Coordinated Feedback–Feedforward Control for Coupled Seat–Suspension Dynamics: A Ride Comfort Enhancement Strategy for In-Wheel-Motor Electric Vehicles

Abstract

Electric vehicles equipped with in-wheel motors provide packaging, controllability, and drivetrain-simplification advantages; however, the increase in wheel-side unsprung mass can intensify vibration transmission to the chassis, seat, and occupant. This paper presents a coordinated active seat and active suspension control strategy for an integrated 8-DOF quarter-car model that includes an in-wheel motor, an active seat suspension, and a 4-DOF seated driver body model. The proposed controller combines a Harmony Search (HS)-optimized proportional–integral–derivative (PID) feedback baseline with a repeatable-disturbance feedforward compensation term. The HS-PID loop provides baseline transient attenuation, while the feedforward term compensates the repeatable component of the bump-induced disturbance transmitted through the coupled seat–vehicle system. The controller is evaluated against passive suspension, active-seat-only control, active-vehicle-suspension-only control, and an HS-PID baseline under repeated bump/shock excitation. The results show that coordinated actuation reduces occupant displacement and acceleration responses relative to the benchmark cases. The discussion explains the active-seat-only peak-acceleration amplification, the different magnitudes of displacement and acceleration improvements, and the practical implications of suspension stroke and actuator-force limits. The reported conclusions are therefore confined to the repeated bump/shock condition considered in this numerical study; broader ride-comfort generalization requires standardized whole-body vibration metrics, random-road validation, speed variation, parametric uncertainty analysis, and drivetrain energy evaluation.

1. Introduction

Electric vehicle (EV) development has accelerated because of the need to reduce transportation-related energy consumption and emissions [1,2]. Advanced EV propulsion architectures have become important for improving packaging efficiency, controllability, and vehicle-dynamics performance [3,4].

Among EV propulsion layouts, in-wheel-motor (IWM) systems are attractive because they eliminate conventional driveline components, enable independent wheel-torque control, and support direct integration with vehicle stability and ride-control systems [5,6]. However, locating the motor at the wheel increases the effective unsprung mass, which can modify wheel-hop dynamics, increase tire-force variation, and degrade both road holding and ride comfort [5,6,7]. Therefore, vibration suppression remains a central design requirement for practical IWM-EV implementation [8,9].

Vehicle suspension control is governed by a trade-off between ride comfort and road holding. A wide range of active and semi-active suspension controllers has been studied, including PID-based, robust, fuzzy, model-predictive, and learning-based methods [6,7,9]. Feedback controllers provide strong baseline attenuation for broadband transient disturbances, but they do not directly exploit repeatability when the vehicle encounters the same finite road feature multiple times. A feedforward compensation term based on repeatable disturbance information can therefore complement feedback control for repeated bump scenarios. This idea is rooted in the classical concept of iterative learning control [10], in which control actions can be improved over repeated finite-duration tasks. In this work, the iterative-learning concept is used only as a design motivation for the feedforward compensation term; the proposed controller is not presented as a demonstrated multi-iteration ILC implementation.

The seated occupant experiences vibration after it has propagated through the tire, suspension, chassis, seat frame, and cushion. Biodynamic driver models allow head, torso, and thigh responses to be evaluated directly [11,12,13]. This motivates an integrated vehicle–seat–driver formulation in which main-suspension and seat-suspension actuation are coordinated rather than controlled independently.

The specific research gap addressed in this study is the limited investigation of coordinated feedback–feedforward control for an integrated IWM-EV, active-seat, and seated-driver model. Previous work has often examined vehicle or seat suspension separately, whereas the present study evaluates their coordinated action in a coupled model.

Recent developments in higher-order intelligent control suggest promising extensions for adaptive vibration suppression. Type-3 adaptive neuro-fuzzy inference systems have been proposed for robust learning and uncertainty compensation under noisy conditions [14]. Such structures could be integrated in future seat–suspension controllers for online gain adaptation.

The main contributions are as follows. First, an 8-DOF IWM-seat-driver model is used to evaluate ride comfort at the occupant level. Second, main-suspension and seat-suspension actuation are coordinated. Third, an HS-PID feedback baseline is combined with repeatable feedforward compensation. Fourth, the results are interpreted physically, and the claims are limited to the repeated bump/shock excitation tested in this study.

