Motion Sickness Suppression Strategy Based on Dynamic Coordination Control of Active Suspension and ACC

Abstract

With the development of electrification and intelligent technologies in vehicles, ride comfort issues represented by motion sickness have become a key constraint on the performance of autonomous driving. The occurrence of motion sickness is influenced by the comprehensive movement of the vehicle in the longitudinal, lateral, and vertical directions, involving ACC, LKA, active suspension, etc. Existing motion sickness control method focuses on optimizing the longitudinal, lateral, and vertical directions separately, or coordinating the optimization control of the longitudinal and lateral directions, while there is relatively little research on the coupling effect and coupled optimization of the longitudinal and vertical directions. This study proposes a coupled framework of ACC and active suspension control system based on MPC. By adding pitch angle changes caused by longitudinal acceleration to the suspension model, a coupled state equation of half-car vertical dynamics and ACC longitudinal dynamics is constructed to achieve integrated optimization of ACC and suspension for motion suppression. The suspension active forces and vehicle acceleration are regulated coordinately to optimize vehicle vertical, longitudinal, and pitch dynamics simultaneously. Simulation experiments show that compared to decoupled control of ACC and suspension, the integrated control framework can be more effective. The research results confirm that the dynamic coordination between the suspension and ACC system can effectively suppress the motion sickness, providing a new idea for solving the comfort conflict in the human vehicle environment coupling system.

1. Introduction

Motion sickness is a physiological functional disorder syndrome that occurs in specific motion environments, characterized by typical symptoms such as motion sickness, nausea, vomiting, and cold sweats. Its underlying mechanism stems from neural compensatory imbalance triggered by perceptual conflicts among the vestibular, visual, and proprioceptive systems [1]. With the accelerated transformation of the automotive industry toward the “new four modernizations”, L2 and above-intelligent EVs have become core components of urban intelligent transportation systems [2]. However, this shift has been accompanied by a significant increase in the incidence of in-vehicle motion sickness, which compromises the comfort of transportation experiences [3].

From the perspective of vehicle dynamics, the longitudinal and vertical dynamic characteristics of EVs are key factors aggravating motion sickness. The high torque and rapid response of electric motors, combined with electro-mechanical braking, result in nonlinear fluctuations during acceleration/deceleration, suspension vibrations induced by road excitation reduce ride comfort, the coupling effect between suspension vibrations and longitudinal dynamic induces pitch motion, significantly increasing motion sickness risk [4]. Autonomous driving tends to cause sensory conflict between visual and vestibular systems, thereby increasing the likelihood of motion sickness occurrence [5].

Thus, against the backdrop of electrification and intelligentization, motion sickness-related ride comfort has emerged as a critical issue that cannot be overlooked. There is an urgent need to incorporate motion sickness mitigation metrics into vehicle control systems. Current research on motion sickness in intelligent EVs primarily focuses on two aspects: motion sickness prediction and motion sickness suppression control. Research on motion sickness prediction can be further divided into intrinsic physiological mechanisms of motion sickness and the correlation between vehicle motion parameters and motion sickness incidence.

In the study of intrinsic physiological mechanisms of motion sickness, Keshavarz et al. [6] systematically summarized the physiological mechanisms of neural compensatory imbalance, while Laessoe et al. [7] and Ng et al. [8] demonstrated the regulatory effect of visuo-vestibular synchronization on symptoms. Gruden et al. [9] further validated through EGG that such conflicts directly translate into quantifiable physiological signals. Studies also identified significant individual variability in susceptibility, with motion sickness-prone individuals exhibiting higher sensitivity to perceptual mismatches [10,11].

In the study of the relationship between vehicle motion parameters and motion sickness, longitudinal, lateral, and vertical accelerations are found to significantly correlate with motion sickness [12]. Zhao et al. [13] established a prediction model using vehicle accelerations through driving tests, and Tian et al. [14] further added trip duration and individual variability in the model to improve prediction accuracy. Iskander et al. [15] specifically investigated non-driving-related activities in autonomous vehicles, developing a predictive framework for such scenarios. Kia et al. [16] experimentally verified that active suspension seats could reduce WBV and corresponding motion sickness. Jin et al. [17] demonstrate that semi-active suspension can effectively alleviate motion sickness by suppressing vertical acceleration and pitch angular velocity.

