Multi-objective control and optimization of active energy-regenerative suspension based on road recognition

LI Yi-nong, ZHU Zhe-wei, ZHENG Ling, HU Yi-ming. Multi-objective control and optimization of active energy-regenerative suspension based on road recognition[J]. Journal of Traffic and Transportation Engineering, 2021, 21(2): 129-137. doi: 10.19818/j.cnki.1671-1637.2021.02.011

Citation:

LI Yi-nong, ZHU Zhe-wei, ZHENG Ling, HU Yi-ming. Multi-objective control and optimization of active energy-regenerative suspension based on road recognition[J]. Journal of Traffic and Transportation Engineering, 2021, 21(2): 129-137. doi: 10.19818/j.cnki.1671-1637.2021.02.011

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Multi-objective control and optimization of active energy-regenerative suspension based on road recognition

doi: 10.19818/j.cnki.1671-1637.2021.02.011

College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400030, China

Funds:

National Key Research and Development Program of China 2017YFB0102603-3

Science and Technology Project of Chongqing CSTC2018JCYJAX0630

More Information

Author Bio:
LI Yi-nong(1961-), male, professor, PhD, ynli@cqu.edu.cn
Received Date: 2020-11-01
Publish Date: 2021-04-01

Abstract

Abstract

For the problem that the vibration reduction performance and energy-regenerative characteristics of active suspension are less adaptable under different road classes, a nonlinear electromagnetic active suspension model was constructed. Considering the suspension sprung mass uncertainty during vehicle driving, an adaptive sliding mode controller of active suspension was proposed. An adaptive fuzzy neural network and the dynamics data of suspension under different roads were used to recognize road classes and determine the objective coefficient of the controller. Then, the coordination between safety and comfort of active suspension was realized. The energy-regeneration characteristics and switch control strategies of electromagnetic active suspension were studied. On this basis, the suspension dynamic performance and energy-regeneration characteristic were taken as the design objectives, and the contradictory relationships between the safety, comfort, and energy efficiency of electromagnetic active suspension were considered to comprehensively optimize the controller and suspension structure parameters through the multi-objective particle swarm optimization (MOPSO). The optimal solution was acquired from the Pareto solution set after the multi-objective optimization according to the fuzzy set theory. Research result reveals that the fuzzy neural network gives a maximum recognition error within 10% for various road classes when the nonlinear electromagnetic active suspension is employed. Thus, it meets the requirement of recognition accuracy. For C-class roads, the vibration acceleration of sprung mass of optimized active suspension reduces by 35.3% compared with the traditional passive suspension. The tire dynamic displacement increases by 7.7%, but it is still within 10%, ensuring safety. Compared with the original active suspension, the optimized suspension has 10.5% less sprung mass vibration acceleration and 1.7% higher energy-regeneration efficiency. The optimized adaptive sliding mode controller can better balance the energy-regeneration and vibration reduction characteristics of suspension. The established nonlinear electromagnetic active suspension model can realize the comprehensive optimization of safety, comfort, and energy efficiency of suspension system under different road classes. 5 tabs, 9 figs, 30 refs.

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0. introduction

As an important component of the automotive chassis system, the suspension system mainly functions to reduce body vibration, improve driving safety and comfort. Compared with traditional passive suspension, active suspension can improve the smoothness and handling stability of vehicles, thereby achieving the best dynamic performance of vehicles under different road conditions, which is one of the main research issues for future intelligent electric vehicles.

1. 汽车悬架非线性模型

1.1 Active Suspension Dynamics Model

Figure 1For the 1/4 vehicle active suspension model, where:z_rInput for road surface;z_tDisplacement of the mass under the spring;z_sDisplacement of the mass on the spring;k_tFor tire stiffness;k_sFor suspension stiffness;C_sFor suspension damping coefficient;m_sFor spring quality;m_tFor the quality under the spring;FProvide electromagnetic power for the motor.

Figure 1. Active suspension model with two degree of freedom

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The damping force of the shock absorber isF_cThe speed damping force characteristic can be expressed as

$\begin{aligned} F_{\mathrm{c}}=& C_{1}\left({\dot{z}}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right)+C_{2}\left|\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right|+\\ & C_{3} \sqrt{\left|\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right|} \operatorname{sgn}\left(\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right) \end{aligned}$

(1)

In the formula:C₁andC₂They are linear and nonlinear damping coefficients, respectively;C₃The coefficient related to the asymmetry of the damper^[29]Sgn (·) is a step function.

