utilized to connect the sprung mass and the unsprung masses to provide active forces. Active forces are inputs of active interruption systems.

According to Newton's 2d police force, the equations of movement are derived as follows. The move equation of forepart body is given by:

(1)

$m_{1f}{\ddot{z}}_{1f}-k_f\left(z_{2f}-z_{1f}\right)-c_f\left({\dot{z}}_{2f}-{\dot{z}}_{\mathrm{i}f}\right)-F_1+k_{tf}\left(z_{\mathrm{one}f}-q_f\right)=0.$

For the rear torso:

(2)

$k_{\mathrm{ane}r}{\ddot{z}}_{\mathrm{ane}r}-k_r\left(z_{2r}-z_{1r}\right)-c_r\left({\dot{z}}_{\mathrm{two}r}-{\dot{z}}_{1r}\right)-F_{\mathrm{ii}}+k_{tr}\left(z_{\mathrm{one}r}-q_r\right)=0.$

For the car body:

(three)

$g_{\mathrm{ii}}{\ddot{z}}_c-{\mathrm{yard}}_f\left(z_{\mathrm{ii}f}-z_{1f}\right)+c_f\left({\dot{z}}_{2f}-{\dot{z}}_{\mathrm{ane}f}\right)+F_{\mathrm{i}}+{\mathrm{one\; thousand}}_r\left(z_{2r}-z_{1r}\right)+c_r\left({\dot{z}}_{2r}-{\dot{z}}_{1r}\right)+F_2=0.$

Moreover, the equation of movement for pitch motion (moment of residue) is written as Eq. (4):

(4)

$J\ddot{\phi }+b\left[{\mathrm{yard}}_r\left(z_{2r}-z_{\mathrm{one}r}\right)+c_r\left({\dot{z}}_{2r}-{\dot{z}}_{\mathrm{one}r}\right)+F_{\mathrm{ii}}\right]-a[k_f\left(z_{\mathrm{ii}f}-z_{1f}\right)+c_f\left({\dot{z}}_{2f}-{\dot{z}}_{\mathrm{ane}f}\right)+F_1]=0.$

From the half-car interruption system, the relationships amongst vertical displacements of the front end sprung$z_{2f}$, rear sprung $z_{2r}$ and vehicle trunk $z_c$ are expressed in Eqs. (5) to (8).

Eq. (5) expresses the front body:

(5)

$z_{\mathrm{ii}f}=z_c-a\mathrm{t}\mathrm{k}\phi .$

Rear body is written past Eq. (6):

(6)

$z_{2r}=z_c+b\mathrm{t}\mathrm{chiliad}\phi .$

With small pitch angle supposition $\phi$, the relationships among $z_{2f}$, $z_{2r}$ and $z_c$ tin exist rewritten by Eq. (7) and (8).

For the front trunk we have in Eq. (7) as:

(vii)

${\dot{z}}_{\mathrm{two}f}={\dot{z}}_c-a\dot{\phi }.$

Rear body is expressed in Eq. (8) as:

(8)

${\dot{z}}_{2r}={\dot{z}}_c+b\dot{\phi }.$

In club to determine the vehicle pitch and heave motion, the two route surfaces are introduced, that is, sine road and white noise road, respectively. The sine road is expressed every bit:

(9)

$z_r=h_0+\sin \left(\omega t\right),$

where $h_0$ is the aamplitude of road surface, $\omega =2\pi v/\lambda$, $v$ is the vehicle velocity, $\lambda$ is the wavelength of route surface, $t$ is time.