2. System Description and Problem Formulation

2.1. Integrated Vehicle–Seat–Driver Model

An integrated vertical dynamic model is considered, as illustrated in Figure 1. The model combines a quarter-car IWM-EV suspension, an active seat suspension, and a 4-DOF seated driver model.

The vertical equations of motion are

$$(m_u+m_d){\ddot{z}}_u=-k_t(z_u-z_r)-c_t({\dot{z}}_u-{\dot{z}}_r)+k_s(z_s-z_u)+c_s({\dot{z}}_s-{\dot{z}}_u)+u_s,$$

(1)

$$m_s{\ddot{z}}_s=-k_s(z_s-z_u)-c_s({\dot{z}}_s-{\dot{z}}_u)+k_{ss}(z_f-z_s)+c_{ss}({\dot{z}}_f-{\dot{z}}_s)-u_s+u_f,$$

(2)

$$m_f{\ddot{z}}_f=-k_{ss}(z_f-z_s)-c_{ss}({\dot{z}}_f-{\dot{z}}_s)+k_c(z_c-z_f)+c_c({\dot{z}}_c-{\dot{z}}_f)-u_f,$$

(3)

$$m_c{\ddot{z}}_c=-k_c(z_c-z_f)-c_c({\dot{z}}_c-{\dot{z}}_f)+k_1(z_1-z_c)+c_1({\dot{z}}_1-{\dot{z}}_c),$$

(4)

$$m_i{\ddot{z}}_i=-k_i(z_i-z_{i-1})-c_i({\dot{z}}_i-{\dot{z}}_{i-1})+k_{i+1}(z_{i+1}-z_i)+c_{i+1}({\dot{z}}_{i+1}-{\dot{z}}_i),i=1,2,3,$$

(5)

$$m_4{\ddot{z}}_4=-k_4(z_4-z_3)-c_4({\dot{z}}_4-{\dot{z}}_3).$$

(6)

Here, $m_s$, $m_u$, $m_d$, $m_f$, $m_c$, and $m_1$–$m_4$ are the sprung, unsprung, IWM, seat-frame, cushion, and driver-body masses. The control forces $u_s$ and $u_f$ are generated by the active vehicle- and seat-suspension actuators.

2.2. State-Space Representation

$$\dot{x}=Ax+B_u\overline{u}+B_{w}w,y=C_{s}x,$$

(7)

where $w={\dot{z}}_r$ and $\overline{u}={[{\overline{u}}_s,{\overline{u}}_f]}^T$ is the saturated actuator vector. The output matrix $C_s$ selects comfort-related occupant-body and suspension-deflection variables for feedback regulation. The desired regulated output is $y_d=0$.

$${\overline{u}}_i=\mathrm{sat}\left(u_i\right)=\left\{\begin{array}{cc}-U_{\lim ,i},\hfill & u_i<-U_{\lim ,i},\hfill \\ u_i,\hfill & |u_i|\le U_{\lim ,i},\hfill \\ U_{\lim ,i},\hfill & u_i>U_{\lim ,i},\hfill \end{array}\right.i\in \{s,f\}.$$

(8)

2.3. Model Parameters

Table 1. Mechanical parameters of the integrated IWM-seat-driver suspension model.

Parameter	Value	Unit
$m_u$	20	kg
$m_s$	300	kg
$m_f$	15	kg
$m_c$	1	kg
$m_1$	12.78	kg
$m_2$	8.62	kg
$m_3$	28.49	kg
$m_4$	5.31	kg
$m_d$	10	kg
$c_t$	0	N s/m
$c_s$	2000	N s/m
$c_{ss}$	830	N s/m
$c_c$	200	N s/m
$c_1$	2064	N s/m
$c_2$	4585	N s/m
$c_3$	4750	N s/m
$c_4$	400	N s/m
$k_t$	180,000	N/m
$k_s$	10,000	N/m
$k_{ss}$	31,000	N/m
$k_c$	18,000	N/m
$k_1$	90,000	N/m
$k_2$	162,800	N/m
$k_3$	183,000	N/m
$k_4$	310,000	N/m

lists the fixed mechanical plant parameters. Active behavior is produced by $u_s$ and $u_f$. The tire damping $c_t=0$ represents the standard quarter-car simplification.