Based on the foregoing analysis, motion sickness primarily stems from two physiological mechanisms: sensory conflict between visual and vestibular inputs and the impact of vehicle motion states. Critical vehicle-induced motion sickness parameters include vertical acceleration at the center of mass, pitch angular velocity, and longitudinal acceleration, all of which demonstrate strong correlations with motion sickness incidence.

In the field of motion sickness suppression control, researchers have achieved preliminary results in both vehicle dynamics optimization and intelligent motion planning algorithms.

Cui et al. [18] proposed an adaptive wheelbase preview robust H_∞ control method that can accurately identify road roughness information and suppress vehicle body vibration. It not only satisfies driving smoothness but also takes into account passenger driving experience. Chen et al. [19] proposed an intelligent chassis-coordinated control algorithm that combines wheel ground tangential force control that effectively improves the vertical vibration acceleration level of the body, reduces the incidence rate of motion sickness, and improves the driving comfort and other comprehensive performance of intelligent chassis vehicles. Feng et al. [20] proposes a model predictive control-based integrated torque vectoring and active suspension strategy, optimizing longitudinal and vertical dynamics via a linear time-varying half-vehicle model, effectively enhancing energy efficiency and ride comfort of four-wheel independently driven electric vehicles while ensuring stability. Liang et al. [21] proposed a decentralized cooperative control framework of AFS and ASS by applying MDMPC, effectively enhancing the vehicle lateral and vertical stability during path tracking. Zheng et al. [22] propose a nonlinear model predictive control method for curve tilt function for active suspension in vehicle lateral motion to counteract inertial lateral acceleration. The lateral acceleration is significantly reduced to suppress the occurrence of motion sickness. Winkel et al. [23] demonstrate that discomfort increases with acceleration and jerk and propose a motion comfort prediction model.

In motion planning, researchers have developed various comfort-oriented trajectory planning methods. Htike et al. [24] and Geng et al. [25] achieved a balance among motion sickness reduction, driving safety, and driving efficiency through multi-objective optimization. Li et al. [26] developed a motion-planning algorithm incorporating frequency-shaping techniques and significantly reduced MSDV compared to conventional methods. Rajesh et al. [27] applied DRL to autonomous vehicle trajectory planning to minimize low-frequency accelerations and thereby suppress motion sickness symptoms. Additionally, Gysen et al. [28] and Papaioannou et al. [29] investigated the structure and performance of active suspension systems, demonstrating their effectiveness in mitigating motion sickness.

Although the aforementioned studies have achieved significant progress in vehicle dynamics control and intelligent motion planning, most results have focused on longitudinal–lateral cooperative control and steady-state lateral–vertical control during steering maneuvers. Research on the coupling mechanisms and cooperative control of vertical–longitudinal excitations, which significantly influence motion sickness, remains insufficient. The longitudinal acceleration changes generated by ACC systems during car-following or speed adjustments can aggravate vehicle pitch motion, acting on the front and rear suspensions. Traditional suspension control primarily targets the suppression of road-induced vibrations transmitted through tires, often lacking coordinated optimization for ACC-induced pitch motion or merely treating speed/acceleration as disturbances to the controller, resulting in suboptimal performance. Moreover, current ACC algorithms mainly focus on safety and fuel efficiency, paying less attention to the impact of acceleration/deceleration profiles on passenger comfort. Meanwhile, suspension control often overlooks the interference of longitudinal vehicle motion on body posture. Such fragmented control strategies make it difficult to fundamentally address motion sickness. Therefore, the coordinated control of ACC and suspension systems is crucial for motion sickness suppression. By integrating ACC acceleration planning with active suspension control and incorporating both suspension control forces and longitudinal vehicle acceleration as control variables, it is possible to optimize body pitch and vertical vibration characteristics during acceleration/braking. This approach enables coordinated longitudinal–vertical dynamics coupling control, effectively suppressing the occurrence of motion sickness.

Based on the above analysis, this study focuses on motion sickness suppression control technologies for autonomous vehicles. The main approach involves coupled modeling and control of active suspension and ACC to coordinately regulate longitudinal and vertical dynamics and suppress motion sickness. The paper is structured as follows: Section 2 presents coupled dynamic modeling of the suspension and ACC systems along with control system design; Section 3 provides simulation verification; and Section 4 offers conclusions and future perspectives.

2. Materials and Methods

2.1. Vertical Dynamics

In this study, the vehicle’s pitch motion induced by front and rear suspension interactions is identified as one of the contributing factors to motion sickness. Half-car suspension model is introduced to characterize this feature. This model integrates two quarter-car suspensions; model construction is shown in Figure 1.