The international organization for standardization (ISO) has a series of standards of route roughness classification using power spectral density (P.Southward.D) (ISO1982). The road displacement P.S.D is described in Eq. (10):

(10)

$G\left(n\right)={\mathrm{Yard}}_0\frac{{\mathrm{northward}}^{-w}}{n_0},$

here, $n$ is the space frequency (yard^-i), $n_0$ is the reference space frequency, $G\left(n\right)$ is the route deportation P.S.D, $M_0$ and $w$ are the coefficient of road roughness and the coefficient of linear fitting, respectively, where, $\mathrm{west}=\text{two}$. The road surface input model is created through an inform filter via Gaussian white dissonance and which is also applied in many presented studies [18-20]. It tin be described as time domain mathematical modeling, expressed in Eq. (11) equally:

(11)

${\dot{z}}_r\left(t\right)=-2\pi f_0{z}_r\left(t\right)+2\pi \sqrt{G_{0}v}w\left(t\right),$

where $z_r\left(t\right)$ is power of route random, $f_0$ and $w\left(t\right)$ are lower limit cutoff frequency of filter and Gaussian white noise, respectively.

Combing the vehicle model equations and the road input equations, the system model and the output equations in state space form is expressed by:

(12)

$\dot{X}=AX+BU+H\mathrm{Westward},$

The country and the output variables are displayed past Eqs. (fourteen) and (15):

(14)

$X={(z_{\mathrm{ane}f},z_{1r},z_c,\phi ,{\dot{z}}_{1f},{\dot{z}}_{1r}{,\dot{z}}_c,\dot{\phi })}^T,$

(15)

$Y={(z_c,\phi ,{\dot{z}}_c,\dot{\phi })}^T.$

The input variables are, respectively, written in Eqs. (16) and (17):

(sixteen)

$U={\left(F_{\mathrm{i}}{,F}_{\mathrm{two}}\right)}^T,$

(17)

$W={\left(q_f{,q}_r\right)}^T,$

where:

$A=\left[\begin{array}{cccccccc}0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& \mathrm{one}\\ -\frac{{\mathrm{one\; thousand}}_f+k_{tf}}{{\mathrm{thousand}}_{1f}}& 0& \frac{{\mathrm{1000}}_f}{m_{1f}}& -\frac{a{k}_f}{m_{\mathrm{i}f}}& -\frac{c_f}{m_{1f}}& 0& \frac{c_f}{m_{\mathrm{ane}f}}& -\frac{a{c}_f}{{\mathrm{thou}}_{1f}}\\ 0& -\frac{k_r+k_{tf}}{m_{\mathrm{ane}r}}& \frac{m_r}{{\mathrm{chiliad}}_{1r}}& \frac{b{k}_r}{m_{1r}}& 0& -\frac{c_r}{m_{\mathrm{ane}r}}& \frac{c_r}{{\mathrm{grand}}_{1r}}& \frac{b{c}_r}{m_{1r}}\\ \frac{g_f}{{\mathrm{grand}}_{\mathrm{ii}}}& \frac{k_r}{{\mathrm{chiliad}}_2}& -\frac{k_f+{\mathrm{yard}}_r}{m_2}& \frac{a{\mathrm{chiliad}}_f-b{k}_f}{m_{\mathrm{two}}}& \frac{c_f}{{\mathrm{one\; thousand}}_2}& \frac{c_r}{m_2}& -\frac{c_f+c_r}{{\mathrm{chiliad}}_2}& \frac{a{c}_f-b{c}_r}{k_{\mathrm{ii}}}\\ -\frac{a{k}_f}{J}& \frac{b{m}_r}{J}& \frac{a{k}_f-b{k}_r}{J}& -\frac{a^2{\mathrm{chiliad}}_f+b^{\mathrm{ii}}{k}_r}{J}& -\frac{a{c}_f}{J}& \frac{b{c}_r}{J}& \frac{a{c}_f-b{c}_r}{J}& -\frac{a^{\mathrm{two}}{c}_f+b^{\mathrm{two}}{c}_r}{J}\end{array}\right],$

$B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ \frac{\mathrm{i}}{{\mathrm{chiliad}}_{1f}}& 0\\ 0& \frac{1}{m_{1f}}\\ -\frac{1}{m_2}& -\frac{\mathrm{i}}{{\mathrm{one\; thousand}}_{\mathrm{two}}}\\ \frac{a}{J}& -\frac{b}{J}\end{array}\right],H=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ \frac{k_{tf}}{k_{1f}}& 0\\ 0& \frac{{\mathrm{1000}}_{tr}}{m_{1r}}\\ 0& 0\\ 0& 0\end{array}\right],C=\left[\begin{array}{llllllll}0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& \mathrm{ane}& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right].$