$F_{\mathrm{k}}=k_{1}\left(z_{\mathrm{s}}-z_{\mathrm{t}}\right)+k_{2}\left(z_{\mathrm{s}}-z_{\mathrm{t}}\right)^{3}$

(2)

In the formula:k₁andk₂They are the linear and nonlinear coefficients of spring stiffness, respectively.

This article uses filtered white noise to obtain the time-domain signal of the road surface. Based on the nonlinear characteristics of a two degree of freedom suspension, the vibration differential equation of a 1/4 vehicle active suspension nonlinear system is obtained

$\left\{\begin{array}{l} m_{\mathrm{s}} \ddot{z}_{\mathrm{s}}+F_{\mathrm{c}}+F_{\mathrm{k}}+F=0 \\ m_{\mathrm{t}} \ddot{z}_{\mathrm{t}}-F_{\mathrm{c}}-F_{\mathrm{k}}-F+k_{\mathrm{t}}\left(z_{\mathrm{t}}-z_{\mathrm{r}}\right)=0 \end{array}\right.$

(3)

1.2 Active suspension energy feedback circuit model

The electromagnetic active suspension actuator structure is a linear actuator that senses electromotive forceU₀And induced currentI₀Can be expressed as

$\left\{\begin{array}{l} U_{0}=K_{\mathrm{e}}\left(\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right) \\ I_{0}=U_{0} / R_{0} \end{array}\right.$

(4)

In the formula:K_eThe coefficient of back electromotive force for linear motors;R₀The internal resistance of the motor.

Electric motor electromagnetic actuation forceFIt can be expressed as

$F=K_{\mathrm{f}} I_{0}$

(5)

In the formula:K_fFor thrust coefficient.

When a linear motor is used as a generator, its equivalent damping isC_edo

$C_{\mathrm{e}}=K_{\mathrm{f}} K_{\mathrm{e}} / R_{0}$

(6)

$I_{1}=\left(U_{1}-U_{0}\right) / R_{0}$

(7)

When a linear motor is used as a generator, the energy feeding circuit is as followsFigure 2As shown, where:R_lFor load resistance;L₀For internal inductance;L₁For external inductance, inductance can be ignored in calculation.

Figure 2. Energy-regenerative circuit

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Table 1. System parameters of active suspension

参数	数值
m_s/kg	285
m_t/kg	40
k₁/(N·m^-1)	15 680
k₂/(N·m^-3)	1 568
C₁/(N·s·m^-1)	1 780
C₂/(N·s·m^-2)	100
C₃/(N·s·m^-1)	1 000
k_t/(N·m^-1)	180 000
K_e/(V·s·m^-1)	69
K_f/(V·s·m^-1)	78
R₀/Ω	5
R_l/Ω	0~1 000

| Show Table

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2. 基于路面识别的自适应滑模控制器

2.1 Design of Adaptive Sliding Mode Controller

Due to the nonlinear characteristics of the suspension model in this article, a sliding mode controller can be used to control the active suspension. At the same time, considering that in the actual driving process of vehicles, the spring-loaded mass has a certain degree of uncertainty due to differences in fuel consumption, passenger quantity, and cargo situation, this paper designs an adaptive sliding mode controller to eliminate the influence of the uncertainty of spring-loaded mass on the control effect of the controller.

Define Parameterse₁、e₂ande₃respectively

$\left\{\begin{array}{l} e_{1}=z_{\mathrm{s}}-z_{\mathrm{t}} \\ e_{2}=z_{\mathrm{s}} \\ e_{3}=z_{\mathrm{t}}-z_{\mathrm{r}} \end{array}\right.$

(8)

set upc₁, c₂, c₃> 0, all are controller parameters, design sliding mode functionsdo

$s=c_{1} e_{1}+c_{2} e_{2}+c_{3} e_{3}+\dot{e}_{2}$

(9)

Define Lyapunov functionVdo

$V=\frac{1}{2} m_{\mathrm{s}} s^{2}+\frac{1}{2 \gamma} m_{\mathrm{s}}^{2}$

(10)

