## 1. Introduction

In recent years, to solve the challenges resulting from the increasing energy crisis and environmental pollution, the electric vehicles (EVs) have been widely developed as an essential part of future efficient and green transportation plans. Being different from the traditional EVs with centralized powertrains, the in-wheel-motor (IWM) EVs feature electric motors mounted in the wheel hubs. By replacing the mechanical transmission system with an independent and direct drive system, IWMEVs have great potential to achieve better dynamic control, smaller space utilization, higher driving efficiency, and redundant driving system, etc. [

1,

2,

3], so as to improve overall vehicle performance. As an ideal carrier for advanced vehicle dynamics control system, IWMEVs have played a significant role in defining the development direction for the next generation EVs. Nevertheless, challenges, such as vehicle ride comfort, still remain with IWMEVs due to the heavy electric wheels. As a matter of fact, the unsprung mass with the IWMs usually results in harsh vertical negative effects, such as reduction of vehicle ride comfort [

4,

5,

6], deterioration of road friendliness [

7], invalidation of suspension control methods [

8], and reduction of motor reliability under the large wallop [

9,

10,

11], which have greatly restricted the practical development of IWMEVs.

For vehicles with a centralized powertrain, the unsprung mass is relatively small, and therefore vehicle comfort is mainly determined by suspension performance, while for IWMEVs, the wheel is an integrated system composed of tire, motor, brakes, etc. When road vibration acts on the wheel, the tire and motor are directly impacted. It is worth noting that the huge wallop can cause relative radial motion between the stator and rotor of the electric motor, which can deteriorate its performance and eventually shorten its service life [

12]. Additionally, the vibration in the electric wheel is coupled with that of the vehicle body, leading to complicated vehicle dynamics characteristics.

In order to improve IWMEVs’ ride comfort, intensive research activities have focused on the suppression of vertical negative effects. A rich literature has contributed to several solutions, such as motor weight reduction, unsprung mass transfer, and optimization of vibration transmission, etc.

The use of lightweight motors is an effective approach for reducing electric wheel mass. The axial flux motor, featured with high torque density, power density, and reduced cogging effect [

13,

14], meets most of electrical requirements and physical limits for EV applications. More importantly, it naturally matches the shape and dimension of the classical-vehicle wheel rim so that it can be readily applied in electric wheels. Nikam et al. [

15] designed a permanent magnet brushless DC motor with a segmented rotor type construction for IWMEVs, in which, the concentrated winding method is adopted to minimize end-winding effects and to reduce copper loss and motor weight. Takahashi et al. [

16] presented a ferrite permanent magnet-based low cost in-wheel axial gap motor design. To further reduce the size and weight, an open slot structure was used instead of a semi-closed slot structure. Experimental results showed that the semi-closed slot structure was more effective to achieve size and weight reduction. However, light weight motors have not been widely applied because of material performance and manufacturing cost issues.

Alternatively, the IWM can be transferred to the sprung mass as a vibration absorber by utilizing a suspended device, which is beneficial to improve vehicle ride comfort within a wide range of frequencies. Bridgestone Corporation [

17] developed an electric wheel with a dynamic vibration absorber, which controls the negative effects on the vertical vibration by utilizing the motor mass as the absorber. Shao et al. [

18] designed a dynamic-damping in-wheel-motor driven system, where the suspended motor functioned as a dynamic absorber and a fault-tolerant fuzzy approach was utilized to control the active suspension of the IWMEV. Luo and Tan [

19] proposed an electric wheel structure topological scheme with a built-in mount system, in which the IWM was separated elastically from the unsprung mass by rubber bushings, making the mass of the motor parallel to the sprung mass. The rubber bushing absorbed the vibration energy transferred from the road to the motor, reducing the effects of road excitation on motor air gap and hence improving the vertical dynamics characteristics of the vehicle. Nevertheless, suspended devices, such as rubber bushings, are essentially all just different kinds of passive vibration absorbers. Since the parameters are determined under the typical working conditions, the effectiveness of the method shall be weakened when working under real conditions on the complicated and varied pavement.

Another method to suppress the vertical negative effects of an IWM is to optimize the vibration transmission. Oliveira [

20] designed an in-wheel semi-active suspension, where the damper can be continuously adjusted within a certain range to meet the vibration requirements. Ma [

21] achieved the active control of the vertical vibration of the motor by adding a linear motor between the stator and the axle. Jin [

22] proposed a magneto-rheological (MR) semi-active suspension system, based on a structural design and parameter matching. The proposed system provided an adjustable damping force to improve the vehicle ride comfort. Vibration absorbers under active or semi-active control are considered as adaptive methods for ride comfort improvement [

23,

24]. However, it is difficult to install the absorbers into wheels due to the space limitations. What’s more, the in-wheel absorbers change the vibration transmission properties. The comprehensive control of in-wheel vibration absorbers and vehicle suspension has seldom been studied.