In Figure 1, m_s is the sprung mass, m_us1 and m_us2 represent the unsprung masses of the front and rear suspensions, respectively, F_s1 and F_s2 represent the spring forces of the front and rear suspensions, k_s1 and k_s2 represent the spring stiffnesses of the front and rear suspensions, F_d1 and F_d2 represent the damping forces of the front and rear suspensions, c_s1 and c_s2 represent their respective damping coefficients, F₁ and F₂ represent the active control forces of the front and rear suspensions, F_t1 and F_t2 represent the elastic forces generated by the front and rear tires, k_t1 and k_t2 represent the equivalent spring stiffnesses of the front and rear tires, z_s represents the vertical displacement of the sprung mass center, z_s1 and z_s2 represent the vertical displacements at the connection points between the sprung mass and the front/rear suspensions, z_us1 and z_us2 represent the vertical displacements of the front and rear unsprung mass centers, z_r1 and z_r2 represent the vertical road excitations acting on the front and rear tires, I_y represents the moment of inertia of the sprung mass about the Y-axis, and θ represents the pitch angle. The combined action of the front and rear suspensions induces variations in the pitch angle, with displacements and forces defined as positive in the upward direction.

Based on the vertical force balance analysis, the vertical dynamics equation of the sprung mass m_s is:

$$m_s{\ddot{z}}_s=F_{s1}+F_{d1}+F_{s2}+F_{d2}+F_1+F_2$$

(1)

In which:

$$F_{s1}=-k_{s1}(z_{s1}-z_{us1})$$

(2)

$$F_{d1}=-c_{s1}({\dot{z}}_{s1}-{\dot{z}}_{us1})$$

(3)

$$F_{s2}=-k_{s2}(z_{s2}-z_{us2})$$

(4)

$$F_{d2}=-c_{s2}({\dot{z}}_{s2}-{\dot{z}}_{us2})$$

(5)

Based on the geometric kinematics of the sprung mass pitching:

$$z_{s1}=z_s-l_{f}sin\theta$$

(6)

$$z_{s2}=z_s+l_{r}sin\theta$$

(7)

Based on the moment balance analysis about the Y-axis, the pitch dynamics equation of the sprung mass m_s is:

$$I_y{\ddot{\theta }}_s=-l_f(F_{s1}+F_{d1}+F_1)+l_r(F_{s2}+F_{d21}+F_2)$$

(8)

The vertical dynamics equation for the front unsprung mass m_us1 is derived as:

$$m_{us1}{\ddot{z}}_{s1}=-F_{s1}-F_{d1}-F_1+F_{t1}$$

(9)

$$F_{t1}=-k_{t1}(z_{us1}-z_{ur1})$$

(10)

The vertical dynamics equation for the rear unsprung mass m_us2 is derived as:

$$m_{us2}{\ddot{z}}_{s2}=-F_{s2}-F_{d2}-F_2+F_{t2}$$

(11)

$$F_{t2}=-k_{t2}(z_{us2}-z_{ur2})$$

(12)

Furthermore, since vehicle acceleration/deceleration induces pitch motion and affects front/rear suspension dynamics, the disturbance input from longitudinal acceleration a_ego is incorporated into the half-car suspension model. During acceleration/deceleration, ground reaction forces generate a pitch moment about the Y-axis at the center of mass. This moment is added to the equations to characterize the coupling effect of a_ego on suspension dynamics. Consequently, Equation (8) is modified as:

$$I_y{\ddot{\theta }}_s=-l_f(F_{s1}+F_{d1}+F_1)+l_r(F_{s2}+F_{d21}+F_2)-m_s{a}_{ego}{h}_g$$

(13)

In which, a_ego represents ego car acceleration, h_g is sprung mass center of gravity height.