3. Controller Design

The controller is formulated as an HS-PID + Feedforward scheme. The HS-PID component provides the feedback baseline, while the feedforward component compensates the repeatable part of the bump-induced disturbance. The actuator command is

$$u\left(t\right)=K{u}_1\left(t\right)+u_2\left(t\right),$$

(9)

where K is the actuator-allocation matrix, $u_1\left(t\right)$ is the HS-PID feedback signal, and $u_2\left(t\right)$ is the feedforward compensation signal. The feedback signal is defined by

$$u_1\left(t\right)=k_{p}e\left(t\right)+k_d\dot{e}\left(t\right)+k_i{\int }_0^{t}e\left(\tau \right)d\tau ,e\left(t\right)=-y\left(t\right).$$

(10)

For a repeated finite road segment, the disturbance is decomposed as $w\left(t\right)=w_r\left(t\right)+w_n\left(t\right)$, where $w_r\left(t\right)$ is the repeatable component and $w_n\left(t\right)$ is bounded nonrepeatable variation. The feedforward term $u_2\left(t\right)$ compensates $w_r\left(t\right)$, while the HS-PID loop handles both components in real time.

Simulation Setup and Reproducibility Parameters

Table 2. Simulation and controller parameters for reproducibility.

Item	Value/Description
Simulation software	MATLAB/Simulink (R2021b or later)
Numerical solver	ode45 (Runge–Kutta 4/5), fixed step
Integration step	$\Delta t=1\times {10}^{-4}$ s
Simulation duration	$T=5$ s
Initial conditions	All states zero at $t=0$
Bump profile	Half-sine, height 0.05 m, length 0.5 m, speed 20 km/h
Regulated output y	Driver-head vertical acceleration ($m_4$)
Output matrix $C_s$	Selects head acceleration and suspension deflections
PID gains $(k_p,k_d,k_i)$	Tuned by Harmony Search minimizing $\mathrm{RMS}\left({\ddot{z}}_4\right)$
HS objective function	Minimize $\mathrm{RMS}\left({\ddot{z}}_4\right)$ subject to stroke and force limits
Actuator limits	$U_{\lim ,s}=3000$ N, $U_{\lim ,f}=1500$ N
Allocation matrix K	Diagonal; maps PID output to ${[u_s,u_f]}^T$
Feedforward $u_2\left(t\right)$	Fixed signal derived from the repeatable bump response

summarizes the numerical, road-input, and controller parameters used in the simulations. These parameters define the regulated output, actuator limits, road excitation, solver settings, and feedforward formulation required for reproducibility.

4. Results and Discussion

The controller was evaluated under repeated bump/shock excitation. The following results should therefore be interpreted as a repeated-shock numerical benchmark rather than as a general real-road validation. Generalization to real-world random-road conditions requires ISO 8608 road profiles [15], ISO 2631 frequency-weighted comfort metrics [16], multiple speeds, parametric uncertainty analysis, and energy assessment.

4.1. Human Body Response

The HS-PID + Feedforward controller improves ride comfort under repeated bump excitation relative to all benchmark controllers. The HS-PID feedback loop attenuates the transient response, while the feedforward term reduces the repeatable component.

The active-seat-only controller slightly increases peak-to-peak head acceleration compared with the passive case. This is physically meaningful: when only the seat actuator is active, the vehicle body remains uncontrolled and the seat subsystem reacts to amplified chassis motion, locally increasing acceleration peaks through relative-motion dynamics and seat resonance. Coordinated control avoids this effect.

The driver-head acceleration responses are presented in Figure 2, the actuator forces in Figure 3, and the feedback–feedforward comparison in Figure 4. The segmental acceleration and displacement responses are shown in Figure 5 and Figure 6, respectively.

Compared with the passive case, the HS-PID + Feedforward controller reduces peak-to-peak head acceleration from 16.10 to 6.785 $\mathrm{m}/{\mathrm{s}}^2$ (≈57.9%) and RMS head acceleration from 3.007 to 1.058 $\mathrm{m}/{\mathrm{s}}^2$ (≈64.8%).

