# Multi-Mode Switching Control Strategy for IWM-EV Active Energy-Regenerative Suspension Based on Pavement Level Recognition

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dynamic Modeling

#### 2.1. Active Energy-Regenerative Suspension Model

_{s}denotes the body mass, m

_{u}denotes the wheel mass, θ represents the pitch angle, φ represents the roll angle, c

_{sij}represents the damping of the main suspension, k

_{si}represents the spring stiffness of the main suspension, k

_{ti}represents the tire stiffness, k

_{di}represents the spring stiffness of the secondary suspension, F

_{i}represents the control force of the main suspension, f

_{i}represents the control force of the secondary suspension, F

_{b}represents the vertical force generated by the torque fluctuation of the switched reluctance motor (the subscripts i = 1, 2, 3, 4 represent the left front, right front, left rear, right rear, respectively), d

_{f}and d

_{b}represent the distance from the center of mass to the front axle and the rear axle, d

_{l}and d

_{r}represent the distance from the left and right wheels to the center of mass, and I

_{x}and I

_{y}represent the moment of inertia when the vehicle rolls and pitches. The linear motor actuators M1 and M2 are placed at the main suspension and the secondary suspension, respectively, and the active control force is the output according to the different road surfaces and vehicle speeds. Figure 1 shows the vehicle suspension dynamics model of the in-wheel motor drive electric vehicle.

#### 2.2. Motor Vertical Force Model

_{e}is the electromagnetic torque of the in-wheel motor, a is the motor speed, b is the air gap length, R is the stator inner radius, r is the rotor cooling radius, L

_{min}is the minimum inductance, K is the ratio of inductance to rotor angular displacement, T is the torque ripple frequency, and N

_{r}is the number of rotor poles. i is the motor winding current, n = 1, 2, 3, 4… As shown in Table 2 and Figure 3, the vertical force of the in-wheel motor is due to torque fluctuation during the driving process of the vehicle.

#### 2.3. Active Suspension Energy-Regenerative Circuit Model

_{0}and U

^{*}

_{0}are the electromotive force of the main suspension and the secondary suspension, respectively, and I

_{0}and I

^{*}

_{0}are the induced current of the main suspension and the secondary suspension, respectively, K

**is the back electromotive force coefficient of the linear motor, R**

_{e}_{0}is the motor internal resistance. When the linear motor is used as the motor, the main suspension motor electromagnetic power F

_{i}and the secondary suspension motor electromagnetic power f

_{i}can be expressed as follows:

_{f}is the thrust coefficient. When the linear motor is used as the generator, the equivalent damping C

_{e}is as follows:

_{1}, and the current through the shock absorber is as below:

_{1}is the load resistance, L

_{1}is the internal inductance, L

_{0}is the external inductance, and the inductance can be ignored in the calculation. The parameters of the energy-feeding circuit model of the linear motor are shown in the following Table 3.

#### 2.4. Improved CVD Skyhook Reference Model of Vehicle

_{de}is the actual damping force, C

_{max}, C

_{min}is the upper and lower limits of the damping force coefficient of the suspension. Then the upper and lower limits of the damping coefficient are set to 6000 N/m and 500 N/m, respectively.

## 3. The Active Control Strategy of Energy-Regenerative Suspension Based on Road Recognition

#### 3.1. Design of Main Suspension Controller

_{z}, u

_{x}, and u

_{y}, which are the control force and torque required to track the vertical, pitch, and the roll motion of the body spring mass of the CVD improved skyhook reference model, respectively. It is generated by the linear motor actuator M1 and can be expressed as follows:

_{sr}is the vertical displacement of the reference model, and the sliding surface is defined as follows:

_{eq}and the switching control u

_{sw}, namely,

_{zij}is the vertical load of four wheels (ij represents left front, right front, left rear, and right rear, respectively). The switch control output is as given:

_{z}is determined by the performance and stability conditions of the actuator. The stability condition of Lyapunov is as given:

_{z,eq}is to let s

_{z}= 0, then Formula (23) can be expressed as follows:

_{z}$\ge $ η, the sliding mode control system satisfies the Lyapunov stability condition, at the same time, in order to avoid the problem of ‘chattering’ caused by the unsatisfactory switching control output in the actual control system, the sign function in the formula can be replaced by the saturation function to form a quasi-sliding mode. The output of the sliding mode controller can be expressed as below:

_{r}and φ

_{r}are the rolling angle and pitching angle of the reference model. According to Formula (24), the corresponding control damping force of each suspension is expressed as below:

^{+}denotes inverse pseudo-matrix.

