Research on Active Suspension Control Based on Vehicle Speed Control Under Transient Pavement Excitation

Abstract

Transient road excitation can cause high-frequency impacts to the vehicle, leading to deterioration of smoothness and operational stability, and seriously impairing system life and performance. To address this problem, the vehicle model and the road model containing transient road excitation is first established, and the impact mechanism of transient excitation is simulated and analyzed, from which the fuzzy control of vehicle speed and the model predictive control of the suspension system are designed respectively. The suspension control method based on the speed control is further proposed, which sets the strategy to use fuzzy control to regulate the vehicle speed after the on-board sensors identify the bumpy road excitation, and at the same time to implement the model predictive control for the active suspension system, and dynamically adjusts the control weight parameters to be compatible with the vehicle speed control. The simulation results show that compared with the single suspension control, the control strategy improves in all stages, and the root mean square values of body acceleration, pitch angle acceleration, and front and rear tire dynamic loads are reduced by 9.52%, 4.55%, 29.5% and 17.8%, respectively, and the peaks are reduced by 23.8%, 39.9%, 44.7% and 33.2%, respectively, which further enhances the safety and ride comfort of the vehicle. Finally, the effectiveness and correctness of the strategy are verified by a hardware-in-the-loop test.

1. Introduction

Today, smart electric vehicles are becoming increasingly important, not only playing a key role in addressing the energy crisis and environmental issues but also providing innovative ideas for improving the active safety of vehicles [1]. Intelligent electric vehicles have led technological innovation through their high control flexibility, excellent transmission efficiency and powerful environment sensing capability, and have specially made significant progress in improving vehicle stability, optimizing drive efficiency and simplifying chassis design [2,3,4,5].

However, road surface excitations have a significant impact on the comfort and safety of smart electric vehicles. Among them, transient road excitations, such as bumpy packs and potholes, are particularly important to the vehicle [6,7]. These transient excitations not only reduce vehicle comfort and safety but also may lead to vehicle failure or loss of control. Therefore, an in-depth study of transient road excitations is essential to improve the smoothness and operational stability of intelligent electric vehicles.

In the face of transient roads, the driver often alleviates the impact and improves the ride comfort by braking deceleration. However, due to the lack of reasonable control of vehicle speed, the actual effect is limited. In addition, some vehicles equipped with passive suspension systems cannot adjust according to real-time road conditions, resulting in a significant decline in the ride comfort of electric vehicles on such roads. In reference [8], a road identification method based on instantaneous frequency and a switching control strategy of skyhook and groundhook control algorithm is proposed for transient road surface. The ride comfort of the vehicle on the mixed road with transient pavement is improved, but although a single suspension control can improve the overall vehicle dynamics performance, it does not take into account the peak deterioration on the transient pavement, resulting in the deficiency of vehicle driving stability. In reference [9], a preview control method for suspension system is proposed, which can detect the road roughness profile caused by the transient excitation in the front, and calculate the optimal control force required by the semi-active suspension system, however; the maximum control force provided by the suspension cannot suppress the huge impact caused by the transient road very well. The literature [10] proposed the use of deep reinforcement learning to stabilize the vertical motion of a vehicle traveling on rough terrain, while considering the influence of vehicle structural parameter variations on the controller performance; but in practical applications, the proposed method can be used to stabilize the vertical motion of a vehicle traveling on rough terrain. It is difficult to obtain the external environment information, and the algorithm is complex, so it is difficult to ensure the real-time and stability of the suspension system control. The single suspension control strategy is difficult to deal with the huge impact caused by the transient road.

Therefore, speed control is considered to improve the control effect of the suspension system when facing the transient road surface. For the joint control of longitudinal vehicle speed and vertical suspension system, the literature [11] helped design an ABS and ASS fuzzy cooperative control strategy with a supervisor. The cooperative controller does not work to prevent excessive interference with driver behavior. When the vehicle braking intensity is greater than or equal to the critical value, the cooperative controller is involved, and the compensation vertical load to be provided by the active suspension is solved by fuzzy control. This method emphasizes the performance of the brake system with the suspension system but ignores the improvement of the vertical suspension performance by the longitudinal speed control. By analyzing the relationship between vehicle speed and ride comfort on continuous uneven roads and the influence of vehicle speed change on ride comfort, an online description method of vehicle comfort performance index is given in the literature [12]. The optimization method of vehicle speed variation on continuous uneven roads is given, which emphasizes the optimization of vehicle speed control combined with suspension data, however, the peak performance of the vehicle impacting the road surface is not considered, which leads to the instability and safety of the vehicle.