4.2. Vehicle Suspension Stroke and Seat Suspension Stroke Responses

Figure 7, Figure 8, Figure 9 and Figure 10 distinguish the vehicle suspension stroke $z_s-z_u$ from the seat suspension stroke $z_f-z_s$, with both quantities reported in meters. The captions, notation, and discussion are consistent with these physical definitions. Larger transient seat-suspension stroke during severe bump excitation is interpreted as an actuator-design consideration. The saturation limits in Equation (8) provide the framework for enforcing stroke and force constraints in practical implementation.

4.3. Ride-Quality Evaluation

All displacement and stroke quantities in

Table 3. Peak-to-peak displacement under repeated bump excitation (m).

Controller	Head	Improve (%)	Upper Torso	Improve (%)	Lower Torso	Improve (%)	Thighs	Improve (%)
Passive	1.3050	—	1.3000	—	1.2600	—	1.2080	—
Active seat	1.2420	4.8	1.2370	4.8	1.1960	5.1	1.1430	5.4
Active suspension	1.1280	13.6	1.1250	13.5	1.0950	13.1	1.0590	12.3
HS-PID	1.0490	19.6	1.0460	19.5	1.0160	19.4	0.9756	19.2
HS-PID + Feedforward	0.4155	68.2	0.4131	68.2	0.3940	68.7	0.3698	69.4

,

Table 4. Peak-to-peak acceleration under repeated bump excitation ($\mathrm{m}/{\mathrm{s}}^2$).

Controller	Head	Improve (%)	Upper Torso	Improve (%)	Lower Torso	Improve (%)	Thighs	Improve (%)
Passive	16.10	—	16.02	—	15.31	—	14.42	—
Active seat	16.40	−1.9	16.30	−1.7	15.50	−1.2	14.50	−0.6
Active suspension	12.74	20.9	12.68	20.8	12.22	20.2	11.62	19.4
HS-PID	13.05	18.9	12.98	19.0	12.42	18.9	11.74	18.6
HS-PID + Feedforward	6.785	57.9	6.700	58.2	6.301	58.8	5.892	59.1

and

Table 5. RMS displacement under repeated bump excitation (m).

Controller	Head	Improve (%)	Upper Torso	Improve (%)	Lower Torso	Improve (%)	Thighs	Improve (%)
Passive	0.2298	—	0.2292	—	0.2230	—	0.2148	—
Active seat	0.2095	8.8	0.2089	8.9	0.2030	9.0	0.1953	9.1
Active suspension	0.2094	8.9	0.2089	8.9	0.2047	8.2	0.1990	7.4
HS-PID	0.1856	19.2	0.1851	19.2	0.1805	19.1	0.1743	18.9
HS-PID + Feedforward	0.0655	71.5	0.0653	71.5	0.0628	71.8	0.0596	72.3

are reported in meters, and all acceleration quantities are reported in $\mathrm{m}/{\mathrm{s}}^2$. The proposed method is consistently labeled HS-PID + Feedforward.

The displacement reductions are larger than the acceleration reductions because the feedforward compensation primarily reduces low-frequency repeatable relative motion, whereas acceleration contains stronger high-frequency transient content from the bump impact. The present evaluation uses PTP and RMS measures appropriate for repeated bump/shock excitation. ISO 2631-1 [16] frequency-weighted acceleration and vibration dose value should be used in future work for broader road profiles.

5. Conclusions

This paper presented a coordinated HS-PID + Feedforward controller for an integrated IWM-EV seat–suspension–driver model. The feedforward term is motivated by the iterative learning control concept [10]; however, the reported numerical evidence does not constitute a demonstration of multi-iteration ILC convergence. The feedforward signal is treated as a fixed compensating term derived from the known repeatable bump response.

The HS-PID + Feedforward controller reduces occupant displacement and acceleration responses compared with passive, active-seat-only, active-suspension-only, and HS-PID-only baselines under repeated bump/shock excitation.

The conclusions are limited to the tested repeated bump scenario. More general claims require ISO 8608 random-road profiles [15], different vehicle speeds, parametric uncertainty studies, ISO 2631 frequency-weighted metrics [16], actuator-energy analysis, and hardware-in-the-loop validation. Advanced intelligent controllers, including type-3 fuzzy and neuro-fuzzy methods such as T3-ANFIS [14], may be integrated in future work for online uncertainty compensation and adaptive gain tuning.