Based on the above analysis, a control-oriented model for the half-car suspension system is constructed as follows:

• Model Control Variables: $U_{sus}={[F_1,F_2]}^T$
• Model Disturbance Inputs: $U_{dsus}={[z_{r1},z_{r2},a_{ege}]}^T$
• Model State Variables: $X_{sus}=[z_s,\theta ,z_{us1},z_{us2},{\dot{z}}_s,\dot{\theta },{\dot{z}}_{us1},{\dot{z}}_{us2}]$
• Model Output Variables: $Y_{sus}=[{\dot{z}}_s,\theta ,z_{s1}-z_{us1},z_{s2}-z_{us2}]$

System model is

$$\left\{\begin{array}{c}{\dot{X}}_{sus}=A_{sus}{X}_{sus}+B_{sus}{U}_{sus}+B_{dsus}{U}_{dsus}\\ Y_{sus}=C_{sus}{X}_{sus}\end{array}\right.$$

(14)

Based on the model above, system matrix A_sus, B_sus, B_dsus, and C_sus are represented as:

$$A_{sus}={\left(\begin{array}{cccccccc}0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ -{\displaystyle \frac{k_{s1}+k_{s2}}{m_s}}& {\displaystyle \frac{k_{s1}{l}_f-k_{s2}{l}_r}{m_s}}& {\displaystyle \frac{k_{s1}}{m_s}}& {\displaystyle \frac{k_{s12}}{m_s}}& -{\displaystyle \frac{c_{s1}+c_{s2}}{m_s}}& {\displaystyle \frac{c_{s1}{l}_f-c_{s2}{l}_r}{m_s}}& {\displaystyle \frac{c_{s1}}{m_s}}& {\displaystyle \frac{c_{s2}}{m_s}}\\ {\displaystyle \frac{k_{s1}{l}_f-k_{s2}{l}_r}{I_y}}& -{\displaystyle \frac{k_{s1}{l}_f^2+k_{s2}{l}_r^2}{I_y}}& -{\displaystyle \frac{k_{s1}{l}_f}{I_y}}& {\displaystyle \frac{k_{s2}{l}_r}{I_y}}& {\displaystyle \frac{c_{s1}{l}_f-c_{s2}{l}_r}{I_y}}& -{\displaystyle \frac{c_{s1}{l}_f^2+c_{s2}{l}_r^2}{I_y}}& -{\displaystyle \frac{c_{s1}{l}_f}{I_y}}& {\displaystyle \frac{c_{s2}{l}_r}{I_y}}\\ {\displaystyle \frac{k_{s1}}{m_{s1}}}& -{\displaystyle \frac{k_{s1}{l}_f}{m_{s1}}}& -{\displaystyle \frac{k_{s1}+k_{r1}}{m_{s1}}}& 0& {\displaystyle \frac{c_{s1}}{m_{s1}}}& -{\displaystyle \frac{c_{s1}{l}_f}{m_{s1}}}& -{\displaystyle \frac{c_{s1}}{m_{s1}}}& 0\\ {\displaystyle \frac{k_{s2}}{m_{s2}}}& -{\displaystyle \frac{k_{s2}{l}_r}{m_{s2}}}& 0& -{\displaystyle \frac{k_{s2}+k_{r2}}{m_{s2}}}& {\displaystyle \frac{c_{s2}}{m_{s2}}}& -{\displaystyle \frac{c_{s2}{l}_r}{m_{s2}}}& 0& -{\displaystyle \frac{c_{s2}}{m_{s2}}}\end{array}\right)}_{8\times 8}$$

(15)

$$B_{\mathit{sus}}={\left(\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ \frac{1}{m_{\mathrm{s1}}}& \frac{1}{m_{\mathrm{s1}}}\\ \frac{l_f}{I_y}& -\frac{l_r}{I_y}\\ -\frac{1}{m_{\mathrm{s1}}}& 0\\ 0& -\frac{1}{m_{\mathrm{s2}}}\end{array}\right)}_{8\times 2}{B}_{\mathit{dsus}}={\left(\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 0& 0& -\frac{m_s{h}_g}{I_y}\\ \frac{k_{\mathrm{r1}}}{m_{\mathrm{s1}}}& 0& 0\\ 0& \frac{k_{\mathrm{r2}}}{m_{\mathrm{s2}}}& 0\end{array}\right)}_{8\times 3}$$

(16)

$$C_{sus}={\left(\begin{array}{cccccccc}0& 0& 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 1& -l_f& -1& 0& 0& 0& 0& 0\\ 1& l_r& 0& -1& 0& 0& 0& 0\end{array}\right)}_{4\times 8}$$

(17)

2.2. ACC Control

ACC is a L2 ADAS. It calculates target acceleration and executes control based on information such as set speed, preceding vehicle speed, and relative distance. Typically, ACC is implemented using MPC. Below is a generic MPC-based ACC control methodology.

The ACC working principle is shown in Figure 2.