Considering the shortcomings of the above research, this article takes convex road surfaces as the research object and designs an active suspension control method based on vehicle speed control (hereinafter referred to as LV control). It proposes longitudinal vehicle speed control and vertical body vibration suppression methods to control the vehicle speed passing through transient road surfaces and considers the adverse effects of vehicle speed changes on suspension control. Relative to previous studies, it can improve the overall comfort of the driving process, reduce the impact of transient road surfaces on the vehicle and enhance stability. The effectiveness of the method was verified through simulation analysis and further validated through hardware-in-the-loop testing.

2. Model Construction

2.1. Road Model Construction

2.1.1. Stochastic Pavement Modeling

In this study, the time domain model of pavement input is constructed by introducing filtered white noise [13,14,15]. The pavement elevation and pavement displacement satisfy the following equation:

$${\dot{z}}_q\left(t\right)=-2\pi f_0{z}_q\left(t\right)+2\pi n_0\sqrt{G_q\left(n_0\right)v}W\left(t\right)$$

(1)

where $z_q\left(t\right)$ is the pavement elevation; $n_0$ is the standard spatial frequency; $G_q\left(n_0\right)$ is the pavement unevenness coefficient; which takes the value of 64 × 10⁻⁶ m³ in this paper, i.e., class B pavement; $v$ is the vehicle speed; and $W\left(t\right)$ is the stochastic Gaussian white noise with the mean value of one.

2.1.2. Model Construction of Bumpy Pavement

The impact of transient road surface excitations such as bumpy packs and speed bumps seriously affects the driving stability and comfort of the vehicle when the smart electric vehicle is in motion. In this paper, the bumpy packet road excitation refers to the related literature [16] and establishes the bumpy packet road as shown in Figure 1.

The pavement represents a bump with a height of 0.1 m and a width of 4 m. The pavement elevation satisfies the following equation:

$$z_r={\displaystyle \frac{0.1}{2}}\left(1-\mathit{cos}\left(2\pi ·{\displaystyle \frac{x}{4}}\right)\right)$$

(2)

where $z_r$ is the convex packet pavement elevation, $x\in \left[0, 4\right]$.

In this study, a pavement with bumps is set up and the bumps are set at 100 m from the starting point, and the mathematical model of the unevenness of the longitudinal section of the pavement can be expressed as:

$$y=\left\{\begin{array}{c} { z}_q 0\le x\le 100 \mathrm{m}\\ z_r={\displaystyle \frac{0.1}{2}}\left(1-\mathit{cos}\left(2\pi ·{\displaystyle \frac{x-100}{4}}\right)\right) 100\le x\le 104 \mathrm{m}\\ z_q 104\le x\le 110 \mathrm{m}\end{array}\right.$$

(3)

where $x$ is the distance from the starting point.

Equations (1) and (3) were modeled and the pavement elevation data for this pavement was outputted to create a class B pavement with transient pavement excitation required for simulation.

2.2. Mechanism of the Effect of Transient Road Excitation on Vehicle Dynamics

2.2.1. Brake Model

The brake is a widely used disc brake, and the friction in the brake meets the following requirements:

$$F\left(v\right)=\mu \left|F_N\right|sign\left(v\right)$$

(4)

$$F_f=\mu F_N\mathit{tan}\left({\displaystyle \frac{2v_r}{v_d}}\right)$$

(5)

where $F\left(v\right)$ is the brake friction, $F_f$ is the brake disc friction, $F_N$ is the brake positive pressure, μ is the coefficient of friction, $sign\left(v\right)$ is the relative velocity function, $v_r$ is the relative velocity between the brake friction pad and the brake disc and $v_d$ is the threshold velocity magnitude.

The mechanical expression for this brake is as follows:

$$P_c={\displaystyle \frac{T}{k·r_{b}A}}$$

(6)

where $P_c$ is the brake master cylinder pressure, T is the brake target torque, $k$ is the efficiency factor, $r_b$ denotes the brake equivalent friction radius and $A$ is the equivalent contact area.

2.2.2. Active Suspension Model

Since the lateral changes of the vehicle are not considered in the scenario studied in this paper, only the semi-vehicle active suspension model as shown in Figure 2 is required for modeling the suspension.