#### 3.2. Design of Secondary Suspension Controller

_{p}is the proportional gain in the PID controller, K

_{i}is the integral gain in the PID controller, K

_{d}is the differential gain in the PID controller, and U is the control signal transmitted by the PID control to the controlled object (in-wheel motor); that is, the secondary suspension linear actuator M2 outputs the control force f

_{i}.

#### 3.3. Road Recognition Model

#### 3.4. Design of Working Mode Switching Strategy for Active Regenerative Suspension

## 4. Controller Parameter Optimization

#### 4.1. Particle Swarm Optimization

_{i}= (x

_{i1}, x

_{i}

_{2},…, x

_{i}

_{D}) for the first particle, v

_{i}= (v

_{i}

_{1}, v

_{i}

_{2},…, v

_{i}

_{d}) for the velocity of the first particle, p

_{besti}= (p

_{i}

_{1}, p

_{i}

_{2},…, p

_{i}

_{D}) represents the best position that the first particle has ever experienced, gbest = (g

_{1}, g

_{2},…, g

_{D}) is the best position the population has ever experienced. The ith particle’s d-dimensional velocity is updated to the following:

^{k}

^{+1}

_{id}is the d-dimensional component of the flight velocity vector of the ith particle in the k + 1 iteration, V

^{k}

_{id}is the d-dimensional component of the position vector of the ith particle in the kth iteration, c

_{1}, c

_{2}are the numbers of the accelerated constant, r

_{1}, r

_{2}are two random functions, ω is the inertia weight, X

^{k}

_{id}is the position of the kth particle, X

^{k}

^{+1}

_{id}is the position of the k + 1st particle, P

^{k}

_{id}is the dth dimension of the individual extreme value of i variable in the kth iteration, and P

^{k}

_{gd}is the dth dimension of the global optimal solution of the kth iteration. The flow chart of the particle swarm optimization algorithm is shown in Figure 9.

#### 4.2. Selection of Objective Functions

_{z}, c

_{x}, c

_{y}, K

_{p}, K

_{i}, K

_{d}are used as optimization variables, and the optimal variables range from 1 to 100. Taking the vertical acceleration of body mass center ${\ddot{z}}_{s}$, the dynamic deflection of suspension ${z}_{s1}-{z}_{u1}$, the vertical acceleration of in-wheel motor ${\ddot{z}}_{d}$, the pitch angle acceleration $\ddot{\phi}$, the roll angle acceleration $\ddot{\theta}$, the tire run-out, the energy efficiency as optimization objectives, then the subscript 0 represents the index of passive suspension. Because the energy saving and dynamic performance of the system are inversely proportional, the system’s energy saving will be sacrificed while improving the dynamic performance. Therefore, this paper has the following considerations. When the working mode is active-energy feeding mode, L

_{2}is taken as the objective function to improve the system’s dynamic performance. When the actuator working mode is active mode, L

_{1}is taken as the objective function.

_{z}, c

_{x}, c

_{y}, K

_{p}, K

_{i}, K

_{d}]; the main suspension variable constraint is c

_{z}∈[1,100], c

_{x}∈[1,100], c

_{y}∈[1,100]; the secondary suspension variable constraints are K

_{p}∈[1,100], K

_{i}∈[1,100], K

_{d}∈[1,100].

#### 4.3. Controller Parameter Optimization Results

_{z}, c

_{x}, c

_{y}, and PID controller parameters K

_{p}, K

_{i}, and K

_{d}are optimized by particle swarm optimization. Shown in Figure 11 is the function value convergence curve of the objective function L

_{1}under the A-level road speed of 25 m/s, etc. Under other road grades and vehicle speeds, the optimization results are shown in Table 6.