In Figure 2, v_lead represents lead car velocity, d represents the distance between lead car and ego car, v_ego represents ego car velocity, and a_ego represents ego car acceleration. According to the vehicle motion equation, it can be concluded that:

$$\dot{d}=-v_{ego}+v_{lead}$$

(18)

$${\dot{v}}_{ego}=a_{ego}$$

(19)

For vehicles, the execution of acceleration and deceleration signals requires passing through the actuator, introducing a time delay. Therefore, the target acceleration a_cmd is defined, and a first-order delay is assumed between a_cmd and a_ego:

$${\dot{a}}_{ego}={\displaystyle \frac{1}{\tau }}(a_{cmd}-a_{ego})$$

(20)

In Equation (20), τ represents the actuator time constant. In this study, the EV actuator comprises the drive motor and other potential transmission mechanisms, and τ is selected as 0.2 s to represent the dynamic characteristics of them.

The control model of ACC is defined as follows:

• Model Control Variables: $U_{acc}=a_{cmd}$
• Model Disturbance Inputs: $U_{dacc}=v_{lead}$
• Model State Variables: $X_{acc}={[d,v_{ego},a_{ego}]}^T$
• Model Output Variables: $Y_{acc}={[d,v_{ego},a_{ego}]}^T$

According to the model above, system matrix is:

$$\begin{array}{l}{A}_{acc}={\left(\begin{array}{ccc}0& -1& 0\\ 0& 0& 1\\ 0& 0& -{\displaystyle \frac{1}{\tau }}\end{array}\right)}_{3\times 3},B_{acc}={\left(\begin{array}{c}0\\ 0\\ {\displaystyle \frac{1}{\tau }}\end{array}\right)}_{3\times 1},B_{dacc}={\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right)}_{3\times 1}\\ C_{acc}={\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)}_{3\times 3},D_{acc}=[]\end{array}$$

(21)

2.3. Coupled Dynamics Integration

The suspension control model described by Equations (14)–(17) is integrated with the ACC control model represented by Equation (21). During this integration process, a_ego transitions from an external disturbance to a controllable state variable.

• Model Control Variables: $U={[F_1,F_2,a_{cmd}]}^T$
• Model Disturbance Inputs: $U_d={[z_{r1},z_{r2},v_{lead}]}^T$
• Model State Variables: $X=[z_s,\theta ,z_{us1},z_{us2},{\dot{z}}_s,\dot{\theta },{\dot{z}}_{us1},{\dot{z}}_{us2},d,v_{ego},a_{ego}]$
• Model Output Variables: $Y=[{\dot{z}}_s,\theta ,z_{s1}-z_{us1},z_{s2}-z_{us2},d,v_{ego},a_{ego}]$

The integrated matrix A is represented as:

$$A={\left(\begin{array}{cc}{A}_{sus}& A_{acc\to sus}\\ A_{sus\to acc}& A_{acc}\end{array}\right)}_{11\times 11}$$

(22)

Matrix A_acc→sus has dimensions of 8 × 3, representing the direct influence of the 3 variables in X_acc on the 8 variables in X_sus; in X_acc = [d, v_ego, a_ego], d and v_ego do not have any direct effect on X_sus, so the first two columns of A_acc→sus are entirely 0; only a_ego exerts a direct influence on a_ego. As a_ego corresponds to the third component of the disturbance vector B_dsus in the suspension control model, its mathematical relationship with X_sus is represented by the third column of B_dsus. Therefore, the third column of A_acc→sus is identical to the third column of B_dsus, A_acc→sus = [0_8×2, B_dsus(:,3)].

Matrix A_sus→acc has dimensions of 3 × 8, representing the direct influence of the 8 variables in X_sus on the 3 variables in X_acc. However, since X_sus does not directly affect X_acc, A_sus→acc is a zero matrix.

Matrix A is represented as:

$$A={\left(\begin{array}{cc}{A}_{sus}& [0_{8\times 2},B_{dsus}(:,3)]\\ 0_{3\times 8}& A_{acc}\end{array}\right)}_{11\times 11}$$

(23)

The integrated disturbance matrix B_dsus characterizes the direct influence of external disturbances U_d = [z_r1, z_r2, v_lead] on state vector X_sus.

Since a_ego from U_dsus has been converted to a state variable, its corresponding column in B_dsus has been transferred to the state matrix A. Consequently, B_dsus now retains only the first two columns, representing the direct effects of z_r1 and z_r2 on the system states.