According to the vehicle dynamics, the differential equation of motion of the suspension system is as follows:

$$\left\{\begin{array}{c}{\displaystyle \genfrac{}{}{0pt}{}{m_b{\ddot{x}}_b+k_{s1}\left(x_{b1}-x_{w1}\right)+C_{s1}\left({\dot{x}}_{b1}-{\dot{x}}_{w1}\right)-u_1+k_{s2}\left(x_{b2}-x_{w2}\right)+C_{s2}\left({\dot{x}}_{b2}-{\dot{x}}_{w2}\right)-u_2=0}{I_{yy}\ddot{\theta }-a\left(k_{s1}\left(x_{b1}-x_{w1}\right)+C_{s1}\left({\dot{x}}_{b1}-{\dot{x}}_{w1}\right)-u_1\right)+b\left(k_{s2}\left(x_{b2}-x_{w2}\right)+C_{s2}\left({\dot{x}}_{b2}-{\dot{x}}_{w2}\right)-u_2\right)=0}}\\ m_{w1}{\ddot{x}}_{w1}+k_{u1}\left(x_{w1}-x_{r1}\right)-k_{s1}\left(x_{b1}-x_{w1}\right)-C_{s1}\left({\dot{x}}_{b1}-{\dot{x}}_{w1}\right)+u_1=0\\ {\displaystyle \genfrac{}{}{0pt}{}{m_{w2}{\ddot{x}}_{w2}+k_{u2}\left(x_{w2}-x_{r2}\right)-k_{s2}\left(x_{b2}-x_{w2}\right)-C_{s1}\left({\dot{x}}_{b2}-{\dot{x}}_{w2}\right)+u_1=0}{\begin{array}{c}{x}_{b1}=x_b-a\theta \\ x_{b2}=x_b+b\theta \end{array}}}\end{array}\right.$$

(7)

where the subindex, $b$ is the car body, $w$ is the wheel, $r$ is the road, $s$ is the spring and u is the tire. As for the other variables, $m_b$ is the body mass, $k_{s1}$ and $k_{s2}$ are the spring stiffnesses of the front and rear suspensions, respectively, $C_{s1}$ and $C_{s2}$ are the damping coefficients of the front and rear shock absorbers, $I_{yy}$ is the inertia of rotation of the body, a and b are the distances from the front and rear axles to the center of mass of the vehicle, $m_{w1}$ and $m_{w2}$ are the mass of the front and rear wheels, $k_{u1}$ and $k_{u2}$ are the stiffnesses of the front and rear tires, and θ is the body pitch angle and $u_1$ and $u_2$ are the active force of the active suspension.

2.2.3. Transient Pavement Excitation Characterization

In order to analyze the specific effects of transient road excitation on vehicle dynamics performance, the dynamics response of the vehicle passing through the bumpy pavement was simulated at different driving speeds, and the peak changes in the dynamic performance of the vehicle at different speeds are shown in Figure 3, Figure 4, Figure 5 and Figure 6.

The simulation results show that the vehicle’s body acceleration and tire dynamic load indicators increase with increasing speed as the vehicle passes through the bumpy pack section. This is due to the fact that the increase in speed leads to a reduction in the response time of the vehicle system to the high-frequency excitation, making the process similar to a rigid body collision, which in turn leads to a deterioration in performance. The increase in vehicle speed also reduces the magnitude of the body attitude response, so that the pitch angle acceleration index of the body appears to decrease with the increase in vehicle speed.

This shows that vehicle speed has a very important influence on vehicle dynamics under transient road excitation. In order to improve the dynamic performance of the vehicle under transient road excitation, this paper carries out research in longitudinal speed control and vertical suspension system control.

3. Speed and Suspension Control Strategy Design

3.1. Speed Control

In this study, it is set that the vehicle starts to decelerate at 80 m from the bump, and the speed of the vehicle traveling is controlled by inputting the appropriate brake master cylinder pressure.

In order to cope with the complexity and variability of the actual traffic environment and the poor real-time accuracy of the specific brake pressure calculation, this study adopts the fuzzy control method, which has good stability and robustness in dealing with similar problems.

According to the actual driving process, the process of the vehicle passing through the convex bag is divided into three stages, which are: the uniform speed driving stage under the normal driving of the vehicle, the braking stage in which the sensor recognizes the convex bag ahead for braking and decelerating and the convex bag stage in which the vehicle arrives at the convex bag and glides through the convex bag.

In this study, a detailed setting is carried out for the process of vehicle passing through the bumpy road surface, the initial speed is set to 50 km/h, and based on the actual driving experience, the speed of passing through the bumpy road surface is controlled to be 20 to 25 km/h. According to the speed difference $e_v$ and the distance of the bumpy road surface identified by the sensors $e_s$, the braking torque is dynamically adjusted in order to achieve smooth deceleration and to improve the passing efficiency. The structure diagram of the system is shown in Figure 7. The fuzzy control rules are shown in

Table 1. Fuzzy control rule table.