$\begin{aligned} \dot{V}=& s\left(m_{\mathrm{s}} c_{1} \dot{e}_{1}+m_{\mathrm{s}} c_{2} \dot{e}_{2}+m_{\mathrm{s}} c_{3} \dot{e}_{3}-F_{\mathrm{c}}-\right.\\ &\left.F_{\mathrm{k}}-F\right)+\frac{1}{\gamma} \tilde{m}_{\mathrm{s}} \dot{\hat{m}}_{\mathrm{s}} \end{aligned}$

(11)

$\begin{aligned} F=& \hat{m}_{\mathrm{s}}\left(c_{1} \dot{e}_{1}+c_{2} \dot{e}_{2}+c_{3} \dot{e}_{3}\right)-\\ & F_{\mathrm{c}}-F_{\mathrm{k}}-\varepsilon_{1} s-\varepsilon_{2} \operatorname{sgn}(s) \end{aligned}$

(12)

Then there are

$\begin{aligned} \dot{V}=&s\left[\hat{m}_{s}\left(c_{1} \dot{e}_{1}+c_{2} \dot{e}_{2}+c_{3} \dot{e}_{3}\right)-\varepsilon_{1} s-\varepsilon_{2} \operatorname{sgn}(s)-\right. \\ &\left.m_{s}\left(c_{1} \dot{e}_{1}+c_{2} \dot{e}_{2}+c_{3} \dot{e}_{3}\right)\right]+\frac{1}{\gamma} \tilde{m}_{\mathrm{s}} \dot{\hat{m}}_{\mathrm{s}}=-\varepsilon_{1} s^{2}- \\ & \varepsilon_{2}|s|+\tilde{m}_{\mathrm{s}}\left[s\left(c_{1} \dot{e}_{1}+c_{2} \dot{e}_{2}+c_{3} \dot{e}_{3}\right)+\frac{1}{\gamma} \dot{\hat{m}}_{\mathrm{s}}\right] \end{aligned}$

(13)

Taken from the fitness rate as

$\dot{\hat{m}}_{\mathrm{s}}=-\gamma{s}\left(c_{1} \dot{e}_{1}+c_{2} \dot{e}_{2}+c_{3} \dot{e}_{3}\right)$

(14)

$\dot{V}=-\varepsilon_{1} s^{2}-\varepsilon_{2}|s| \leqslant-\varepsilon_{1} s^{2} \leqslant 0$

(15)

According to the LaSalle invariance principle^[30]The closed-loop system is asymptotically stable, that is, whent→+∞，sAt 0 o'clock, due toV≥0，$\dot{V}$≤ 0, then whentWhen →+∞,VBounded, therefore, it can be proven$\hat{m}$_sThere is a boundary, but it cannot be guaranteed$\hat{m}$_sconverges tom_sIn order to prevent$\hat{m}$_sExcessive electromagnetic force inputFToo large or$\hat{m}$_sIn the case of ≤ 0, it is necessary to design an adaptive rate to$\hat{m}$_sThe changes are[m_{s, min}, m_{s, max}]Within the scope, this article adopts a mapping adaptive algorithm to correct the adaptive rate

$\dot{\hat{m}}_{\mathrm{s}}=\left\{\begin{array}{ll} & \hat{m}_{s} \geqslant m_{\mathrm{s}, \max } \text { 且 } \dot{\hat{m}}_{\mathrm{s}}>0 \\ 0 &\\ & \hat{m}_{\mathrm{s}} \leqslant m_{\mathrm{s}, \min } \text { 且 } \dot{\hat{m}}_{\mathrm{s}}<0 \\ \dot{\hat{m}}_{\mathrm{s}} & \text { 其他 } \end{array}\right.$

(16)

2.2 路面识别算法设计

This article uses an adaptive fuzzy neural network algorithm to identify road surface grades. This algorithm uses Takagi Sugeno fuzzy model and weighted sum method to calculate the final output. Compared with the centroid method of traditional fuzzy systems, it simplifies data processing and greatly reduces computation time. The structure of adaptive fuzzy neural network is as followsFigure 3As shown.