Matrix B_d can be expressed as:

$$B_d={\left(\begin{array}{cc}{B}_{dsus}(:,1:2)& 0_{8\times 1}\\ 0_{3\times 2}& B_{dacc}\end{array}\right)}_{11\times 3}$$

(24)

In Equation (24), 0_8×1 indicates that v_lead does not directly disturb X_sus, while 0_3×2 indicates that z_r1 and z_r2 do not directly disturb X_acc.

Matrix B and C are integrated using a similar approach, and the final integrated system matrix is expressed as:

$$\begin{array}{l}A={\left(\begin{array}{cc}{A}_{sus}& [0_{8\times 2},B_{dsus}(:,3)]\\ 0_{3\times 8}& A_{acc}\end{array}\right)}_{11\times 11},B={\left(\begin{array}{cc}{B}_{sus}& 0_{8\times 1}\\ 0_{3\times 2}& B_{acc}\end{array}\right)}_{11\times 3},\\ B_d={\left(\begin{array}{cc}{B}_{dsus}(:,1:2)& 0_{8\times 1}\\ 0_{3\times 2}& B_{dacc}\end{array}\right)}_{11\times 3},C={\left(\begin{array}{cc}{C}_{sus}& 0_{4\times 3}\\ 0_{3\times 8}& C_{acc}\end{array}\right)}_{7\times 11}\end{array}$$

(25)

2.4. MPC-Based Integrated Controller Design

MPC is a modern control theory based on receding horizon optimization and feedback correction. Its core principle involves constructing and solving finite-horizon optimization problems online, converting the optimization into a QP problem, as is shown in Figure 3. It computes the optimal control sequence for MIMO systems and dynamically applies this sequence to achieve real-time system regulation. In the context of motion sickness mitigation, MPC can reconcile conflicting objectives between suspension vertical forces and ACC longitudinal acceleration while handling system constraints.

MPC predicts future system dynamics based on a discretized state-space model. For the integrated half-vehicle suspension and ACC coupled system, the state equation can be formulated as:

$$\left\{\begin{array}{c}\dot{X}=AX+BU+B_d{U}_d\\ Y=CX\end{array}\right.$$

(26)

At each time step k, MPC generates a control sequence by solving the following optimization problem:

$$min{\displaystyle \sum _{i=0}^{N_p-1}(||y(k+i|k)-y_{ref}(k+i|k)|{|}_Q^2+\left|\right|u(k+i|k)|{|}_R^2)+\rho {\epsilon }^2}$$

(27)

After determining hyperparameters, weighting factors, and constraint parameters, the MPC algorithm transforms the control problem into a standard QP formulation as follows:

$$min{\displaystyle \frac{1}{2}}\Delta U^{T}H\Delta U+f^T\Delta U$$

(28)

where $\Delta U={[\Delta u(k|k),\Delta u(k+1|k),\dots ,\Delta u(k+N_c-1|k)]}^T$ represents the control increment sequence applied to the system.

3. Results

3.1. Coupled Control System Architecture

The vehicle dynamics model and MPC-based control system incorporating both vertical and longitudinal motions was developed in Matlab/Simulink (R2024b). The model consists of two main components: the plant and the control system, as illustrated in Figure 4. The control system receives measured signals Y and noise U_d from the plant, estimates system states, solves the MPC optimization problem to derive control signals U, and finally applies them to the plant for closed-loop control.

Vehicle parameters are detailed in

Table 1. Parameters of the vehicle.

Parameter	Value
ms	1200 kg
Iy	1500 kg·m2
mus1	40 kg
mus1	45 kg
ks1	25,000 N/m
ks2	27,000 N/m
cs1	1500 N·s/m
cs2	1600 N·s/m
kt1	200,000 N/m
kt2	210,000 N/m
lf	1.2 m
lr	1.5 m
hg	0.5 m

.

The designed MPC control system hyperparameters are listed in

Table 2. MPC parameters.

Hyperparameter	Value
Discretization Period	0.02 s
Prediction Horizon	30
Control Horizon	20

. The discretization period was determined by integrating suspension control and ACC requirements: while ACC typically operates at around 100 ms control cycles, suspension control requires shorter cycles of 5–20 ms to respond to high-frequency road excitations. Balancing ACC/suspension control demands and system complexity, a 20 ms control period was selected.

The constructed controller is a linear MPC. According to the hyperparameter analysis in Table 2 and the control model architecture in Equation (25), the dimension of the Hessian matrix is 60 × 60, with a computational complexity of approximately O(60³). It can stably run on automotive controllers and meet the real-time update requirement of 20 ms.