T		${\mathit{e}}_{\mathit{V}}$
		O	S	M	L	V
${\mathit{e}}_{\mathit{s}}$	O	O	M	L	V	V
	S	O	M	L	V	V
	M	O	S	M	L	L
	L	O	S	M	M	L
	V	O	S	S	M	M

, where the speed control requirements in this study are not complex, and it can meet the basic needs; so, the fuzzification of the input and output quantities selected five more basic fuzzy subsets, which are O (very low), S (medium-low), M (medium), L (medium-high) and V (very high). The control rules are based on the following situations: when the speed difference $e_v$ is large and the distance from the bump $e_s$ is small, the braking torque is increased to decelerate quickly; when the speed difference $e_v$ is small and the distance from the bump $e_s$ is large, the braking torque is reduced to rely on skidding and friction to decelerate; when the speed difference $e_v$ is large and the distance to the convex packet $e_s$ is large, the speed is moderately adjusted and the control continues to be optimized according to the real-time conditions.

The final speed control is shown in Figure 8.

3.2. Suspension Control

3.2.1. Model Predictive Controller Design

Model predictive control (MPC) can satisfy the need to control various types of performance metrics to effectively cope with abrupt changes such as transient road excitation [17]. The established suspension model is a nonlinear system, therefore, a general form of the discrete model as shown in Equation (8) can be considered as follows:

$$\left\{\begin{array}{c}\xi \left(t+1\right)=f\left(\xi \left(t\right),u\left(t\right)\right)\\ \eta \left(t+1\right)=h\left(\xi \left(t\right)\right)\end{array}\right.$$

(8)

where $f\left(x\right)$ denotes the system state transfer function, $h\left(x\right)$ denotes the system output transfer function, $\xi \left(t\right)$ denotes the system state variable, $u\left(t\right)$ denotes the system control variable, $\xi \left(t\right)\in X,u\left(t\right)\in \Gamma$, $X,\Gamma$ denotes the constraints on the system state variable, and output variable and $\eta \left(t\right)$ denotes the system output variable.

Further processing yields a linear time-varying discrete model:

$$\epsilon \left(k+1\right)=A_{k,t}\epsilon \left(k\right)+B_{k,t}\omega \left(k\right)$$

(9)

where $\epsilon \left(k\right)$ is the system state quantity at moment $k$, $\omega \left(k\right)$ is the system control quantity at moment and $k$, $A_{k,t}$ and $B_{k,t}$ are the coefficient matrices at moment.

Combining the system output variables and setting $\tilde{\epsilon }(k\mid t)=\left[\begin{array}{c}\epsilon (k\mid t)\\ \omega (k-1\mid t)\end{array}\right]$, implying the predicted value of the variable, other cases are synonymous. We obtain the new state space expression:

$$\left\{\begin{array}{c}\tilde{\epsilon }\left(k+1∣t\right)={\tilde{A}}_{k,t}\tilde{\epsilon }\left(k∣t\right)+{\tilde{B}}_{k,t}\mathrm{\Delta }\omega \left(k∣t\right)\\ \eta \left(k∣t\right)={\tilde{C}}_{k,t}\tilde{\epsilon }\left(k∣t\right)+{\tilde{D}}_{k,t}\mathrm{\Delta }\omega \left(k∣t\right)\end{array}\right.$$

(10)

where $\eta \left(t\right)$ is the system output variable, ${\tilde{A}}_{k,t}=\left[A_{k,t},B_{k,t}\right],{\tilde{B}}_{k,t}=B_{k,t},{\tilde{C}}_{k,t}=\left[C_{k,t},D_{k,t}\right],{\tilde{D}}_{k,t}=D_{k,t},\mathrm{\Delta }\omega (k\mid t)=\omega (k\mid t)-\omega (k-1\mid t)$.

The stability of the control process cannot be separated from the appropriate optimization objective, here we set the k-moment step size as $N_P$ and establish the optimization objective function:

$$J\left(k\right)=\sum _{i=1}^{N_p}{\eta }^T\left(k+i∣k\right)Q\eta \left(k+i∣k\right)$$

(11)

where Q is the matrix of weight coefficients set at moment k, the smoothness of the control system, along with the optimization priorities representing the system’s performance indicators.