## 5. Simulation and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Control strategy of active regenerative suspension based on particle swarm optimization algorithm.

Parameter | Numerical Value | Parameter | Numerical Value |
---|---|---|---|

m_{s}/kg | 1400 | d_{b}/m | 2.23 |

m_{u}/kg | 45 | d_{r}/m | 0.89 |

k_{si}/(N·m^{−1}) | 3.500 × 10^{4} | d_{l}/m | 0.89 |

k_{ti}/(N·m^{−1}) | 3.6 × 10^{5} | I_{x}/(kg·m^{2}) | 480 |

k_{di}/(N·m^{−1}) | 4.1 × 10^{4} | I_{y}/(kg·m^{2}) | 1800 |

c_{si}/(N·m^{−1}) | 500 | ||

d_{f}/m | 1.07 |

Parameter | T_{e}/(N·m) | a/(r/min) | R/m | r/m | i/A | L_{min} | K | T/s | N_{r} |

Numerical Value | 165 | 1540 | 0.05 | 0.047 | 1 | 4.95 | 82.50 | 0.0064 | 6 |

Parameter | K_{e} (V·s·m^{−1}) | K_{f} (V·s·m^{−1}) | R_{0}/Ω | R_{1/}Ω |

Numerical Value | 69 | 78 | 5 | 500 |

Road Grade Coefficient (cm ^{2}·circle/m) | Road Grade |
---|---|

R ≤ 0.01 | A, B |

0.01 ≤ R ≤ 1 | C, D |

R ≥ 1 | E, F |

Speed | High-Speed 20–30 m/s | Medium-Speed 10–20 m/s | Low-Speed 5–10 m/s | |
---|---|---|---|---|

Road Grade | ||||

A/B | Active mode ^{1} | Active energy feeding mode ^{1} | Energy feeding mode ^{1} | |

Active mode ^{2} | Active energy mode ^{2} | Energy feeding mode ^{2} | ||

C/D | Active mode ^{1} | Active mode ^{1} | Active energy feeding mode ^{1} | |

Active mode ^{2} | Active mode ^{2} | Active energy feeding mode ^{2} | ||

E/F | Active mode ^{1} | Active mode ^{1} | Active energy feeding mode ^{1} | |

Active mode ^{2} | Active mode ^{2} | Active energy feeding mode ^{2} |

^{1}, and the control mode on the side of the in-wheel motor of the secondary suspension is marked as

^{2}.

Road Grade | Controller Parameters | Vehicle Speed | ||
---|---|---|---|---|

High-Speed 25–30 m/s | Medium-Speed 10–25 m/s | Low-Speed 5–10 m/s | ||

AB | c_{z} | 59.0427 | 89.7925 | 63.2703 |

c_{x} | 35.6352 | 72.9580 | 56.2085 | |

c_{y} | 29.2819 | 29.5297 | 30.5650 | |

K_{d} | 36.5386 | 91.3970 | 59.6403 | |

K_{i} | 31.6952 | 69.1895 | 89.4170 | |

K_{d} | 35.4991 | 27.6442 | 90.2060 | |

CD | c_{z} | 83.5590 | 83.7802 | 86.3358 |

c_{x} | 46.8541 | 43.3376 | 28.1757 | |

c_{y} | 57.3479 | 76.6079 | 34.2089 | |

K_{d} | 72.4460 | 65.7413 | 49.9052 | |

K_{i} | 22.0542 | 52.1048 | 24.6754 | |

K_{d} | 88.1771 | 24.1279 | 62.4685 | |

EF | c_{z} | 93.5972 | 88.0484 | 99.0934 |

c_{x} | 28.2999 | 26.6679 | 24.3074 | |

c_{y} | 80.1341 | 47.6035 | 55.4561 | |

K_{d} | 79.2126 | 43.5261 | 21.1017 | |

K_{i} | 65.8949 | 80.7297 | 92.9954 | |

K_{d} | 34.0715 | 20.7073 | 35.3321 |

Root Mean Square Value | Passive Suspension | Active Suspension | Optimized Active Energy-Regenerative Suspension | A (%) | B (%) |
---|---|---|---|---|---|