In the methods discussed above, the vehicle suspension control system improves the vehicle ride comfort, handling stability and safety. However, vehicle performance, such as ride comfort, IWM vertical wallop, and road-holding stability, often display conflicting control requirements. In addition, the nonlinear disturbance and uncertainties of the actuator influence the vehicle performance. To deal with the trade-off between these conflicting expectations, various control methods have been proposed. Zhang and Wang [

25,

26] proposed a linear parameter-varying (LPV) control strategy to improve the stability and handling of an IWMEV, in which, the trade-off between the tracking performance and the control input energy is achieved by using a fault-tolerant robust LQR-based

${H}_{\infty}$ controller. Wang and Jing [

18] designed a finite-frequency state-feedback

${H}_{\infty}$ controller for the active suspension in an IWMEV to achieve the targeted disturbance attenuation in the concerned frequency range. According to [

27], a robust

${H}_{\infty}$ control strategy can deal with complexities such as unsprung mass uncertainty, damper time delay, and time constant uncertainty. Besides, fuzzy control [

28], neural network method [

29], linear optimal control [

30], adaptive control [

31] are all utilized to control suspension system and optimize vehicle performance.

To overcome the drawbacks mentioned above, in this paper an integrated electric wheel with a controllable in-wheel vibration absorber is proposed to improve the vehicle ride comfort of an IWM EV. The proposed in-wheel vibration absorber, composed of a spring, an annular rubber bushing, and a controllable damper, aims to reduce the vertical wallop of the IWM. An improved particle swarm optimization (IPSO) algorithm is developed to determine the parameters of the in-wheel spring and rubber bushing under typical working conditions. In order to coordinate the vehicle suspension with the in-wheel absorber, the linear quadratic regulator algorithm (LQR) is utilized to actively control the suspension so as to improve the vehicle ride comfort. Meanwhile, a fuzzy PID algorithm is developed to control the in-wheel controllable damper so as to adaptively reduce the vertical wallop of the IWM. The effectiveness of the proposed method is validated through simulation, using MATLAB/Simulink models for various typical conditions.

The remaining sections of this paper are organized as follows: the structure of the electric wheel with in-wheel vibration absorber and a quarter vehicle dynamics model are introduced in

Section 2. The comprehensive control strategy of suspension and in-wheel absorber is elaborated in

Section 3.

Section 4 provides details about simulations of the proposed control strategy, followed by a summary of the key conclusions in

Section 5.

## 3. Optimization Control of In-Wheel Vibration Absorber and Vehicle Suspension

As mentioned in the previous section, the proposed in-wheel vibration absorber and vehicle suspension can be controlled to reduce motor wallop so as to improve the vehicle ride comfort. In this study, four factors are considered as the evaluation indexes to evaluate the control effectiveness, including vehicle body vertical acceleration

a_{s}, suspension dynamic deflection

f_{d}, wheel dynamic load

F_{d}, and motor wallop

F_{e}. As shown in

Figure 4, the comprehensive control strategy of the in-wheel absorber and vehicle suspension mainly include the following two aspects:

- (1)
Parameter matching of the in-wheel vibration absorber. The in-wheel spring and annular rubber bushing are both utilized to absorb vibration passively. Under typical conditions, the improved particle swarm optimization (IPSO) algorithm can be utilized to solve the in-wheel spring stiffness K_{e} and the damper coefficient of the annular rubber bushing C_{e}.

- (2)
Comprehensive control of the vehicle suspension force and the in-wheel damper force. In order to restrain the vertical vibration of vehicle body and the IWM, the body acceleration a_{s} and the motor wallop F_{e} can be chosen as the primary optimization variables, and the suspension dynamic deflection f_{d} and the wheel dynamic load F_{d} as auxiliary optimization variables. In this study, the linear quadratic regulator algorithm (LQR) algorithm is suggested to control vehicle suspension force u_{s} to suppress vehicle body vibration, and meanwhile the fuzzy PID controller is suggested to adjust the in-wheel damper force u_{e} to reduce motor wallop.

The vehicle ride comfort improvement is achieved by the suspension controlled force u_{s} and the in-wheel controlled damper force u_{e}. It should be mentioned that the realization of the controlled force differs in different types of actuators, such as magnetorheology (MR), electrorheology (ER), electromagnetic actuator, linear electric motor actuator and so on. In addition, the nonlinear disturbance and uncertainties of actuators are in practice various too. Therefore, in this study, we mainly focus on the damper force control for vibration absorbing, and it is assumed that the controllable damper can deliver a controlled force to meet the vehicle performance requirements as expected.