The transient road excitation scenarios considered in this paper require a fast response from the suspension system and need to deal with multiple constraints. Transforming the optimized performance metrics into a quadratic programming form:

$${\displaystyle \genfrac{}{}{0pt}{}{min\sum _{i=1}^{N_p}{\eta }^T\left(k+i∣k\right)Q\eta \left(k+i∣k\right)}{s.\mathrm{t}.{\theta }_t\mathsf{\Delta }U\left(t\right)\le \alpha }}$$

(12)

where $\mathsf{\Delta }U\left(t\right)$ is a vector matrix consisting of the optimal suspension control forces obtained from each calculation, and $\alpha$ is a threshold matrix set to prevent the vehicle suspension from exceeding the limit block, which limits the dynamic suspension deflection of the wheels. The specific form is as follows:

$$\mathrm{\Delta }U\left(t\right)={\left[\begin{array}{cccc}\mathrm{\Delta }\omega \left(t∣t\right)& \mathrm{\Delta }\omega \left(t+1∣t\right)& \cdots & \mathrm{\Delta }\omega \left(t+N_c∣t\right)\end{array}\right]}^T$$

(13)

$$\alpha =f{d}_{max}{I}_{n\times 1}-D\epsilon$$

(14)

$${\theta }_t={\left[\begin{array}{cccc}{\tilde{C}}_t{\tilde{B}}_t& 0& \cdots & 0\\ {\tilde{C}}_t{\tilde{A}}_t{\tilde{B}}_t& {\tilde{C}}_t{\tilde{B}}_t& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{C}}_t{\tilde{A}}_t^{N_c-1}{\tilde{B}}_t& {\tilde{C}}_t{\tilde{A}}_t^{N_c-2}{\tilde{B}}_t& \cdots & {\tilde{C}}_t{\tilde{B}}_t\\ {\tilde{C}}_t{\tilde{A}}_t^{N_c}{\tilde{B}}_t& {\tilde{C}}_t{\tilde{A}}_t^{N_c-1}{\tilde{B}}_t& \cdots & {\tilde{C}}_t{\tilde{A}}_t{\tilde{B}}_t\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{C}}_t{\tilde{A}}_t^{N_p-1}{\tilde{B}}_t& {\tilde{C}}_t{\tilde{A}}_t^{N_p-2}{\tilde{B}}_t& \cdots & {\tilde{C}}_t{\tilde{A}}_t^{N_p-N_c-1}{\tilde{B}}_t\end{array}\right]}_{p\times c}$$

(15)

Assuming that the system state quantity $\epsilon \left(k\right)$ is available at each moment in time and solved by the quadratic programming method in each control cycle, thus obtaining the control input increment in the control time domain, the first element in the control matrix is applied to the system as the control input increment, i.e., $\omega \left(t\right)=\omega (t-1)+\mathrm{\Delta }{\omega }_t$, and the subsequent process model predicts that the controller will loop through this process.

3.2.2. Determination of Control Parameters

In this paper, the prediction step is defined as 30 and the control step as 20, and the body acceleration, pitch angle acceleration, and tire dynamic load are selected as the performance evaluation indexes and different weight parameters are specified on different road surfaces so as to improve the overall control effect. The parameters are selected according to the optimization-seeking objective function:

$$P_{\mathrm{optional} }=min\left\{\sqrt{\left[q_1{⟨{\displaystyle \frac{rms\left(a\right)}{rms(a{)}_{\mathrm{passive} }}}⟩}^2\right]+\left[q_2{⟨{\displaystyle \frac{rms\left(r\right)}{rms(r{)}_{\mathrm{passive} }}}⟩}^2\right]+\left[q_3{⟨{\displaystyle \frac{rms\left(F\right)}{rms(F{)}_{\mathrm{passive} }}}⟩}^2\right]}\right\}$$

(16)

where $q_1$, $q_2$ and $q_3$ represent the weighting coefficients of vehicle body acceleration, pitch angle acceleration and tire dynamic load, respectively. When the vehicle is driving on the B road surface, comfort is the main focus and priority is given to optimizing body acceleration, and when the vehicle passes the bumpy road surface, body pitch is hard to avoid and priority is given to improving the tire dynamic load in order to ensure safety. $rms\left(a\right)$, $rms\left(r\right)$ and $rms\left(F\right)$ are the root mean square (RMS) of the three performance indicators. $rms(a{)}_{\mathrm{passive} }$, $rms(r{)}_{\mathrm{passive} }$ and $rms(F{)}_{\mathrm{passive} }$ are the RMS of the reference passive suspension.

3.3. Design of Active Suspension Control Strategy Based on Vehicle Speed Control

This study proposes a longitudinal and vertical control method as shown in Figure 9. The longitudinal fuzzy control has better real-time performance relative to other control methods and has relatively low requirements for sensors and other configurations, whereas the vertical suspension MPC control can effectively satisfy the various needs of the control, but the arithmetic is relatively slow and combining it with the longitudinal control can make up for this disadvantage to ensure the real-time performance of the entire control.