Vertical acceleration of the center of mass (m/s^{2}) | 0.092 | 0.073 | 0.068 | −20.7 | −6.8 |

Dynamic deflection of the suspension (m) | 0.00137 | 0.0011 | 0.0008 | −16.1 | −27.3 |

Dynamic displacement of in-wheel motor (m) | 0.0032 | 0.0024 | 0.0021 | −25 | −12.5 |

Vertical acceleration of in-wheel motor (m/s^{2}) | 0.07 | 0.051 | 0.048 | −27.1 | −5.9 |

Angular acceleration of roll angle (rad/s^{2}) | 0.028 | 0.018 | 0.013 | −0.36 | −27.8 |

Angular acceleration of pitch angle (rad/s^{2}) | 0.18 | 0.0911 | 0.076 | −48.9 | −16.6 |

Tire runout (m) | 0.0012 | 0.001 | 0.0007 | −16.7 | −30 |

Root Mean Square Value | Passive Suspension | Active Suspension | Optimized Active Energy-Regenerative Suspension | A (%) | B (%) |
---|---|---|---|---|---|

Vertical acceleration of the center of mass (m/s^{2}) | 0.281 | 0.277 | 0.251 | −1.4 | −5.1 |

Dynamic deflection of the suspension (m) | 0.011 | 0.0098 | 0.0088 | −10.9 | −10.2 |

Dynamic displacement of in-wheel motor (m) | 0.024 | 0.0223 | 0.018 | −7.1 | −19.3 |

Vertical acceleration of in-wheel motor (m/s^{2}) | 0.527 | 0.461 | 0.431 | −12.5 | −6.5 |

Angular acceleration of roll angle (rad/s^{2}) | 0.1154 | 0.0884 | 0.06652 | −23.4 | −24.8 |

Angular acceleration of pitch angle (rad/s^{2}) | 0.138 | 0.132 | 0.121 | −4.3 | −8.3 |

Tire runout (m) | 0.0114 | 0.0111 | 0.01 | −2.6 | −9.9 |

Energy-regenerative efficiency (m/s^{2}) | - | - | 17% | - | - |

Root Mean Square Value | Passive Suspension | Active Suspension | Optimized Active Energy-Regenerative Suspension | A (%) | B (%) |
---|---|---|---|---|---|

Vertical acceleration of the center of mass (m/s^{2}) | 0.143 | 0.121 | 0.091 | −15.4 | −24.8 |

Dynamic deflection of the suspension (m) | 0.0046 | 0.0044 | 0.0037 | −4.3 | −15.9 |

Dynamic displacement of in-wheel motor (m) | 0.0104 | 0.0098 | 0.0088 | −5.8 | −10.2 |

Vertical acceleration of in-wheel motor (m/s^{2}) | 0.24 | 0.203 | 0.162 | −15.4 | −20.2 |

Angular acceleration of roll angle (rad/s^{2}) | 0.099 | 0.095 | 0.088 | −4.04 | −7.4 |

Angular acceleration of pitch angle (rad/s^{2}) | 0.063 | 0.056 | 0.044 | −11.1 | −21.4 |

Tire runout (m) | 0.005 | 0.0048 | 0.0044 | −4 | −8.3 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, Z.; Shi, Z.; Ding, X.
Multi-Mode Switching Control Strategy for IWM-EV Active Energy-Regenerative Suspension Based on Pavement Level Recognition. *World Electr. Veh. J.* **2023**, *14*, 317.
https://doi.org/10.3390/wevj14110317

**AMA Style**

Zhou Z, Shi Z, Ding X.
Multi-Mode Switching Control Strategy for IWM-EV Active Energy-Regenerative Suspension Based on Pavement Level Recognition. *World Electric Vehicle Journal*. 2023; 14(11):317.
https://doi.org/10.3390/wevj14110317

**Chicago/Turabian Style**

Zhou, Zhigang, Zhichong Shi, and Xinqing Ding.
2023. "Multi-Mode Switching Control Strategy for IWM-EV Active Energy-Regenerative Suspension Based on Pavement Level Recognition" *World Electric Vehicle Journal* 14, no. 11: 317.
https://doi.org/10.3390/wevj14110317