3. Hydraulic actuator organization

The hydraulic actuator consists of a hydraulic cylinder and an electric spool valve. The force formula of linear electro-hydraulic actuator is represented by [21-23]:

(18)

${\dot{f}}_a=\frac{4\beta A_p{k}_v}{V_o}{\mathrm{10}}_v-\frac{4\beta A_p^{\mathrm{two}}}{V_o}\left({\dot{z}}_s-{\dot{z}}_u\right)-\frac{\mathrm{iv}\beta \left(k_c+L\right)}{V_o}{f}_a,$

where $k_c$ is the fluidic force per unit area constant. $k_v$ is valve coefficient, $A_p$ is the expanse of piston, $L$ is the coefficient of fluid leakage, $V_0$ is the book, $\beta$ is the coefficient of volumetric elastic.

The spool valve displacement ${\mathrm{ten}}_5$ is written by:

(19)

${\dot{x}}_v=-\frac{\mathrm{i}}{{\tau }_v}{\mathrm{ten}}_v+\frac{g_{\mathrm{south}\mathrm{five}}{\mathrm{grand}}_a}{{\tau }_a}v,$

where ${\mathrm{yard}}_{s\mathrm{five}}$ is the valve proceeds, ${\mathrm{1000}}_a$ is the servo amplifier gain, $v$ is the input voltage.

four. Controller design

The controller structure of active vehicle suspension consists of two loops shown in Fig. iii. The red dashed line is inner loop which is to track the desired forcefulness for the actual forcefulness. The green dashed line is the main loop which is to calculate the desired force signal. The dashed black color lines represent the mechanical bespeak. A fully benefit of this structure is that the inner loop tin can be directly used for the controller design of outer loop.

A hydraulic actuator is installed to connect the unsprung masses and the sprung mass. The PID controller is employed to the actuator in the inner control loop such that actuator can rail its desired force. The details refer to paper [23]. Information technology is assumed that the organisation does non have measurement noises and parameter uncertainties.

The control system is composed of two fuzzy controllers (the vertical vibration controller and the pitch motion controller) and i logic controller in this paper. As shown in Fig. 4, at that place are two inputs for vertical vibration controller and pitch movement controller, separately, so the 2 outputs from FLC act into one logic controller. The error vertical velocity $v$ and the modify of mistake vertical dispatch $a$ server equally the inputs in the vertical movement. The error pitch angle velocity $w$ and the change of error pitch bending acceleration $\epsilon$ are every bit the inputs in the pitch motion. The two output forces $L_1$ and ${\mathrm{50}}_2$, which are obtained from the fuzzy controller as intermediate variables, serve every bit the ii inputs of logic controller.

Fig. 3. Controller architecture

Fig. 4. Block diagram of logic control arrangement

4.1. Fuzzy logical control pattern

The command performance of a traditional controller greatly depends on an accuracy of a known system dynamic model, co-ordinate to mathematical modeling. To encounter practical requirements in an agile pause system, it is crucial to derive or to place an advisable model for the traditional controller blueprint. Estimating uncertain effects are even more than challenging due to the random noise occurred past road inputs. Hence, some model-free intelligent controllers were introduced to solve these bug, such every bit the FLC. The FLC is credited with being an adequate methodology for designing robust controllers, which is able to deliver satisfactory functioning in the face up of doubt and imprecision. Equally a result, the FLC has become a popular arroyo to nonlinear and uncertain system control in recent years. FLC is widely practical for a multifariousness of challenging control applications since it is based on linguistic synthesis and inexact mathematical model equally well as it provides a convenient method for constructing nonlinear controllers via the use of heuristic data. In other words, designing FLC is based on operator'southward feel which acts as a human being-in-the-loop controller. FLC was first introduced in the early 1970's in an attempt to design controller for systems which are structurally hard to create mathematical model attributable to naturally existing nonlinearities and modeling complexities. The vehicle dynamics by and large includes nonlinearities and uncertainties. Therefore, the FLC is proposed to cope with active suspension organization in this study.