In this control strategy, a synergistic controller is added, aiming at the synergistic control of the two control modes, weakening the problem of control degradation due to the longitudinal and vertical coupling relationship and improving the overall control effect. The driving stages are divided according to the longitudinal speed control information, and the control weight coefficients of the suspension system are adjusted: in the initial uniform speed stage, the smoothness of vehicle driving is ensured, and the focus is on the suppression of body vibration; after identifying the transient excitation, the speed controller starts to adjust the vehicle speed, and the resulting changes in the body attitude lead to the decrease of comfort, and the focus is on the suppression of body pitch to ensure the comfort of the drivers and passengers; when passing through the transient road surface, the impact brought by the road surface is easy to lead to the safety of the vehicle; at this time, focus on the control of tire dynamic load to ensure the safety of the vehicle.

4. Results

4.1. Analysis of Simulation Results

4.1.1. Analysis of Single Control Simulation Results

To evaluate the effectiveness of the vehicle control strategy proposed in this paper under transient road excitation, the vehicle response under single longitudinal control, single suspension control and no control conditions are compared through simulation. In the simulation, a bumpy road surface is modeled at 100 m in front of the vehicle:

(1)

Single speed control: the vehicle performs braking and passes with reduced speed upon detection of the bumpy pack, aiming to assess the effect of deceleration on smoothness;

(2)

Single suspension control: the vehicle speed is kept constant and the active suspension is adjusted by model predictive control (MPC) to optimize the performance when passing the bump;

(3)

No control condition: the vehicle passes through the bumpy pack at 50 km/h, equipped with a passive suspension, which serves as a control group.

The relevant simulation parameters are shown in

Table 2. Model-related parameters.

Parametric	Value	Parametric	Value
$m_b$[kg]	1270	$k_{s1}[\mathrm{N}·{\mathrm{m}}^{-1}]$	27,000
$m_{w1}$[kg]	66.3	$k_{s2}[\mathrm{N}·{\mathrm{m}}^{-1}]$	30,000
$m_{w2}$[kg]	66.3	$C_{s1}[\mathrm{N}·\mathrm{s}{·\mathrm{m}}^{-1}]$	6000
a[m]	1.015	$C_{s2}[\mathrm{N}·\mathrm{s}{·\mathrm{m}}^{-1}]$	6000
b[m]	1.895	$k_{u1}[\mathrm{N}·{\mathrm{m}}^{-1}]$	268,000
$I_{yy}[\mathrm{k}\mathrm{g}·{\mathrm{m}}^2]$	1536.7	$k_{u2}[\mathrm{N}·{\mathrm{m}}^{-1}]$	268,000

:

The control weight coefficients selected in the simulation are shown in

Table 3. Selection of control weight parameters for model prediction based on pavement type.

Pavement	$\mathbf{Body} \mathbf{Acceleration} {\mathit{q}}_1$	$\mathbf{Pitch} \mathbf{Acceleration} {\mathit{q}}_2$	$\mathbf{Tire} \mathbf{Dynamic} \mathbf{Load} {\mathit{q}}_3$
Class B	8	1	1
Bumpy road	3	1	6

, which are based on the control demands of different road surfaces analyzed in the previous section, with a certain degree of subjectivity, and similar results can be obtained for other similar parameters.

Figure 10, Figure 11, Figure 12 and Figure 13 demonstrate the simulation results of body acceleration, pitch angle acceleration and front and rear tire dynamic loads under different control conditions.

Due to the short time for the vehicle to pass through the bumpy pack road surface, the peak data of the performance indexes better reflect the transient performance of the suspension system to cope with the impact when studying this transient excitation. Therefore, when analyzing the simulation results, this paper presents the root mean square value data when the vehicle is driving on a graded road surface and the peak data when driving on a bumpy pack road surface, as shown in

Table 4. Comparison of root mean square values of single control and uncontrolled vehicle dynamics performance in class B pavement stage.

Description	Unit	RMS Value			Single Speed Control vs. No Control	Single Suspension Control vs. No Control
		No Uncontrol	Single Speed Control	Single Suspension Control
Body acceleration	m/s2	1.12	0.83	0.63	↓25.9%	↓43.7%
Pitch acceleration	rad/s2	0.53	0.49	0.44	↓7.54%	↓17.0%
Left front tire dynamic load	N	1692	1835	1356	↑8.45%	↓19.9%
Left rear tire dynamic load	N	1803	1753	1534	↓2.77%	↓14.9%

and

Table 5. Comparison of peak vehicle dynamics performance between single control and uncontrolled vehicle dynamics in the convex pack road stage.

Description	Unit	Peak Value			Single Speed Control vs. No Control	Single Suspension Control vs. No Control
		No Uncontrol	Single Speed Control	Single Suspension Control
Body acceleration	m/s2	12.6	6.76	5.00	↓46.3%	↓60.3%
Pitch acceleration	rad/s2	6.39	3.76	1.98	↓41.1%	↓69.0%
Left front tire dynamic load	N	22,245	12,212	5472	↓45.1%	↓75.4%
Left rear tire dynamic load	N	23,162	11,833	6629	↓48.9%	↓71.4%

, respectively.