Figure 3. Structure of adaptive fuzzy neural network

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Figure 3The functions of each layer in the middle are: the first layer will input variablesx₁、x₂Fuzzy processing is performed using fuzzy rules A1, A2, B1, and B2; The second layer multiplies the fuzzified input signal algebraically to obtain the outputω₁、ω₂The third layer handles the triggering strength of each ruleNObtain standardized trigger strengthω₁、ω₂The fourth layer calculates the output through the defuzzification rules C1 and C2; The fifth layer sums up all signals to obtain the total outputy.

$z_{\mathrm{r}}=f\left[\ddot{z}_{\mathrm{t}}, z_{\mathrm{t}},\left(z_{\mathrm{s}}-z_{\mathrm{t}}\right),\left(\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right)\right]$

(17)

Figure 4. Road recognition by adaptive fuzzy neural network

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Table 2. Recognition errors in different roads

路面等级	识别误差均方根/mm	识别误差率/%
A	8.3×10^-6	0.26
B	3.2×10^-4	1.37
C	3.6×10^-3	4.65
D	9.4×10^-3	8.12

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2.3 基于路面识别的控制器参数选取

Table 3. Control objective coefficients under different road classes

路面等级	q₁	q₂	q₃
良好(A、B级)	0.80	0.80	1.20
一般(C、D级)	0.90	0.90	1.10
较差(E、F级)	0.95	0.95	1.05

| Show Table

DownLoad: CSV

$\left\{\begin{array}{l} \ddot{z}_{\mathrm{s}}<0.9 \ddot{z}_{\mathrm{s} 0} \\ z_{\mathrm{s}}-z_{\mathrm{t}}<0.9\left(z_{\mathrm{s}}-z_{\mathrm{t}}\right)_{0} \\ z_{\mathrm{t}}-z_{\mathrm{r}}<1.1\left(z_{\mathrm{t}}-z_{\mathrm{r}}\right)_{0} \end{array}\right.$

(18)

3. 主动悬架馈能切换策略设计

3.1 主动悬架馈能特性

$P_{\mathrm{c}}=C_{\mathrm{s}}\left(\dot{\dot{z}_{\mathrm{s}}}-\dot{z}_{\mathrm{t}}\right)^{2}$

(19)

$P_{\circ}=\frac{1}{T} \int_{0}^{T} U_{1} I_{1} \mathrm{~d} t$

(20)

Average energy feeding efficiencyηdo

$\eta=\frac{1}{T} \int_{0}^{T} P_{0} / P_{\mathrm{c}} \mathrm{d} t$

(21)

3.2 Switching strategy for energy feedback suspension control

Whether the active suspension is in active mode or feedback mode depends on the actual working conditions and corresponding control switching strategies. The traditional feedback suspension control switching strategy is:$\dot{\dot{z}}_{\mathrm{s}}\left(\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right)>0$When the mass on the spring is aligned with the direction of motion of the actuator, the active suspension is in energy feeding mode; equal$\dot{z}_{\mathrm{s}}\left(\dot{z}_{\mathrm{s}}-\dot{z}_{\mathrm{t}}\right)<0$When the mass on the spring is opposite to the direction of motion of the actuator, the motor is in active mode to suppress the vibration of the suspension.

Table 4. Energy-regenerative switch control strategies of active suspension

路面等级	切换控制策略
良好(A、B级)	馈能模式
一般(C、D级)	馈能-主动模式
较差(E、F级)	主动模式

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4. 基于安全、舒适、节能的主动悬架多目标粒子群综合优化

The structure of the active suspension controller described in this article is as followsFigure 5As shown, it is mainly divided into three parts: road recognition, suspension control, and multi-objective optimization of feedback suspension. Road surface recognition identifies the current road surface level based on the quality signal on the spring, and inputs the road surface level into the control section and the feedback section; Select control target coefficients and energy feeding switching strategies based on road surface grade to achieve coordinated optimization of active energy feeding suspension comfort, safety, and energy efficiency; Considering that the suspension system is not only affected by the control parameters of the actuators, but also by the structural parameters of the suspension itself and the current vehicle speed, with safety, comfort, and energy-saving indicators as the control objectives, the particle swarm algorithm is used to perform multi-objective optimization on the overall model of the active feedback suspension in the feedback active mode.