Fig. 5. Block diagram of a typical fuzzy control system

The active control of suspension is constructed based on FLC shown in Fig. 5. The FLC controller structure has two inputs and one output. The error of velocity $e$ (vertical velocity and pitch angle velocity) and change of the error $ec$ (vertical acceleration and pitch bending acceleration) are utilized for producing a command output $u$ (moment).

FLC has three stages that are fuzzification, fuzzy inference and defuzzification. Fuzzification is to map variable from numerical values to linguistic variables. The triangular-shaped membership function is applied since they are quite basic and broadly employed. 5 grades of linguistic variables are applied to the 4 inputs: vertical velocity, vertical acceleration, and pitch angle velocity and pitch angle acceleration. Negative large (NL), negative modest (NS), NULL, positive small (PS), positive large (PL) prevarication in a scope of [–1-one]. The membership functions of positive, negative are introduced such that they encompass large ranges of uncertainties.

Defuzzification is scaled to real numbers from linguistic variables. The seven elements in the fuzzy sets of FLC outputs are employed for active suspension. The negative middle (NM) and positive middle (PM) are used as well such that the force tin be precisely controlled. The employed membership functions of the FLC are triangular for the input and output variables, respectively, shown in Fig. 6 and Fig. 7.

Fig. 6. Membership functions for the inputs $(5,a,w,\epsilon )$

Fig. 7. Membership functions for the outputs $\left(L\right)$

The relationship between inputs of the fault and mistake-in-change is defined by the rule bases. The rules are expressed by if-so rules, which extract from fundamental noesis and experience of the system and cover the input-output relations that define the control strategy. Based on the linguistic variables, the 25 fuzzy rules are divers based on the human experience. The dominion-based of active suspension organisation is displayed in Tabular array i (Bounce dominion) and Tabular array 2 (Pitch motion rule), which came from previous experience. A general form of the FLC rules tin can be defined equally: IF $e=E_i$ and $c={EC}_i$, Then $U=U_{(i,f)}$.

The fuzzy inference generates the linguistic output variable with the dominion base of operations. A Mamadani method is applied in the fuzzy inference to defuzzificate outputs. A detailed analysis and description of the FLC for vehicle suspension systems can refer in [23-25]. In add-on, stability of FLC is generally analyzed based on the traditional Lyapunov stability theory or extended Lyapunov theory. The details analysis of stability for the vehicle suspension systems tin refer to the newspaper [6, 7].

Table i. Bounce rule bases

Intermediate variable $L$		"Change-in-Error" EC $\left(a\right)$
		NL	NS	Zilch	PS	PL
"Error" $E\left(v\right)$	NL	PL	PL	PL	NS	NS
	NS	PL	PM	PS	NS	NM
	Aught	PL	PS	Nix	NS	NL
	PS	PM	PS	NS	NM	NL
	PL	PS	PS	NL	NL	NL

Table 2. Pitch rule bases

Intermediate variable $\mathrm{50}$		"Change-in-Error" EC $\left(\epsilon \right)$
		NL	NS	Zippo	PS	PL
"Error" $\mathrm{East}\left(\mathrm{westward}\right)$	NL	PL	PL	PL	PS	Nil
	NS	PL	PM	PS	NULL	NS
	Zippo	PL	PS	NULL	NS	NL
	PS	PS	Naught	NS	NM	NL
	PL	NULL	NS	NL	NL	NL

iv.2. Logic controller

Two types of motion are practical in this section. The showtime type is called translation motion (boost motion). The second 1 is called rotational motility (pitch motion). The input quantity force $F_{\mathrm{one}}$, $F_{\mathrm{two}}$ tin can be obtained from logic controller in which the intermediate variables ${\mathrm{Fifty}}_{\mathrm{i}}$, $L_{\mathrm{ii}}$ serve as the inputs to the logic controller. It can exist considered as the vibration motion of vehicle body is constructed by the resultant move both translation along the vertical management and rotational movement around C.1000.

four.2.ane. Translation motility

When a vehicle only does a translation motion, the forces $L_1$ from the front and the rear actuators are equal due to translation of vehicle torso. The activeness of the front end and the rear force actuators are shown in Fig. eight.