The simulation results show that under single speed control, the speed reduction effectively reduces the peaks of body acceleration, pitch angle acceleration and tire dynamic load when the vehicle passes through the bumpy pack road surface, but the improvement of pitch angle acceleration is limited during braking deceleration and the tire dynamic load sometimes even deteriorates.

Although the single suspension control strategy improves the overall dynamic performance, the lack of effective longitudinal speed control results in poor control of the smoothness of passing through the convex pack, which is affected by the speed of the vehicle.

In summary, although the single speed and suspension control strategies have positive effects on improving the dynamics of smart electric vehicles, they are still insufficient in different driving phases and more integrated control strategies are needed to achieve better performance.

4.1.2. Comparative Analysis of LV Control Simulations

The control weights are reclassified according to the driving phases, i.e., body acceleration is preferred to be improved in the uniform speed phase, pitch angle acceleration is preferred in the braking phase, wheel dynamic load is preferred when passing through the cambered pack, the parameters of the suspension control weights based on the speed control are shown in

Table 6. Selection of control weight parameters for model prediction based on driving phases.

Traveling Stage	$\mathbf{Body} \mathbf{Acceleration} {\mathit{q}}_1$	$\mathbf{Pitch} \mathbf{Acceleration} {\mathit{q}}_2$	$\mathbf{Tire} \mathbf{Dynamic} \mathbf{Load} {\mathit{q}}_3$
Uniform speed	8	1	1
Decelerations	2	6	1
Bumpy	1	1	6

, Figure 14, Figure 15, Figure 16 and Figure 17 show the comparison between the LV control strategy and the single control strategy in terms of body acceleration, pitch angle acceleration and front and rear wheel tire dynamic loads. The related root mean square values and peak values are shown in

Table 7. Comparison of root mean square values of vehicle dynamics performance between LV control and single control in class B pavement stage.

Description	Unit	RMS Value			LV Control vs. Single Speed Control	LV Control vs. Single Suspension Control
		Single Speed Control	Single Suspension Control	LV Control
Body acceleration	m/s2	0.83	0.63	0.57	↓31.3%	↓9.52%
Pitch acceleration	rad/s2	0.49	0.44	0.46	↓6.12%	↑4.55%
Left front tire dynamic load	N	1835	1356	955.8	↓47.9%	↓29.5%
Left rear tire dynamic load	N	1753	1534	1261	↓28.1%	↓17.8%

and

Table 8. Comparison of peak vehicle dynamics performance between LV control and single control in the convex pack road stage.

Description	Unit	Peak Value			LV Control vs. Single Speed Control	LV Control vs. Single Suspension Control
		Single Speed Control	Single Suspension Control	LV Control
Body acceleration	m/s2	6.76	5.00	3.81	↓43.6%	↓23.8%
Pitch acceleration	rad/s2	3.76	1.98	1.19	↓68.3%	↓39.9%
Left front tire dynamic load	N	12,212	5472	3024	↓75.2%	↓44.7%
Left rear tire dynamic load	N	11,833	6629	4429	↓44.0%	↓33.2%

.

There is a significant improvement in body acceleration with the introduction of this control strategy. As shown in Figure 14, the LV control strategy reduces the root mean square values of body acceleration by 31.3% (compared with speed control) and 9.52% (compared with suspension control) on class broad surfaces and reduces the peak values by 43.6% and 23.8% on bumpy pack road surfaces, respectively, compared with the single control.

Figure 15 further reveals the effect of the strategy on pitch angle acceleration control, where the peaks are reduced by 68.3% and 39.9%, respectively, on convex packet pavements. The RMS value is improved by 4.55% compared to the single suspension control on class B pavements, which is because of the speed variation on the body pitch.

Figure 16 and Figure 17 demonstrate the benefits of tire dynamic load control. The RMS and peak values of front and rear wheel dynamic loads are significantly reduced compared to both the single speed control and the single suspension control for both B-road and cambered pavement.

In summary, the active suspension control strategy based on speed planning brings better improvement in vehicle dynamics, both on the relatively smooth class B road surface and on the high-impact cambered pack road surface.

4.2. Hardware-in-the-Loop Test Validation and Analysis

To verify the effectiveness of the LV control method designed in this paper, the specific simulation process will be verified using HIL hardware-in-the-loop (HIL) experiments. HIL experiment is a kind of testing method that connects real controllers or devices to a simulated simulation environment. In this way, the function and performance of the controller or device can be tested comprehensively and systematically without relying on real physical objects. The experiment can save cost and ensure the safety of the experimental process and improve the efficiency of the research. The effectiveness of the control method proposed in this paper can be verified by comparing the obtained experimental results with the simulation results.