The control system’s input/output constraints are listed in

Table 3. Input/output constraints.

Parameter	Min.	Max.
F1	−2000 N	2000 N
F2	2000 N	2000 N
acmd	−5 m/s2	5 m/s2
${\dot{z}}_s$	−0.3 m/s	0.3 m/s
θ	−8·π/180 rad	8·π/180 rad
$\dot{\theta }$	−3·π/180 rad/s	3·π/180 rad/s
zs1−zus1	−0.1 m	0.1 m
zs2−zus2	−0.1 m	0.1 m
d	50 m	250 m
vego	0 m/s	50 m/s
aego	−5 m/s2	5 m/s2

.

3.2. System Decoupled Simulation

3.2.1. Suspension Control Simulation

Based on the half-car suspension described in Section 2.1, simulation is conducted without considering disturbances from ACC. Suspension simulation is performed on a Class B road surface, with the results shown in Figure 5. It can be observed that the vertical velocity of the sprung mass is constrained within 0.1, and the pitch angle does not exceed 0.01 rad. These results demonstrate the multi-objective coordination capability of MPC.

3.2.2. ACC Simulation

The ACC simulation is conducted using the MPC parameters listed in Table 2, with engineering constraints provided in Table 3.

First, a following scenario is simulated. The lead car traveled at a sinusoidal speed, while the ego car starts from an initial speed of 0 m/s with a desired speed of 30 m/s. The simulation results are shown in Figure 6. It can be observed that the lead car speed significantly affects the ego car acceleration, which undoubtedly further influences the vertical dynamic characteristics.

Then, the cruise with constant velocity simulation is conducted with the target speed set at 20 m/s. As shown in Figure 7, the controller effectively tracks the target speed and rapidly converges to 20 m/s, and the acceleration remains strictly within predefined constraints.

3.3. System Integrated Simulation

In conventional vehicle control architectures, ACC and suspension control systems typically operate in isolation. Therefore, this study first simulates such a decoupled control scheme as a baseline for comparison. Under this architecture, the acceleration computed by the ACC is treated as an external disturbance to the suspension control system, and suspension control performance does not feedback to influence the ACC acceleration.

In contrast, in the proposed control framework, the acceleration command of the ACC serves as a control variable in the integrated controller, introducing coupling with suspension dynamics, optimization of suspension performance consequently affects the vehicle’s acceleration.

A simulation is conducted under steady-state following conditions: lead car velocity is 20 m/s; initial distance between lead car and ego car is 100 m; ego car initial velocity is 10 m/s; both front and rear suspensions are subjected to Class B road excitation.

As evident from Figure 8, Figure 9, Figure 10 and Figure 11, the proposed integrated control strategy demonstrates significant improvements over decoupled control, longitudinal acceleration is effectively reduced, vertical velocity amplitude decreased at most time, pitch angle peak value reduced from 0.06 rad to 0.02 rad, and vehicle pitch dynamics caused by acceleration are effectively suppressed.

A simulation is conducted under car-following conditions: lead car velocity is a sinusoidal waveform with amplitude of 5 m/s, offset of 30 m/s, and frequency of 0.5 Hz; ego car initial velocity is 10 m/s, target velocity is 30 m/s, distance between lead car and ego car is 100 m, and both front and rear suspensions are subjected to Class B road excitation. As evidenced in Figure 12, Figure 13, Figure 14 and Figure 15, the proposed controller reliably maintains core ACC objectives under complex car-following conditions, specifically lead car tracking. Figure 13 demonstrates concurrent optimization of acceleration characteristics, in which the acceleration transition is smoother, and peak values are reduced. In Figure 14 and Figure 15, both vertical velocity and pitch angle are much smaller and smoother than decoupled control, and the disturbance induced by the lead car sinusoidal acceleration is nearly eliminated, achieving near-zero convergence within 10 s after initial oscillations, demonstrating marked superiority. The proposed control strategy demonstrates significant improvements over conventional decoupled control, consequently achieving effective mitigation of motion sickness.

RMS and MSDV of corresponding signals are calculated and compared, listing in

Table 4. RMS and MSDV comparison.