4.2.2. Rotational motion

When a vehicle does pitch motion around C.G., in order to restrain the moment of inertia to reduce its pitch motion, there is an upward thrust force $L_2$ from the force actuator of the front end suspension, while there must be a downward drag force $L$ from the forcefulness actuator of the rear suspensions, shown in Fig. 9. For simplicity, it is causeless that the moments of thrust strength and elevate force are equal from front end and rear intermission, respectively. By applying the analysis to both the translational motility and the rotational motion of the vehicle body, the equations of the intermediate variables $(L_{\mathrm{i}},L_2)$ and desired force $(F_1,F_2)$ are formulated as follows in Eqs. (20) to (22):

(22)

$F_{\mathrm{ii}}=L_1+{\mathrm{50}}_{\mathrm{two}}\bullet \frac{a}{b}.$

Fig. 8. Activity forces of vertical vibration

Fig. nine. Activeness forces of pitching angle vibration

five. ADAMS full car model

The ADAMS program is multibody dynamic analysis software in car application. The total vehicle model is created based on the ADAMS/Motorcar. Fig. 10 shows a total car model built in ADAMS/Auto. The proposed total vehicle model in this newspaper consists of five subsystems: front suspension, rear suspension, steering, front tire and rear tire, where the front and the rear break models are, respectively, comprised of double wishbone model and parallel link suspension.

Fig. 10. ADAMS 3D solid full auto way

Fig. eleven. The principle of Co-simulation between ADAMS/Car and MATLAB

six. Results and discussion

To ready a co-simulation environment, ADAMS/Car provides two modules, ADAMS/Controls and ADAMS/Solver. The ADAMS/Controls module generates a simulation model based on the ADAMS/Auto model, which can be imported into MALAB/Simulink. During a co-simulation, a closed loop between the ADAMS/Car model and command system is formed, every bit shown in Fig. 11. ADAMS/Car inputs of a model enter the ADAMS/Solver, which calculates the output signals from the model. The ADAMS/Solver output signals enter the command system, where MATLAB calculates the control signals, and a new iteration starts by sending the control signals and inputs to the ADAMS/Motorcar model.

To investigate the effectiveness of the integrated command system based on FLC, a simulation mode with ADAMS/Automobile and MATLAB/Simulink is constructed based on the co-simulation. FLC control algorithms are added to ADMAS/Car model. The mass of vehicle, cornering stiffness, distance from center of gravity to the forepart and rear axles are divers. The vehicle speed and the route surface are gear up likewise.

The full process using ADAMS/Car and MATLAB/Simulink was utilized as a command simulation surroundings. The parameters of vehicle model practical in the paper are given in Table 3 and these values are achieved from the ADAMS vehicle model as shown in Fig. 10. The driving speed is 50 km/h under white noise and sinusoid road surface.

Table three. Parameters used in vehicle fashion

Parameters	Value	Unit	Parameters	Value	Unit of measurement
${\mathrm{thousand}}_{1f}$	53	kg	$k_{tf}$	310000	North⁄g
$g_{1r}$	117	kg	$k_{tr}$	31000	N⁄m
$m_{\mathrm{ii}}$	663	kg	$c_f$	4165	(Due north∙s)⁄m
$J$	1067	kg∙10002	$c_r$	4165	(N∙s)⁄1000
$k_f$	58636	N/yard	$a$	i.233	m
$m_r$	58636	N/yard	$b$	i.327	one thousand