Figure 5. Multi-objective optimization structure of active suspension

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4.1 主动悬架多目标粒子群优化

The constraint conditions for design variables need to be analyzed and selected in conjunction with the actual vehicle structure. Considering that the full load offset frequency is generally 1.00-1.45Hz, the range of suspension stiffness values for this model is 75% to 1.25 times the passive suspension reference value. The damping and size of the dampers are closely related and cannot vary within a large range. Therefore, 75% to 1.25 times the reference value is also selected.c₁、c₂andc₃The selection range is from 0 to 100.

Because the suspension structure parameters cannot be changed after the vehicle is manufactured, considering that the main roads in China are mainly B and C grade roads, and B grade roads are relatively flat, with low requirements for comfort and safety, the design of suspension structure parameters takes into account the driving conditions of the vehicle on C grade roads, where the active feedback suspension is in feedback active mode.

The tire travel in the optimization objective mainly affects driving safety, the spring-loaded mass acceleration affects driving comfort, and the energy feeding efficiency affects energy saving. After optimization, the local optimal solution set is obtained as follows:Figure 6As shown in the figure, it can be seen that when the ride comfort and safety reach the comprehensive optimal dynamic performance, the energy feedback efficiency is the lowest, and increasing the energy feedback efficiency will inevitably result in a certain loss of comfort or safety. Therefore, in order to achieve the comprehensive optimization of suspension dynamic performance and energy feedback performance, it is necessary to have reasonable decision-making conditions to select the optimal solution.

Figure 6. Pareto solution set in multi-objective optimization

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4.2 最优解选取策略

$s_{i, j}=\left\{\begin{array}{ll} 1 & f_{i, j} \leqslant f_{i, \min } \\ \frac{f_{i, \max }-f_{i, j}}{f_{i, \max }-f_{i, \min }} & f_{i, \min }<f_{i, j}<f_{i, \max } \\ 0 & f_{i, j} \geqslant f_{i, \max } \end{array}\right.$

(22)

$\varphi_{k}=\sum\limits_{i=1}^{n} s_{i, k} / \sum\limits_{j=1}^{l} \sum\limits_{i=1}^{n} s_{i, j}$

(23)

Select the solution with the highest dominance value according to equations (24) and (25) as the typical solution of the Pareto solution set. The optimal solution isk₁=13 979 N·m^-1, C₁=1 323 N·s·mm^-1，c₁=78，c₂=28，c₃=44.

Compare the original parameters and optimize the active suspension in both time and frequency domains on a C-class road surface at a speed of 60 km · h^-1The dynamic performance and energy feedback performance during vehicle speed are shown inFigure 7~9.

Figure 7. Vibration acceleration responses of sprung mass of optimized active suspension

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Figure 8. Dynamic deflection responses of optimized active suspension

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Figure 9. Tire dynamic displacement responses of optimized active suspension

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Table 5. Dynamics performance and energy-regenerative efficiency of optimized active suspension

参数	优化后主动悬架	原悬架	被动悬架
簧上质量加速度/(m·s^-2)	0.726 1	0.844 4	1.123 0
变化量百分比/%	-35.0	-24.0	0.0
悬架动挠度/m	0.011 8	0.010 0	0.010 7
变化量百分比/%	10.0	-6.5	0.0
车轮动行程/m	0.002 8	0.002 7	0.002 6
变化量百分比/%	7.7	3.8	0.0
馈能效率/%	7.10	5.44	0.00

| Show Table

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The simulation results show that by using multi-objective particle swarm optimization algorithm and fuzzy set theory to select optimized structural parameters and control parameters, active feedback suspension can better achieve the comprehensive optimization of vehicle suspension system safety, comfort, and energy saving.

5. conclusion

(2) Designed an adaptive sliding mode controller to control active suspension, and proposed a strategy for selecting active suspension control parameters under different road surface levels, combined with road recognition algorithms.

(3) Compared with traditional active suspension, the optimized active suspension reduces the spring-loaded mass acceleration by 10.5% and increases the energy feedback efficiency by 1.7%. At the same time, it can control the increase in tire travel within a safe range of 10%, improving the comfort and energy efficiency of the active suspension system while ensuring safety.

(4) Future research will address the issue of unstable control effects caused by the switching between active and feedback modes in practical circuits, and further improve the feedback circuit to design a more robust active feedback suspension controller.

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Multi-objective control and optimization of active energy-regenerative suspension based on road recognition

doi: 10.19818/j.cnki.1671-1637.2021.02.011