Driving Condition	Parameter	Method	RMS	MSDV
Vlead: constant	aego	decoupled	0.936	/
		coupled	0.846	/
	jerk	decoupled	4.18	/
		coupled	1.39	/
	θy	decoupled	0.0057	/
		coupled	0.0036	/
	vsz	decoupled	0.0032	0.0295
		coupled	0.0033	0.1696
	wy	decoupled	0.03	/
		coupled	0.018	/
Vlead: sinusoidal	aego	decoupled	1.72	/
		coupled	1.68	/
	jerk	decoupled	4.4	/
		coupled	1.72	/
	θy	decoupled	0.0068	/
		coupled	0.0035	/
	vsz	decoupled	0.0031	0.0255
		coupled	0.0038	0.1721
	wy	decoupled	0.0296	/
		coupled	0.0176	/

. In Table 4, jerk describes the rate of change of vehicle acceleration over time and directly reflects the smoothness of acceleration variation. Excessive jerk can easily trigger passenger motion sickness, and w_y is pitch angular velocity. MSDV is calculated based on the ISO 2631-1 standard [30].

RMS of parameter a_ego and jerk of the proposed method are obviously smaller than those of the decoupled method, especially jerk, and the proposed method can effectively regulate longitudinal dynamics and suppresses motion sickness-related parameters.

RMS of parameter Θ_y and w_y are also significantly lower than those of decoupled control, indicating that the pitch motion induced by longitudinal acceleration has been effectively suppressed, thereby reducing the likelihood of motion sickness.

Parameter v_sz exhibits counterintuitive data trends—both RMS and MSDV values of the proposed method are higher than those of the decoupled method. However, as shown in Figure 14 and Figure 15, this increase primarily stems from a rapid, large-magnitude signal fluctuation during the very initial control phase. This transient spike results in significantly higher short-term acceleration variations in the MSDV calculation, leading to an inflated MSDV value. Notably, such fluctuations occur only once at startup. From a long-term control perspective, the proposed method still demonstrates exceptionally superior performance.

4. Conclusions

This article proposes a vertical and longitudinal coupling control for vehicles, including active suspension control and ACC. The suspension control system is designed based on a half-car model, and the pitch dynamics of the sprung mass induced by acceleration are also incorporated into the model. In ACC design, acceleration command is one of the control variables optimizing ACC and suspension-related objectives. The coupled control system is designed based on MPC: three control inputs are active control forces of front and rear suspension, and longitudinal acceleration; eleven states are eight suspension states and three ACC states. The target outputs mainly focus on three variables related to motion sickness: vertical velocity and pitch angle of the sprung mass, and longitudinal acceleration of the vehicle. By designing a coupled controller, the acceleration can be adjusted during the suspension control process to suppress pitch motion and optimize the suspension control effect.

The simulation compares the conventional suspension and ACC decoupled control with the proposed coupled method. The results demonstrate that (1) longitudinal acceleration will affect the suspension control effect, thereby exacerbating the parameters related to motion sickness; (2) the proposed coupling controller can optimize suspension control performance by adjusting acceleration while meeting the original objectives of ACC, thereby suppressing motion sickness-related parameters. The proposed method explores the performance of multi-dimensional coupling control of the chassis in terms of motion-related comfort and provides a feasible solution.

However, there are still some limitations to this study: (1) The nonlinear characteristics of the active suspension actuator have not been taken into account, which have a significant impact on suspension performance. Neglecting these factors may result in poor performance of the controller under actual operating conditions, especially under large-amplitude or high-frequency excitations, where the dynamic response of the suspension deviates significantly from the theoretical model, thereby affecting vehicle comfort and stability. (2) This study focuses on vehicle dynamics performance indicators, while motion sickness-related physiological signals (e.g., passenger head acceleration, EEG and visual–vestibular conflict) were not directly included in the optimization objectives, this may result in the control system improving mechanical performance but failing to effectively alleviate passenger motion issues. (3) Motion sickness is caused by the coupled effects of longitudinal, lateral, and vertical dynamics, and may have a cumulative effect; this study mainly focuses on longitudinal–vertical coupling dynamics, ignoring the lateral dynamics and cumulative effect of signals, which may result in inaccurate control effect in real driving conditions.

In future research, we will focus on the following aspects: (1) integrate the nonlinear actuator model into the control system to improve model accuracy; (2) develop a human mechanical model and establish the mathematical relationship between physiological indicators and control signals, directly using acceleration and other signals to regulate comfort metrics, achieving human–vehicle closed-loop control; (3) investigate longitudinal–lateral–vertical coupling control methods and identify the feasible spatial domain of control inputs to simultaneously manage three-dimensional dynamics, thus mitigating motion sickness.