six.1. White dissonance route surface

In the first subsection, the white racket route is employed to demonstrate the efficiency of controller strategy. The ride comfort performance is compared. The vertical and pitch deportation, vertical and pitch dispatch of the vehicle is used to evaluate ride comfort performance. The vehicle responses of the trunk acceleration and the pitch angle acceleration are compared with a passive suspension system. The vehicle vertical displacement and pitch angle are firstly represented in Fig. 12(a) and (b), respectively. The vehicle vertical acceleration and pitch angle acceleration under the disturbance of white noise road are displayed in Fig. 13(a) and (b), respectively. From the results of comparison, the active pause has better performance to isolate route vibration. The Fig. 14 represents the stage plot vehicle body acceleration against vehicle velocity. The vertical motion is displayed in the Fig. 14(a), and Fig. 14(b) is shown the pitch motility. The FLC controller approaches manifestly faster convergence with corroborates the fuzzy active suspension controllable steady country. Fig. 15 shows the vehicle body acceleration aamplitude in frequency domain, in which the left of Fig. 15 is vertical move, the right one is pitch motion. It gives that fuzzy agile suspension tin can reduce at the fundamental of resonance peak points between 10⁰ and 10^ane Hz.

Fig. 12. Vehicle displacement response with passive vs. active methods

a) Vertical deportation

b) Pitch angle

Fig. 13. Vehicle acceleration response with passive vs. active methods

a) Vertical acceleration

b) Pitch bending acceleration

Fig. 14. Vehicle body response phase plot

a)

b)

Fig. 15. Vehicle body dispatch response in frequency domain

a) Vertical acceleration response

b) Pitch angle dispatch response

vi.2. Sinusoid road surface

One of the input conditions, a sinusoid road input, is employed to excite the agile suspension organisation. The vehicle vertical displacement and pitch bending are represented in Fig. 16(a) and (b), respectively. Under a sinusoid input, the responses of the vertical acceleration and the pitch angle dispatch are shown in Fig. 17.

Fig. 16. Vehicle displacement response with passive vs. active methods

a) Vertical displacement

b) Pitch bending

Fig. 17. Vehicle acceleration response with passive vs. active methods

a) Vertical acceleration

b) Pitch bending dispatch

Fig. 18. Vehicle body response phase plot

a)

b)

The stage plot displays the active fuzzy intermission can chop-chop converge in Fig. eighteen. The Fig. 19 displays the vehicle dispatch aamplitude in frequency domain under the sinusoid route surface. It also indicates that the fuzzy agile break tin can reduce the fundamental resonance pinnacle points between the 10⁰ nd 10^ane Hz both the vertical motility and pitch movement. If it is exposed to ride vibrations around nine Hz for vi-vii hours, a vehicle commuter or passengers will feel a full general sense of discomfort such equally lower jaw symptoms, abdominal pains, need to urinate and continuous muscle contraction etc.

As before the graphs were inconclusive, the RMS values of the responses were presented shown in Fig. xx. From these figures, it can be manifested that FLC has an bonny benefits in isolating vibration from road compared with passive vehicle suspension, when the vehicle drives at the white noise and the sinusoid route conditions.

Fig. 19. Vehicle body acceleration response in frequency domain

a) Vertical acceleration response

b) Pitch bending acceleration response

Fig. xx. RSM acceleration of heave and pitch motility

a) White noise road surface

b) Sine road surface

7. Conclusions

In this paper, we have developed a combined simulation scheme for fuzzy logic control of half car suspensions to meliorate ride condolement of passengers based on the heave and the pitch movement. The FLC which introduces the body acceleration and suspension travel velocity as inputs and selects forces equally outputs to control suspension system is feasible. And the 4 DOF half automobile model and decoupling transformations are introduced for simplicity in designing the controller. A multi-DOF nonlinear model, constructed in ADAMS/Automobile, is co-imitation by ADAMS/Automobile and MATLAB/Simulink to evidence the effectiveness of the controller. It is demonstrated that our proposed active interruption design shows a proficient performance to minimize the heave and the pitch angle accelerations. Information technology has been shown that the operation of ride comfort based on FLC is amend than that of the passive intermission under roughness route conditions. Therefore, it has been illustrated that the controller nosotros have designed tin provide passengers' condolement by achieving a better performance in rough road conditions.

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