#### 3.1. Parameters Matching of the In-Wheel Spring and Rubber Bushing

Based on the transfer function, the Fourier transform method is usually adopted to achieve parameter matching [

32]. Since it is difficult to derive the transfer function for a system with multiple degrees-of-freedom, some scholars have suggested using the genetic algorithm to match the vehicle suspension parameters [

22]. As a matter of fact, it is complicated to program the genetic algorithm with memory function characteristics, which weakens its effectiveness.

As shown in

Figure 5, the improved particle swarm optimization (IPSO) algorithm, based on the social behavior of individuals and groups, which features simple programming and easy implementation [

33], is utilized to determine the in-wheel absorber’s parameters. When parameters are matched by IPSO, each particle represents a set of two-dimension constants, in-wheel spring stiffness and damper coefficient. The particles can dynamically update the optimization speed to achieve the optimal trajectory.

#### 3.1.1. Updating Particles’ Lacation and Speed

Considering the parameter matching of the in-wheel spring and rubber bushing as a two-dimensional optimization problem, the updating functions of the particles’ optimization speed and positions can be written as:

In Equations (9) and (10), i is the particle number, j the optimal dimension number, and t the iterations number. v_{ij}(t) and x_{ij}(t) represent the optimization speed and position at the tth iteration, respectively. pbest_{ij}(t) and gbest_{ij}(t) are the partial optimal position and the global optimal position, respectively. W is the inertia weight factor. c_{1} and c_{2} are the cognitive learning factor and the social learning factor, respectively. r_{1} and r_{2} are the random numbers [0,1], respectively.

The inertia weight factor is an important index which greatly affects the optimization effect. When a large inertia weight factor is selected, the global optimization ability of IPSO becomes strong, but the convergence ability gets worse. On the contrary, when a small inertia weight factor is selected, the global search ability becomes weak, but the local search ability becomes strong and the search results can quickly converge. Therefore, it is necessary to dynamically adjust the inertia weight factor to improve the flexibility of the IPSO. In the early stage of the algorithm, a large inertial weight factor is set to enhance the global search ability, while in the later stage, a relatively small value is set to enhance the local search ability of the particle near the optimal solution, while, the convergence is accelerated.

At present, adjustment of the inertia weight factor is realized through linear or nonlinear decreasing methods. The linear method features easy control and intuitive effectiveness, but its parameter matching is often not optimized. In this study, the nonlinear decreasing method is employed to adjust the inertia weight factor. The adjustment scheme for the inertia weight is based on a decreasing function as below:

where

t is the current iteration number, and

t_{max} is the maximum number of iterations.

W_{1} is the inertia weight factor in the early stage, while

W_{2} in the later stage.

W_{1} and

W_{2} are set to 0.9 and 0.4, respectively, i.e.,

W(1) is 0.9 and

W(

t_{max}) = 0.4. The constant of 0.875 is to ensure that

W varies in the range of [0.4,0.9].

#### 3.1.2. Solving Objective Funtio

As the evaluation indexes, the four factors, vehicle body vertical acceleration

a_{s}, suspension dynamic deflection

f_{d}, wheel dynamic load

F_{d}, and motor wallop

F_{e}, can be expressed as:

In order to compare the performance of the proposed electric wheel with that of the conventional electric wheel, taking the in-wheel stiffness

K_{e} and damping coefficient

C_{e} as optimization variables, the objective function is established as:

where

a_{s}(σ),

f_{d}(σ),

F_{d}(σ) and

F_{e}(σ) represent the RMS values of

a_{s},

f_{d},

F_{d} and

F_{e} of IWMs EV with the proposed electric wheel, respectively.

a_{s}(ω),

f_{d}(ω),

F_{d}(ω) and

F_{e}(ω) are the RMS values of the four indexes of the IWMs EV with conventional electric wheel, respectively.

α,

β,

λ and

η are the weight coefficients of the four indexes, respectively.

According to the requirements of “primarily optimizing the body vertical acceleration and the motor wallop, and secondarily optimizing the suspension dynamic deflection and the wheel dynamic load”, both α and η are set to 2, and both β and λ are set to 1.

In order to ensure the wheel-road adhesion and vehicle driving stability, the probability of the wheel moving off the road should be less than 0.15%, and the probability of the suspension impacting the limit block should be less than 0.3%. The constraint condition is as follows:

where

G is the static load on the wheel and

G = (

m_{s} + m_{t} + m_{e}_{1} + m_{e}_{2})

g. [

f_{d}] is the allowable value of the suspension dynamic deflection, and it is set to 80 mm.

In this study, the motor rotor and the rim are connected together through bolts. For better motor performance, the vertical displacement between the hub and motor should be less than 6 mm, and its RMS value is less than 2.5 mm, as shown below:

The basic parameters of the IPSO algorithm are set as follows. The population size is set to 30. The inertia weight factor is based on the nonlinear decreasing adjustment method, where the initial and final values are set to 0.9 and 0.4, respectively. The maximum number of iterations is set to 200. The acceleration factors c_{1} and c_{2} are set to 2. The reference range of parameter K_{e} is set to [0,30,000] N/m and the reference range of C_{e} is set to [0,8000] N·s/m.