4.2.1. Experimental Design

In this study, the ECU hardware design draws on the scheme of the existing literature and selects the MCU model STM32F103VET6. While the core of the software design is the embedded C code, this study is based on the model design (MBD), which is processed with the help of the toolbox (Simulink Coder) of the simulation software to automatically generate the embedded code, and then locally modify and optimize it.

The test system scheme is shown in Figure 18, the host computer is a personal computer, and the target machine is an embedded controller model Yanhua 610 L. The test process is as follows: Firstly, the simulation model is discretized in the host computer, then the controlled system model and environment model are extracted, and then the driver module of the I/O board is added to provide software support for the data transmission between the board and the target machine, and finally the corresponding output module is added to visualize and store the real-time operation data of the target machine; then the host computer downloads the simulation model to the target machine through the TCP/IP protocol. Then, the host machine downloads the simulation model to the target machine through TCP/IP protocol; after the system is running, the target machine outputs the vehicle dynamic information collected by the sensors to the ECU, and the ECU outputs the required actual braking force and suspension force after calculation.

4.2.2. Analysis of Test Results

Based on the hardware-in-the-loop test program, the vehicle is driven on a road surface containing transient road excitations according to a speed control curve for longitudinal and vertical co-control and the vehicle dynamics performance metrics obtained from the tests are compared with the simulation results. In addition, the LQR control algorithm will be introduced for comparison under the same conditions. The objective of the LQR control is to minimize the integral value of the weighted squares of the body acceleration, pitch angle acceleration and the tire dynamic loads in the time domain T, with equal weighting coefficients for each of the performance metrics and the results of the comparisons are shown in Figure 19, Figure 20, Figure 21 and Figure 22.

Specific data comparisons are shown in

Table 9. Comparison of hardware-in-the-loop test and simulation results for the root mean square value of the class B pavement stage.

Description	Unit	RMS Value			HIL vs. LV	LQR vs. LV
		LV	HIL	LQR
Body acceleration	m/s2	0.57	0.58	0.64	↑1.6%	↑10.9%
Pitch acceleration	rad/s2	0.46	0.47	0.57	↑2.1%	↑23.9%
Left front tire dynamic load	N	956	968	1065	↑1.3%	↑11.4%
Left rear tire dynamic load	N	1261	1268	1414	↑0.6%	↑12.1%

and

Table 10. Hardware-in-the-loop test vs. simulation result peaks.

Description	Unit	Peak Value			HIL vs. LV	LQR vs. LV
		LV	HIL	LQR
Body acceleration	m/s2	3.81	4.02	4.57	↑5.5%	↑19.9%
Pitch acceleration	rad/s2	1.19	1.28	1.34	↑7.6%	↑12.6%
Left front tire dynamic load	N	3024	3224	3751	↑6.6%	↑24.0%
Left rear tire dynamic load	N	4429	4648	4976	↑4.9%	↑12.3%

, which compare the root mean square (RMS) values and peak data for the full course of the test and simulation, respectively.

Firstly, by observing the HIL results it can be found that the results of the proposed method in this study applied in real controllers have less error with simulation, which is within the acceptable range. By comparing the simulation results with LQR, it can be found that the overall root mean square value is better than the LQR control when driving on regular road surfaces because the LV control takes into account the effect of the speed change, whereas in the transient road phase, even though the speed is also lowered to the target speed, the LQR control cannot switch the control weights with the road surface, which makes the peak data not as good as that of the LV control as well.

Therefore, through the controller validation of HIL and the comparison of other algorithms, it can be proved that the LV control method proposed in this study can effectively improve the ride comfort and operational stability of the vehicle when coping with transient road surfaces and it also has certain potential for practical application.

5. Conclusions

In this study, an active suspension control strategy based on vehicle speed control is proposed to address the problem of vehicle performance degradation under transient road excitation. Through the establishment of a vehicle model and transient road surface model, a suspension model prediction control method is designed based on longitudinal vehicle speed fuzzy control. The simulation and hardware-in-the-loop test results verify the effectiveness of the strategy in improving vehicle dynamics and enhancing driving safety.

Despite the subjectivity in the selection of weight coefficients, the proposed method in this study points out the necessity of considering longitudinal speed in suspension control, which proves that the upper limit of suspension performance can be improved through the combination of speed and suspension control, and enables the vehicle to better cope with all kinds of road excitations in the process of real driving and provides a new way of thinking for the subsequent research related to speed control and suspension control.