Under the typical conditions of the C-class pavement at a speed of 70 km/h, the optimized parameters of in-wheel spring

K_{e} and damper

C_{e} are as follows:

#### 3.2. LQR Control of the Vehicle Suspension Damper Force

The proposed in-wheel vibration absorber is to reduce motor wallop. Meanwhile, it also changes the dynamics characteristics of vehicle, leading to ineffectiveness of the original suspension. Therefore, it is necessary to control vehicle suspension according vehicle operation conditions. In this study, the vehicle suspension damper force is controlled to improve vehicle ride comfort by utilizing the linear quadratic regulator (LQR) algorithm. From Equations (1)–(3), the quarter vehicle model can be rewritten as the linear state equation as:

where

x is variable states matrix,

y outputs matrix, and

u the controlled force of suspension damper.

**A**,

**B**,

**C**,

**D** and

**G** are coefficient matrixes.

w is road excitation

$\dot{q}(t)$. They are expressed as:

The objective function is established based on the four evaluation indexes, vehicle body vertical acceleration, suspension dynamic deflection, wheel dynamic load and motor vertical acceleration, as shown below:

where

q_{1},

q_{2},

q_{3},

q_{4} are the weighed coefficients of vehicle body vertical acceleration, suspension dynamic deflection, wheel dynamic load, and motor vertical acceleration, respectively.

Based on the Equation (17), the objective function in Equation (18) can be deuced as:

where

**Q** is the weighted coefficient matrix of the state variables and

**R** is the weighted coefficient matrix of the input variables. Both

**Q** and

**R** are positive definite matrices.

**N** is the associated matrix of

**Q** and

**R**. They can be deduced as:

According to the optimal control theory, we can solve the suspension controllable force

u_{s}, as the optimal solution of objective function (Equation (19)):

where

**K** is feedback gain matrix, which can be solved by the Riccati equation as:

With MATLAB software, the feedback gain matrix

**K** can be solved by using the LQR function as:

As shown in the objective function Equation (18), the weighed coefficients

q_{1},

q_{2},

q_{3},

q_{4} enormously influence the optimization effectiveness. In this study,

q_{1},

q_{2},

q_{3},

q_{4} are obtained by using the IPSO introduced above as:

#### 3.3. Fuzzy PID Control of In-Wheel Damper Force

The in-wheel vibration absorber with the matched parameters determined in the previous section can function effectively to reduce motor wallop under most vehicle operation conditions. However, due to the complexity of the road excitation, the in-wheel absorber with fixed parameters cannot exploit this to achieve an optimum performance. Additionally, since the in-wheel absorber is intercoupled with the vehicle suspension, it is essential to control the in-wheel absorber to further improve vehicle ride comfort.

In this section, a fuzzy PID controller is designed to adjust the in-wheel controllable damper force. A two-dimension fuzzy controller is employed to determine the coefficients of the PID controller, K_{p}, K_{i}, and K_{d}. The motor vertical acceleration E_{ae} and its gradient EC_{ae} are taken as inputs for the fuzzy controller. The main parameters of the fuzzy controller are determined as follows:

The basic domains of E_{ae} and EC_{ae} are set to [−6,6] and [−60,60], respectively, and the relevant fuzzy domains are both set to [−6,6]. The quantization factors are set as k_{e} = 1 and k_{ec} = 0.1.

The basic domains of output

K_{p},

K_{i} and

K_{d} are set to [−60,60], [−0.6,0.6], and [−0.00006,0.00006], respectively. The relevant fuzzy domains are all set to [−6,6]. The scale factors are set as

k_{p} = 10,

k_{i} = 0.1,

k_{d} = 0.00001. The initial values of

K_{p},

K_{i} and

K_{d} are set as:

Seven fuzzy languages are selected to describe the values of inputs and outputs. They are Positive-Big (PB), Positive-Medium (PM), Positive-Small (PS), Zero (Z), Negative-Small (NS), Negative-Medium (NM), and Negative-Big (NB).

All fuzzy subsets’ membership functions are selected as triangular functions.

Based on comprehensive simulations, fuzzy rules for

K_{p},

K_{i} and

K_{d} are established, as shown in

Table 1,

Table 2 and

Table 3, respectively. The relevant fuzzy surface of

K_{p},

K_{i} and

K_{d} are shown in

Figure 6a–c.

In order to suppress the motor vibration, motor vertical acceleration

a_{e} is taken as the input of PID controller. The controlled damper coefficient

$\Delta {C}_{ce}$ and force

$\Delta {F}_{ce}$ can be expressed as: