# Multimode Coordination Control of a Hybrid Active Suspension

Authors: Fa-Rong Kou; Dong-Dong Wei; Lei Tian
Journal: Shock and Vibration
 (2018)

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## Abstract

In order to effectively realize the damping control and regenerative energy recovery of vehicle suspension, a new kind of hybrid active suspension structure with the ball screw actuator and magnetorheological (MR) damper is put forward. Firstly, for the analysis of the suspension performance, a quarter dynamic model of vehicle hybrid suspension is established, and at the same time, the mathematical models of MR damper and ball screw actuator are founded. Secondly, the active mode with damping switching control of the hybrid suspension and the semiactive mode with feedback adjustment of the electromagnetic damping force of the hybrid suspension are analyzed. Then, the multimode coordinated control system of the hybrid suspension is designed. Under the cyclic driving condition, the damping performance and energy consumption characteristics of the hybrid suspension are simulated by MATLAB/Simulink software. Finally, the bench tests of the hybrid suspension system are done. The simulation and experimental results show that compared with passive suspension, the root mean square of the sprung mass acceleration of the hybrid suspension with the active mode and semiactive mode is, respectively, reduced by 39% and 16% under the random road. The damping effect of the hybrid suspension system is obvious.


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## Body

## 1. Introduction

A controllable actuator is used to replace the corresponding components of original passive suspension, which is named as an active suspension. Active suspension can adjust suspension stiffness and damping, according to changes in the current road conditions, to improve vehicle riding comfort and handling stability [1, 2]. However, the active suspension actuator needs to consume a large amount of external energy and it reduces the economic performance of the vehicle [3–5].In recent years, domestic and overseas scholars have been studying how to reduce the energy consumption of active suspension from two aspects. On the one hand, the regenerative energy active suspension structures are used to recover vibration energy, which is used for the active control of the suspension. For example, Nakano et al. [6, 7] used two linear motor actuators for active control and vibration energy recovery, respectively, and as a result, the active suspension system was self-powered. Huang et al. [8, 9] proposed a new type of energy-regenerative electromagnetic suspension structure with a parallel-type ball screw actuator, which included a fully active mode and semiactive mode. Huang et al. [10] designed a regenerative energy active suspension system and analyzed the power conversion process of the suspension system, and the simulation results show that under regenerative energy and active mode switching control, the suspension system was self-powered. However, when the regenerative energy active suspension is used to recover vibration energy of the suspension, the active control of the suspension cannot be realized, so the riding comfort and handling and stability of vehicle will be reduced.On the other hand, domestic and overseas scholars researched how to reduce the energy consumption of active suspensions by improving the suspension structures and optimizing the structural parameters of active suspensions. For example, Ebrahimi et al. [11] proposed a hybrid electromagnetic shock absorber, which was applied to an active suspension, developed a prototype of the shock absorber, and carried out the experimental researches; then, the tests show that the electromagnetic shock absorber was beneficial to reduce the energy consumption of the active suspension. Tang et al. [12] proposed an active suspension structure with paralleled three-gear variable damper and designed the switching control strategy of the damper, and the simulation results show that, for the suspension structure, the energy consumption under the active control mode was reduced. Wang et al. [13, 14] proposed a hybrid suspension structure with parallel damping variable shock absorber, designed the variable damping of the suspension in different working modes, and carried out the simulations and experimental research studies; the results show that for the suspension structure, the energy consumption under the active control mode was reduced. However, for the research studies on the active suspension structure and the structural parameters optimization, the energy consumption of the variable damping shock absorber is not taken into account, and the impacts of the energy consumption on the economic performance of the suspension system are not analyzed. Moreover, under different vehicle speeds, the impacts of different damping values of the variable damping shock absorber on vehicle ride comfort, handling and stability, and economic performance are not analyzed.For the MR damper, the continuous variable characteristics of the damping coefficient can be achieved by controlling the magnetic field strength of the MR fluid [15–17]. A new kind of hybrid active suspension structure with ball screw actuator and MR damper is put forward. Moreover, in order to ensure high response speed of the hybrid active suspension, a sky-hook algorithm, which is easy to operate, fast and robust in response, is applied [18–20]. And the semiactive mode and active mode of the hybrid suspension are analyzed under the class B road surface. At the same time, the multimode coordinated control system of the hybrid suspension is designed. Then, the damping performance and energy consumption characteristics of the hybrid suspension under the cyclic driving condition are simulated, and the bench tests of the hybrid suspension system are done.


## 2. Structure and Principle of the Hybrid Active Suspension

The structure of the hybrid active suspension system is shown in Figure1. It is mainly composed of spring, MR damper, ball screw actuator, controller, battery, corresponding signal detection device, and so on.Figure 1
Structure of the hybrid active suspension.The controller performs semiactive control or active control of the hybrid suspension system by detecting and judging the relevant signals. When the hybrid suspension is semiactively controlled, the controller detects the sprung mass acceleration in real time by the sprung mass acceleration sensor, and the semiactive control force of the hybrid suspension is obtained through the sky-hook algorithm. The controller adjusts the controllable current to change the magnetic field strength of the MR fluid. Then, the output damping force of the MR damper is changed, and the semiactive control of the suspension is realized. At the same time, the ball screw actuator transforms the up and down motion of the suspension into the rotation of the motor, and then, the motor generates electric energy which is stored in the battery.When the hybrid suspension is actively controlled, the controller detects the sprung mass acceleration in real time by the sprung mass acceleration sensor, and the active control force of the hybrid suspension is obtained through the sky-hook algorithm. The controller adjusts the controllable current to change the motor output torque. The motor transforms the rotation motion into the up and down motion, and the active control of the suspension is realized. At this time, the energy consumed by the ball screw actuator is supplied by the battery. And when the hybrid suspension is actively controlled, the controller detects the running speed of vehicle and controls the input current of the MR damper according to different vehicle speed values. It makes the MR damper produce a damping value that matches the vehicle speed. In the semiactive and active control of the suspension, the energy consumed by the MR damper is all provided by the battery.


## 3. Modeling of Hybrid Active Suspension Dynamic Model

### 3.1. Dynamic Model of Hybrid Active Suspension

In this paper, a quarter vehicle dynamic model of the hybrid active suspension is established and shown in Figure2.Figure 2
Dynamic model of 2 DOF hybrid active suspension.Based on Newton’s laws of motion, the dynamic motion equations for the quarter vehicle suspension can be expressed as(1)msx¨2+ksx2−x1+csx˙2−x˙1=F,mux¨1−ksx2−x1−csx˙2−x˙1+ktx1−z=−F.The state variable and the output vector are selected as follows:(2)X=x2−x1x˙2x1−zx˙1T,Y=x¨2x2−x1ktx1−zx˙1T,where ms is sprung mass; mu is unsprung mass; ks is spring stiffness coefficient; F is control force of suspension (especially Fb is semiactive control force and Fz is active control force); kt is tire stiffness coefficient; z is displacement of road input; x2 is displacement of sprung mass; x1 is displacement of unsprung mass; and cs is damping coefficient of MR damper.Then, the state-space equations of suspension system can be described as follows:(3)X˙=AX+BU,Y=CX+DU,where A,Β,C, and D are the state matrix, input matrix, output matrix, and transfer matrix, respectively. When the control input force F is 0, it becomes passive suspension.(4)Α=010−1−ksms−csms0csms0001ksmucsmu−ktmu−csmu,B=0001ms−100−1mu,X=−ksms−csms0csms100000kt00001,D=01ms000000,U=z˙F.A filtered white noise is adopted as the road surface input model as follows:(5)z˙t=−2πf0zt+2πG0uωt,where G0 is the coefficient of road irregularity; f0 is lower cutoff frequency; u is vehicle speed; and ωt is unit white noise.The simulation parameters of the hybrid suspension are listed in Table1.Table 1
Simulation parameters of the hybrid suspension.
Parameters
Values
Lower cutoff frequency (Hz)
0.1
Road irregularities coefficient (m3)
64 × 10−6
Sprung mass (kg)
38
Unsprung mass (kg)
210
Spring stiffness coefficient (kN/m)
22
Tire stiffness coefficient (kN/m)
200


### 3.2. MR Damper Mathematical Model

Ignoring the friction and fluid inertia of the MR fluid, the damping force model of the MR damper under mixed operation mode is given as follows [21]:(6)Fa=−24ηAp2lbh3+2ηblhx˙2−x˙1−4lApη+2blτy,where Fa is MR damper output damping force; η is fluid dynamic viscosity; l is the working plate length; h is the working plate distance; τy is MR fluid shear stress; Ap is piston effective area; and b is the working plate width.According to formula (6), the damping force of the MR damper includes the viscous damping force Fn, which has a function relationship with the piston speed of the MR damper, and coulomb damping force Fk, which has a function relationship with the control current of the MR damper. So formula (6) can be transformed into(7)Fa=−cex˙2−x˙1+a1Ik2+a2Ik2+a3sgnx˙2−x˙1,where ce,a1,a2,anda3 are polynomial coefficients and Ik is control current of the MR damper.From formulae (6)∼(7), because the viscous damping force Fn does not consume energy, it can be equivalent to the damping force produced by the traditional hydraulic shock absorber. The variable damping force of the hybrid active suspension is the coulomb damping force Fk, which is achieved by adjusting Ik.In the semiactive control of the hybrid suspension, the instantaneous energy consumption power and the energy consumption of the MR damper are expressed as(8)Pb=Fk⋅x˙2−x˙1ηb,(9)Wb=∫0tPbdt,where ηb is work efficiency of MR damper; Pb is the MR damper instantaneous energy consumption power of the hybrid suspension in semiactive control; and Wb is the MR damper energy consumption of the hybrid suspension in semiactive control.In the active control of the hybrid suspension, the output damping force of the MR damper is expressed as(10)cs=c0+ck,c0=Fnx˙2−x˙1,ck=Fkx˙2−x˙1,where c0 is viscous damping of the MR damper and ck is variable damping of the MR damper.In the active control, the instantaneous energy consumption power and the energy consumption of the MR damper are expressed as(11)Pc=cs−c0⋅x˙2−x˙12ηb,(12)Wc=∫0tPcdt,where Pc is the MR damper instantaneous energy consumption power of the hybrid suspension in active control and Wc is the MR damper energy consumption of the hybrid suspension in active control.The single rod MR damper is used in this paper, and it is shown in Figure3.Figure 3
The MR damper prototype.By carrying out the characteristics test of the MR damper and analyzing the test data, the relation diagrams of the damping force-velocity curves of the MR damper are obtained and shown in Figure4.Figure 4
The damping force-velocity curves of the MR damper.


### 3.3. Ball Screw Actuator Mathematical Model

#### 3.3.1. The Characteristics of Ball Screw Actuator

The ball screw actuator is used not only to realize the active control of the hybrid suspension but also to recover the regenerative energy of the hybrid suspension, the characteristics of which have a great influence on the performance of the hybrid suspension.The characteristics of the ball screw actuator is mainly affected by the back-EMF coefficientke and electric torque coefficient kT of the motor, but the nonlinear characteristics of the motor make ke and kT vary with the speed of the motor [22, 23]. It is necessary to gain the relationship between ke, kT, and the motor speed by the motor test if a precise mathematical model of the ball screw actuator is established.The prototype of the ball screw actuator is shown in Figure5. It is made up of brushless DC motor, ball screw, upper and lower ears, force sensor, and so on.Figure 5
The ball screw actuator.In this paper, the peak value of counter electromotive force of the motor at different rotating speeds is measured by the test. At different rotating speeds, the fitting analyses of the peak value are carried out, and the result is shown in Figure6.Figure 6
The peak value curve of counter electromotive force of the motor.The peak of counter electromotive force of the motor and the back-EMF coefficient meet the following relationships:(13)ke=Vmax22n,where Vmax is the peak of counter electromotive force and n is motor rotating speed.The vibration velocity of the hybrid suspension and the motor rotating speed meet the following relationships:(14)n=ΔvL⋅60,(15)Δv=x˙2−x˙1,where Δv is the suspension vibration velocity and L is ball screw lead.At different suspension vibration velocity, the motor back-EMF coefficient can be obtained from formulae (13)∼(15), and the fitting curve of the motor back-EMF coefficient is shown in Figure 7.Figure 7
The motor back-EMF coefficient curve.In Figure7, the fitting relationship between ke and Δv is expressed as(16)ke=0.0299Δv3−0.0542Δv2+0.0253Δv+0.0049.Then,kT and ke meet the following relationships:(17)kT=30πke.The relationship betweenkT and Δv can be obtained from formulae (16) and (17).(18)kT=0.2855Δv3−0.5176Δv2+0.2416Δv+0.0468.When testing the active output force of the ball screw actuator, the ball screw actuator is powered by the same 72 V constant voltage source as the battery pack terminal voltage. By adjusting PWM duty ratio, the input voltage and current of the motor are controlled by the controller, and as a result, the output force of the motor is gained. The relationship between the active output force of the ball screw actuator and duty ratio is shown in Figure8.Figure 8
Testing curve of the actuator active output force.From Figure8, it can be seen that the ball screw actuator has good active output force characteristics, and the nonlinear relationship between the output force and the duty ratio is consistent with the nonlinear characteristics of the motor.


#### 3.3.2. Ball Screw Actuator Mathematical Model

When the motor inductance is ignored, in the active control of the hybrid suspension, input voltageE and the output torque Tm of the motor meet the following relationships:(19)E=u+Izr,(20)Tm=kT⋅Iz,(21)u=60x˙2−x˙1L⋅ke,(22)Tm=F⋅L2π,(23)ke=kT⋅π30,where u is induced electromotive force; Iz is motor current; and r is internal resistance of the motor.In the active control of the hybrid suspension, the instantaneous energy consumption power of the ball screw actuator can be expressed as(24)Pz=E⋅Izηz.The instantaneous energy consumption power and consumption energy can be obtained from formulae (19)∼(24) as follows:(25)Pz=x˙2−x˙1⋅F+FL/2πkT2⋅rηz,(26)Wz=∫0tPzdt,where Pz is motor instantaneous energy consumption power; ηz is transfer efficiency of ball screw actuator; and Wz is motor energy consumption.In the energy regeneration of the hybrid suspension, the electromagnetic damping force generated by the ball screw actuator is expressed as(27)Fs=−2πkTL2⋅x˙2−x˙1R+rηz,where Fs is the electromagnetic damping force and R is external resistance of the motor.The instantaneous energy-regenerative power and regenerative energy of the ball screw actuator can be expressed as(28)Pk=2πkeL2⋅x˙2−x˙12R+rηz,(29)Wk=∫0tPkdt,where Pk is instantaneous energy-regenerative power and Wk is regenerative energy.


## 3.1. Dynamic Model of Hybrid Active Suspension

In this paper, a quarter vehicle dynamic model of the hybrid active suspension is established and shown in Figure2.Figure 2
Dynamic model of 2 DOF hybrid active suspension.Based on Newton’s laws of motion, the dynamic motion equations for the quarter vehicle suspension can be expressed as(1)msx¨2+ksx2−x1+csx˙2−x˙1=F,mux¨1−ksx2−x1−csx˙2−x˙1+ktx1−z=−F.The state variable and the output vector are selected as follows:(2)X=x2−x1x˙2x1−zx˙1T,Y=x¨2x2−x1ktx1−zx˙1T,where ms is sprung mass; mu is unsprung mass; ks is spring stiffness coefficient; F is control force of suspension (especially Fb is semiactive control force and Fz is active control force); kt is tire stiffness coefficient; z is displacement of road input; x2 is displacement of sprung mass; x1 is displacement of unsprung mass; and cs is damping coefficient of MR damper.Then, the state-space equations of suspension system can be described as follows:(3)X˙=AX+BU,Y=CX+DU,where A,Β,C, and D are the state matrix, input matrix, output matrix, and transfer matrix, respectively. When the control input force F is 0, it becomes passive suspension.(4)Α=010−1−ksms−csms0csms0001ksmucsmu−ktmu−csmu,B=0001ms−100−1mu,X=−ksms−csms0csms100000kt00001,D=01ms000000,U=z˙F.A filtered white noise is adopted as the road surface input model as follows:(5)z˙t=−2πf0zt+2πG0uωt,where G0 is the coefficient of road irregularity; f0 is lower cutoff frequency; u is vehicle speed; and ωt is unit white noise.The simulation parameters of the hybrid suspension are listed in Table1.Table 1
Simulation parameters of the hybrid suspension.
Parameters
Values
Lower cutoff frequency (Hz)
0.1
Road irregularities coefficient (m3)
64 × 10−6
Sprung mass (kg)
38
Unsprung mass (kg)
210
Spring stiffness coefficient (kN/m)
22
Tire stiffness coefficient (kN/m)
200


## 3.2. MR Damper Mathematical Model

Ignoring the friction and fluid inertia of the MR fluid, the damping force model of the MR damper under mixed operation mode is given as follows [21]:(6)Fa=−24ηAp2lbh3+2ηblhx˙2−x˙1−4lApη+2blτy,where Fa is MR damper output damping force; η is fluid dynamic viscosity; l is the working plate length; h is the working plate distance; τy is MR fluid shear stress; Ap is piston effective area; and b is the working plate width.According to formula (6), the damping force of the MR damper includes the viscous damping force Fn, which has a function relationship with the piston speed of the MR damper, and coulomb damping force Fk, which has a function relationship with the control current of the MR damper. So formula (6) can be transformed into(7)Fa=−cex˙2−x˙1+a1Ik2+a2Ik2+a3sgnx˙2−x˙1,where ce,a1,a2,anda3 are polynomial coefficients and Ik is control current of the MR damper.From formulae (6)∼(7), because the viscous damping force Fn does not consume energy, it can be equivalent to the damping force produced by the traditional hydraulic shock absorber. The variable damping force of the hybrid active suspension is the coulomb damping force Fk, which is achieved by adjusting Ik.In the semiactive control of the hybrid suspension, the instantaneous energy consumption power and the energy consumption of the MR damper are expressed as(8)Pb=Fk⋅x˙2−x˙1ηb,(9)Wb=∫0tPbdt,where ηb is work efficiency of MR damper; Pb is the MR damper instantaneous energy consumption power of the hybrid suspension in semiactive control; and Wb is the MR damper energy consumption of the hybrid suspension in semiactive control.In the active control of the hybrid suspension, the output damping force of the MR damper is expressed as(10)cs=c0+ck,c0=Fnx˙2−x˙1,ck=Fkx˙2−x˙1,where c0 is viscous damping of the MR damper and ck is variable damping of the MR damper.In the active control, the instantaneous energy consumption power and the energy consumption of the MR damper are expressed as(11)Pc=cs−c0⋅x˙2−x˙12ηb,(12)Wc=∫0tPcdt,where Pc is the MR damper instantaneous energy consumption power of the hybrid suspension in active control and Wc is the MR damper energy consumption of the hybrid suspension in active control.The single rod MR damper is used in this paper, and it is shown in Figure3.Figure 3
The MR damper prototype.By carrying out the characteristics test of the MR damper and analyzing the test data, the relation diagrams of the damping force-velocity curves of the MR damper are obtained and shown in Figure4.Figure 4
The damping force-velocity curves of the MR damper.


## 3.3. Ball Screw Actuator Mathematical Model

### 3.3.1. The Characteristics of Ball Screw Actuator

The ball screw actuator is used not only to realize the active control of the hybrid suspension but also to recover the regenerative energy of the hybrid suspension, the characteristics of which have a great influence on the performance of the hybrid suspension.The characteristics of the ball screw actuator is mainly affected by the back-EMF coefficientke and electric torque coefficient kT of the motor, but the nonlinear characteristics of the motor make ke and kT vary with the speed of the motor [22, 23]. It is necessary to gain the relationship between ke, kT, and the motor speed by the motor test if a precise mathematical model of the ball screw actuator is established.The prototype of the ball screw actuator is shown in Figure5. It is made up of brushless DC motor, ball screw, upper and lower ears, force sensor, and so on.Figure 5
The ball screw actuator.In this paper, the peak value of counter electromotive force of the motor at different rotating speeds is measured by the test. At different rotating speeds, the fitting analyses of the peak value are carried out, and the result is shown in Figure6.Figure 6
The peak value curve of counter electromotive force of the motor.The peak of counter electromotive force of the motor and the back-EMF coefficient meet the following relationships:(13)ke=Vmax22n,where Vmax is the peak of counter electromotive force and n is motor rotating speed.The vibration velocity of the hybrid suspension and the motor rotating speed meet the following relationships:(14)n=ΔvL⋅60,(15)Δv=x˙2−x˙1,where Δv is the suspension vibration velocity and L is ball screw lead.At different suspension vibration velocity, the motor back-EMF coefficient can be obtained from formulae (13)∼(15), and the fitting curve of the motor back-EMF coefficient is shown in Figure 7.Figure 7
The motor back-EMF coefficient curve.In Figure7, the fitting relationship between ke and Δv is expressed as(16)ke=0.0299Δv3−0.0542Δv2+0.0253Δv+0.0049.Then,kT and ke meet the following relationships:(17)kT=30πke.The relationship betweenkT and Δv can be obtained from formulae (16) and (17).(18)kT=0.2855Δv3−0.5176Δv2+0.2416Δv+0.0468.When testing the active output force of the ball screw actuator, the ball screw actuator is powered by the same 72 V constant voltage source as the battery pack terminal voltage. By adjusting PWM duty ratio, the input voltage and current of the motor are controlled by the controller, and as a result, the output force of the motor is gained. The relationship between the active output force of the ball screw actuator and duty ratio is shown in Figure8.Figure 8
Testing curve of the actuator active output force.From Figure8, it can be seen that the ball screw actuator has good active output force characteristics, and the nonlinear relationship between the output force and the duty ratio is consistent with the nonlinear characteristics of the motor.


### 3.3.2. Ball Screw Actuator Mathematical Model

When the motor inductance is ignored, in the active control of the hybrid suspension, input voltageE and the output torque Tm of the motor meet the following relationships:(19)E=u+Izr,(20)Tm=kT⋅Iz,(21)u=60x˙2−x˙1L⋅ke,(22)Tm=F⋅L2π,(23)ke=kT⋅π30,where u is induced electromotive force; Iz is motor current; and r is internal resistance of the motor.In the active control of the hybrid suspension, the instantaneous energy consumption power of the ball screw actuator can be expressed as(24)Pz=E⋅Izηz.The instantaneous energy consumption power and consumption energy can be obtained from formulae (19)∼(24) as follows:(25)Pz=x˙2−x˙1⋅F+FL/2πkT2⋅rηz,(26)Wz=∫0tPzdt,where Pz is motor instantaneous energy consumption power; ηz is transfer efficiency of ball screw actuator; and Wz is motor energy consumption.In the energy regeneration of the hybrid suspension, the electromagnetic damping force generated by the ball screw actuator is expressed as(27)Fs=−2πkTL2⋅x˙2−x˙1R+rηz,where Fs is the electromagnetic damping force and R is external resistance of the motor.The instantaneous energy-regenerative power and regenerative energy of the ball screw actuator can be expressed as(28)Pk=2πkeL2⋅x˙2−x˙12R+rηz,(29)Wk=∫0tPkdt,where Pk is instantaneous energy-regenerative power and Wk is regenerative energy.


## 3.3.1. The Characteristics of Ball Screw Actuator

The ball screw actuator is used not only to realize the active control of the hybrid suspension but also to recover the regenerative energy of the hybrid suspension, the characteristics of which have a great influence on the performance of the hybrid suspension.The characteristics of the ball screw actuator is mainly affected by the back-EMF coefficientke and electric torque coefficient kT of the motor, but the nonlinear characteristics of the motor make ke and kT vary with the speed of the motor [22, 23]. It is necessary to gain the relationship between ke, kT, and the motor speed by the motor test if a precise mathematical model of the ball screw actuator is established.The prototype of the ball screw actuator is shown in Figure5. It is made up of brushless DC motor, ball screw, upper and lower ears, force sensor, and so on.Figure 5
The ball screw actuator.In this paper, the peak value of counter electromotive force of the motor at different rotating speeds is measured by the test. At different rotating speeds, the fitting analyses of the peak value are carried out, and the result is shown in Figure6.Figure 6
The peak value curve of counter electromotive force of the motor.The peak of counter electromotive force of the motor and the back-EMF coefficient meet the following relationships:(13)ke=Vmax22n,where Vmax is the peak of counter electromotive force and n is motor rotating speed.The vibration velocity of the hybrid suspension and the motor rotating speed meet the following relationships:(14)n=ΔvL⋅60,(15)Δv=x˙2−x˙1,where Δv is the suspension vibration velocity and L is ball screw lead.At different suspension vibration velocity, the motor back-EMF coefficient can be obtained from formulae (13)∼(15), and the fitting curve of the motor back-EMF coefficient is shown in Figure 7.Figure 7
The motor back-EMF coefficient curve.In Figure7, the fitting relationship between ke and Δv is expressed as(16)ke=0.0299Δv3−0.0542Δv2+0.0253Δv+0.0049.Then,kT and ke meet the following relationships:(17)kT=30πke.The relationship betweenkT and Δv can be obtained from formulae (16) and (17).(18)kT=0.2855Δv3−0.5176Δv2+0.2416Δv+0.0468.When testing the active output force of the ball screw actuator, the ball screw actuator is powered by the same 72 V constant voltage source as the battery pack terminal voltage. By adjusting PWM duty ratio, the input voltage and current of the motor are controlled by the controller, and as a result, the output force of the motor is gained. The relationship between the active output force of the ball screw actuator and duty ratio is shown in Figure8.Figure 8
Testing curve of the actuator active output force.From Figure8, it can be seen that the ball screw actuator has good active output force characteristics, and the nonlinear relationship between the output force and the duty ratio is consistent with the nonlinear characteristics of the motor.


## 3.3.2. Ball Screw Actuator Mathematical Model

When the motor inductance is ignored, in the active control of the hybrid suspension, input voltageE and the output torque Tm of the motor meet the following relationships:(19)E=u+Izr,(20)Tm=kT⋅Iz,(21)u=60x˙2−x˙1L⋅ke,(22)Tm=F⋅L2π,(23)ke=kT⋅π30,where u is induced electromotive force; Iz is motor current; and r is internal resistance of the motor.In the active control of the hybrid suspension, the instantaneous energy consumption power of the ball screw actuator can be expressed as(24)Pz=E⋅Izηz.The instantaneous energy consumption power and consumption energy can be obtained from formulae (19)∼(24) as follows:(25)Pz=x˙2−x˙1⋅F+FL/2πkT2⋅rηz,(26)Wz=∫0tPzdt,where Pz is motor instantaneous energy consumption power; ηz is transfer efficiency of ball screw actuator; and Wz is motor energy consumption.In the energy regeneration of the hybrid suspension, the electromagnetic damping force generated by the ball screw actuator is expressed as(27)Fs=−2πkTL2⋅x˙2−x˙1R+rηz,where Fs is the electromagnetic damping force and R is external resistance of the motor.The instantaneous energy-regenerative power and regenerative energy of the ball screw actuator can be expressed as(28)Pk=2πkeL2⋅x˙2−x˙12R+rηz,(29)Wk=∫0tPkdt,where Pk is instantaneous energy-regenerative power and Wk is regenerative energy.


## 4. Multimode Coordination Control of Hybrid Active Suspension

### 4.1. The Active Mode of Damping Switching Control

The sprung mass acceleration is the main evaluation index of vehicle riding comfort, and the dynamic tire load is closely related to vehicle handling and stability. An active control model of the hybrid suspension is established by MATLAB/Simulink software to simulate and analyze the influence of the variable damping for the hybrid active suspension on vehicle riding comfort and handling and stability at different vehicle speeds. During the simulation, the range of vehicle speedv is 0–120 km/h and the vehicle speed is taken every 10 km/h. The variable damping range of the suspension is 200–2000 N·s/m, and the value of the variable damping is taken every interval 100 N·s/m. The simulation time is 10 s, and the value of r is 0.5Ω. The value of ηz is 0.97, and the value of ηb is 0.98. The value of csky is 2000 N·s/m.When the vehicle speed is 30 km/h and 100 km/h, respectively, the RMS of the sprung mass acceleration of the vehicle (aw) and the RMS of the dynamic tire load (DTLrms) change with the variable damping of the hybrid active suspension, as shown in Figures 9 and 10.Figure 9
Relationship between the variable damping and the riding comfort, handling, and stability of vehicle at 30 km/h speed.Figure 10
Relationship between the variable damping and the riding comfort, handling, and stability of vehicle at 100 km/h speed.From Figures9 and 10, it can be seen that when the vehicle speed is 30 km/h, the variable damping values that make aw of vehicle and DTLrms minimum are 400 N·s/m and 1000 N·s/m, respectively, and when the vehicle speed is 100 km/h, the variable damping values that make aw of vehicle and DTLrms minimum are 500 N·s/m and 1100 N·s/m, respectively. Therefore, at a certain vehicle speed, the variable damping of the hybrid active suspension cannot make the best of the vehicle riding comfort and handling and stability at the same time.Suspension performance indexes include the sprung mass acceleration, suspension working space, and dynamic tire load. In this paper, in order to balance vehicle riding comfort and handling and stability, when choosing the variable damping values of the hybrid suspension in the active control, for the sprung mass acceleration, suspension working space, and dynamic tire load of the hybrid active suspension, the quantitative normalizations and comparative analyses are done. That is, at the same vehicle speed, compared with the passive suspension, the improvement amplitudes of each performance index of the hybrid active suspension are multiplied by different quantification factors and summed. And the larger the sum, the better the dynamic performance of vehicle. Among them, the quantification factors ofaw, the RMS value of suspension working space (SWSrms), and DTLrms are 1, 0.2703, and 0.1443, respectively [24, 25]. And when the vehicle speed is 30 km/h and 100 km/h, respectively, the dynamic performance and the active control energy consumption of the hybrid active suspension change with the variable damping, as shown in Figures 11 and 12.Figure 11
Relationship between the variable damping and vehicle dynamic performance at 30 km/h speed.Figure 12
Relationship between the variable damping and vehicle dynamic performance at 100 km/h speed.From Figures11 and 12, when the vehicle speed is 30 km/h, the variable damping value of the hybrid active suspension is 800 N·s/m, which makes the vehicle dynamic performance the best and the active energy consumption the least. When the vehicle speed is 100 km/h, the variable damping value of the hybrid active suspension is 1000 N·s/m, which makes the vehicle dynamic performance the best and active energy consumption the least. Therefore, when the vehicle speed is 30 km/h and 100 km/h, respectively, the optimal damping values of the hybrid active suspension are 800 N·s/m and 1000 N·s/m, respectively. When the vehicle speed is 0–120 km/h, the optimal damping values of the hybrid active suspension at different vehicle speeds are shown in Figure 13. If the damping value which makes the vehicle dynamic performance the best is different from the damping value which makes the active control energy consumption the least, the damping value which makes the vehicle dynamic performance the best is selected as the optimal damping value of the hybrid active suspension at the vehicle speed.Figure 13
Suspension optimal damping at different speeds.When vehicle is in an accelerating or decelerating state, its speed changes rapidly and the range of change is wide, so the vehicle speed value is not easily detected in real time, and in order to reduce the energy consumption of the hybrid suspension active controlled and to improve the vehicle riding comfort and handling and stability, a variable damping switching control strategy of the hybrid active suspension is designed as follows:(30)Fz=−csky⋅x˙2,cs=c0+ck,v˙=0,Fz=−csky⋅x˙2,cs=c0,v˙≠0,where v˙ is vehicle acceleration and csky is sky-hook coefficient.


### 4.2. The Semiactive Mode of Feedback Adjustment of Electromagnetic Damping Force

MR damper can effectively perform semiactive control atx˙2−x˙1x˙2>0, so the ideal semiactive control state for hybrid suspension is(31)Fb=−csky⋅x˙2,x˙2−x˙1x˙2>0,0,x˙2−x˙1x˙2≤0.From equation (31), the ideal semiactive control force of the hybrid suspension −csky⋅x˙2 is only related to x˙2 when the sky-hook coefficient csky is constant. However, at this time, the ball screw actuator, as a power feeding device, generates the electromagnetic damping force Fs and acts on the suspension, so that the actual semiactive control force of the suspension is different from the ideal semiactive control force −csky⋅x˙2. In this paper, the semiactive control model of the hybrid suspension is established, and the change effects of the different output forces on the vehicle riding comfort and handling stability are analyzed by MATLAB/Simulink software. The simulation speed is 70 km/h, the simulation time is 5 s, and the value of R is 0.75 Ω. The damping comparison of the hybrid suspension in semiactive control is shown in Figure 14.Figure 14
Damping comparison of the hybrid suspension in semiactive control.Figure14 shows that compared with the ideal semiactive control force, the actual semiactive control force of the hybrid suspension fluctuates violently, and the absolute value of the actual semiactive control force is greater than the absolute value of the ideal semiactive control force csky⋅x˙2 at certain times. And a drastic change in the actual semiactive control force makes the suspension not reach ideal semiactive control effect. Using electromagnetic damping force feedback adjustment to reduce the difference between the ideal semiactive control force −csky⋅x˙2 and the actual semiactive control force, the method is as follows.Whencsky⋅x˙2>Fs, the semiactive control force of the hybrid suspension is provided by both the MR damper and the ball screw actuator, and at this point, the controller inputs a controllable current Ik to the MR damper, so that the Fk output by the MR damper is −csky⋅x˙2−Fs. And when csky⋅x˙2≤Fs, the semiactive control force of the hybrid suspension is the Fs which is output by the ball screw actuator, and at this point, there is no controllable current Ik input to the MR damper, and the function of the MR damper is equivalent to a traditional shock absorber. Therefore, the semiactive control of the hybrid suspension does not have the dead zone of traditional electromagnetic semiactive suspension, which helps to improve the semiactive control effect of the hybrid suspension.When there is feedback adjustment, the semiactive control force of the hybrid suspension is(32)Fb=Fs,Fs≥csky⋅x˙2,−csky⋅x˙2,Fs<csky⋅x˙2.When there is feedback adjustment, theFk output by the MR damper is(33)Fk=0,Fs≥csky⋅x˙2,−csky⋅x˙2−Fs,Fs<csky⋅x˙2.From equations (31)∼(33), when the electromagnetic damping force feedback adjustment is used, the Fk output by the MR damper decreases, and when Fk decreases, it can be known from equations (8) and (9) that the energy consumption of the MR damper decreases with it.The comparison of the semiactive control force of the hybrid suspension with or without the electromagnetic damping force feedback adjustment is shown in Figure15.Figure 15
Semiactive force of the hybrid suspension.From Figure15, the RMS of the ideal semiactive control force of the hybrid suspension is 327.6 N, and when there is no electromagnetic damping force feedback adjustment, the RMS of the actual semiactive control force of the suspension is 404.1 N, and the difference between the actual semiactive force of the suspension and the ideal semiactive force is 23.35%. When there is electromagnetic damping force feedback adjustment, the RMS of the actual semiactive control force of the suspension is 359.3 N, and the difference between the actual semiactive force of the suspension and the ideal semiactive force is 9.68%. Therefore, when there is electromagnetic damping force feedback adjustment, the actual semiactive control force of the suspension has a smaller fluctuation amplitude, which helps to improve the semiactive control effect of the hybrid suspension.The dynamic responses of the hybrid suspension with or without electromagnetic damping force feedback adjustment are shown in Figure16. Among them, the damper of the passive suspension is the original damper of the vehicle, and its damping value is 1600 N·s/m.Figure 16
The dynamic responses of the hybrid suspension in semiactive control. (a) The response curves of sprung mass acceleration. (b)The response curves of suspension working space. (c) The response curves of dynamic tire load.
(a)
(b)
(c)Table2 shows the response RMS values of the hybrid suspension in semiactive control.Table 2
The response root mean square values of the hybrid suspension in semiactive control.
Indicators
Passive suspension
Without feedback semiactive control
With feedback semiactive control
a
w (m/s2)
2.3638
2.0133
1.9625
SWSrms (m)
0.0185
0.0194
0.0177
DTLrms (N)
505.0077
481.3326
451.0680From Table2, compared with the passive suspension, when there is electromagnetic damping force feedback adjustment, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 16.98%, 4.32%, and 10.68%, respectively, and compared with the nonfeedback semiactive control, when the feedback semiactive control is performed, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 2.52%, 8.63%, and 6.71%, respectively.From equations (9) and (29), the total system energy of the hybrid suspension in semiactive control is(34)W1=Wk−Wb,where W1 is the total system energy of the hybrid suspension in semiactive control.From equation (33), when the hybrid suspension semiactive controlled, the curves of the total system energy change over time are shown in Figure 17.Figure 17
The system energy of the hybrid suspension in semiactive control.From Figure17, when there is the nonfeedback semiactive control, the total system energy of the hybrid suspension is 60 J. And when there is the feedback semiactive control, the total system energy of the hybrid suspension is 307 J.


### 4.3. The Design of Multimode Coordination Controller

When the hybrid suspension is actively controlled, the suspension has good vibration isolation performance but high energy consumption. And when the hybrid suspension is semiactively controlled, the suspension has good economic performance but the control has limitations. Considering that the ball screw actuator can realize active control of the hybrid suspension in any suspension state, a multimode coordinated control strategy of the hybrid suspension is designed:(35)F=Fb=Fs,Fs≥csky⋅x˙2,−csky⋅x˙2,Fs>csky⋅x˙2,cs=c0,x˙2−x˙1x˙2>0,F=Fz=−csky⋅x˙2,cs=c0+ck,x˙2−x˙1x˙2≤0,The frame diagram of the multimode coordinated control strategy of the hybrid suspension is shown in Figure18.Figure 18
The frame diagram of the multimode coordinated control strategy of the hybrid suspension.From equations (9), (12), (26), and (29), the total system energy of the hybrid suspension in multimode coordinated control is(36)W2=Wk−Wb−WZ−Wc,where W2 is the total system energy of the hybrid suspension in multimode coordinated control.A hybrid active suspension simulation model is established by using MATLAB/Simulink software. From Figure11, when the hybrid suspension is actively controlled, the energy consumption of the MR damper is mainly affected by the vehicle speed. In order to verify the vibration isolation performance and energy consumption performance of the hybrid active suspension in the cyclic driving conditions, this article simulates vehicle urban and suburban conditions which is based on GB/T 19233-2003 “Light Vehicle Fuel Consumption Test Method”; among them, the urban conditions include four cycle units, each cycle time is 195 s; the suburban conditions include one cycle unit, and the cycle time is 400 s [26]. And the schematic diagram of the urban conditions unit is shown in Figure 19.Figure 19
The schematic diagram of the urban conditions unit.In order to simulate the vehicle acceleration signal, a vehicle speed variation model in different cycle units is established by using the signal builder function module in Simulink software. On this basis, the vehicle acceleration model in different cycle units is obtained, and the vehicle acceleration model can be used as the switching control model for the variable damping when the hybrid suspension is actively controlled. The shock absorbers of active suspension and passive suspension adopt the original damper of vehicle, and the damping valuec1 is 1600 N·s/m. However, because of the long simulation time, the dynamic response curves of the hybrid active suspension in urban and suburban conditions cannot be displayed. Figure 20 shows the dynamic response curve of the hybrid active suspension in the 145–175 s in the urban circulation unit; among them, vehicle in the 145–155 s is in a constant speed, vehicle in the 155–163 s is in the deceleration state, and vehicle in the 163–175 s is in other constant speed.Figure 20
The dynamic responses of the hybrid suspension. (a) The response curves of sprung mass acceleration. (b) The response curves of suspension working space. (c) The response curves of dynamic tire load.
(a)
(b)
(c)The dynamic response RMS values of the hybrid suspension in urban and suburban circulation units are shown in Tables3 and 4, respectively.Table 3
The dynamic response root mean square values of the hybrid suspension in urban circulation unit.
Indicators
Passive suspension
Active suspension
Hybrid suspension
a
w (m/s2)
1.4440
1.0078
0.8746
SWSrms (m)
0.0089
0.0080
0.0087
DTLrms (N)
334.4223
289.1024
264.8285Table 4
The dynamic response root mean square values of the hybrid suspension in suburban circulation unit.
Indicators
Passive suspension
Active suspension
Hybrid suspension
a
w (m/s2)
2.5204
1.7422
1.5333
SWSrms (m)
0.0159
0.0142
0.0154
DTLrms (N)
585.4460
508.2344
470.9650From Figure20 and Tables 3 and 4, the dynamic responses are good when the hybrid suspension is multimode coordinated control. When in the urban circulation unit, compared with the passive suspension, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 39.43%, 2.25%, and 20.81%, respectively. Compared with the active suspension, aw and DTLrms of the hybrid suspension are reduced by 13.22% and 8.40%, respectively, but SWSrms is increased by 8.05%. When in the suburban circulation unit, compared with the passive suspension, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 39.16%, 3.14%, and 19.55%, respectively. Compared with the active suspension, aw and DTLrms of the hybrid suspension are reduced by 11.99% and 7.32%, respectively, but SWSrms is increased by 8.45%.The system energy of the hybrid suspension in urban and suburban circulation units are shown in Figures21 and 22, respectively.Figure 21
The system energy of the hybrid suspension in urban circulation units.Figure 22
The system energy of the hybrid suspension in suburban circulation units.Then, the system energy values of the hybrid suspension in urban and suburban circulation units are shown in Table5.Table 5
The system energy values of the hybrid suspension (J).
Cycle unit
Active suspension
Hybrid suspension
Urban
−2165
38
Suburban
−15071
−122From Table5, when in the urban circulation unit, the system energy of the active suspension and hybrid suspension is −2165 J and 38 J, respectively. And when in the suburban circulation unit, the system energy of the active suspension and hybrid suspension is −15071 J and −122 J, respectively. The entire operation cycle includes 4 urban cycle units and 1 suburban cycle unit, so the pure energy of the active suspension system during the entire operation cycle is −23731 J, while the pure energy of the hybrid suspension system is 38 J. Therefore, the hybrid suspension system basically realizes energy self-powered in theory.


## 4.1. The Active Mode of Damping Switching Control

The sprung mass acceleration is the main evaluation index of vehicle riding comfort, and the dynamic tire load is closely related to vehicle handling and stability. An active control model of the hybrid suspension is established by MATLAB/Simulink software to simulate and analyze the influence of the variable damping for the hybrid active suspension on vehicle riding comfort and handling and stability at different vehicle speeds. During the simulation, the range of vehicle speedv is 0–120 km/h and the vehicle speed is taken every 10 km/h. The variable damping range of the suspension is 200–2000 N·s/m, and the value of the variable damping is taken every interval 100 N·s/m. The simulation time is 10 s, and the value of r is 0.5Ω. The value of ηz is 0.97, and the value of ηb is 0.98. The value of csky is 2000 N·s/m.When the vehicle speed is 30 km/h and 100 km/h, respectively, the RMS of the sprung mass acceleration of the vehicle (aw) and the RMS of the dynamic tire load (DTLrms) change with the variable damping of the hybrid active suspension, as shown in Figures 9 and 10.Figure 9
Relationship between the variable damping and the riding comfort, handling, and stability of vehicle at 30 km/h speed.Figure 10
Relationship between the variable damping and the riding comfort, handling, and stability of vehicle at 100 km/h speed.From Figures9 and 10, it can be seen that when the vehicle speed is 30 km/h, the variable damping values that make aw of vehicle and DTLrms minimum are 400 N·s/m and 1000 N·s/m, respectively, and when the vehicle speed is 100 km/h, the variable damping values that make aw of vehicle and DTLrms minimum are 500 N·s/m and 1100 N·s/m, respectively. Therefore, at a certain vehicle speed, the variable damping of the hybrid active suspension cannot make the best of the vehicle riding comfort and handling and stability at the same time.Suspension performance indexes include the sprung mass acceleration, suspension working space, and dynamic tire load. In this paper, in order to balance vehicle riding comfort and handling and stability, when choosing the variable damping values of the hybrid suspension in the active control, for the sprung mass acceleration, suspension working space, and dynamic tire load of the hybrid active suspension, the quantitative normalizations and comparative analyses are done. That is, at the same vehicle speed, compared with the passive suspension, the improvement amplitudes of each performance index of the hybrid active suspension are multiplied by different quantification factors and summed. And the larger the sum, the better the dynamic performance of vehicle. Among them, the quantification factors ofaw, the RMS value of suspension working space (SWSrms), and DTLrms are 1, 0.2703, and 0.1443, respectively [24, 25]. And when the vehicle speed is 30 km/h and 100 km/h, respectively, the dynamic performance and the active control energy consumption of the hybrid active suspension change with the variable damping, as shown in Figures 11 and 12.Figure 11
Relationship between the variable damping and vehicle dynamic performance at 30 km/h speed.Figure 12
Relationship between the variable damping and vehicle dynamic performance at 100 km/h speed.From Figures11 and 12, when the vehicle speed is 30 km/h, the variable damping value of the hybrid active suspension is 800 N·s/m, which makes the vehicle dynamic performance the best and the active energy consumption the least. When the vehicle speed is 100 km/h, the variable damping value of the hybrid active suspension is 1000 N·s/m, which makes the vehicle dynamic performance the best and active energy consumption the least. Therefore, when the vehicle speed is 30 km/h and 100 km/h, respectively, the optimal damping values of the hybrid active suspension are 800 N·s/m and 1000 N·s/m, respectively. When the vehicle speed is 0–120 km/h, the optimal damping values of the hybrid active suspension at different vehicle speeds are shown in Figure 13. If the damping value which makes the vehicle dynamic performance the best is different from the damping value which makes the active control energy consumption the least, the damping value which makes the vehicle dynamic performance the best is selected as the optimal damping value of the hybrid active suspension at the vehicle speed.Figure 13
Suspension optimal damping at different speeds.When vehicle is in an accelerating or decelerating state, its speed changes rapidly and the range of change is wide, so the vehicle speed value is not easily detected in real time, and in order to reduce the energy consumption of the hybrid suspension active controlled and to improve the vehicle riding comfort and handling and stability, a variable damping switching control strategy of the hybrid active suspension is designed as follows:(30)Fz=−csky⋅x˙2,cs=c0+ck,v˙=0,Fz=−csky⋅x˙2,cs=c0,v˙≠0,where v˙ is vehicle acceleration and csky is sky-hook coefficient.


## 4.2. The Semiactive Mode of Feedback Adjustment of Electromagnetic Damping Force

MR damper can effectively perform semiactive control atx˙2−x˙1x˙2>0, so the ideal semiactive control state for hybrid suspension is(31)Fb=−csky⋅x˙2,x˙2−x˙1x˙2>0,0,x˙2−x˙1x˙2≤0.From equation (31), the ideal semiactive control force of the hybrid suspension −csky⋅x˙2 is only related to x˙2 when the sky-hook coefficient csky is constant. However, at this time, the ball screw actuator, as a power feeding device, generates the electromagnetic damping force Fs and acts on the suspension, so that the actual semiactive control force of the suspension is different from the ideal semiactive control force −csky⋅x˙2. In this paper, the semiactive control model of the hybrid suspension is established, and the change effects of the different output forces on the vehicle riding comfort and handling stability are analyzed by MATLAB/Simulink software. The simulation speed is 70 km/h, the simulation time is 5 s, and the value of R is 0.75 Ω. The damping comparison of the hybrid suspension in semiactive control is shown in Figure 14.Figure 14
Damping comparison of the hybrid suspension in semiactive control.Figure14 shows that compared with the ideal semiactive control force, the actual semiactive control force of the hybrid suspension fluctuates violently, and the absolute value of the actual semiactive control force is greater than the absolute value of the ideal semiactive control force csky⋅x˙2 at certain times. And a drastic change in the actual semiactive control force makes the suspension not reach ideal semiactive control effect. Using electromagnetic damping force feedback adjustment to reduce the difference between the ideal semiactive control force −csky⋅x˙2 and the actual semiactive control force, the method is as follows.Whencsky⋅x˙2>Fs, the semiactive control force of the hybrid suspension is provided by both the MR damper and the ball screw actuator, and at this point, the controller inputs a controllable current Ik to the MR damper, so that the Fk output by the MR damper is −csky⋅x˙2−Fs. And when csky⋅x˙2≤Fs, the semiactive control force of the hybrid suspension is the Fs which is output by the ball screw actuator, and at this point, there is no controllable current Ik input to the MR damper, and the function of the MR damper is equivalent to a traditional shock absorber. Therefore, the semiactive control of the hybrid suspension does not have the dead zone of traditional electromagnetic semiactive suspension, which helps to improve the semiactive control effect of the hybrid suspension.When there is feedback adjustment, the semiactive control force of the hybrid suspension is(32)Fb=Fs,Fs≥csky⋅x˙2,−csky⋅x˙2,Fs<csky⋅x˙2.When there is feedback adjustment, theFk output by the MR damper is(33)Fk=0,Fs≥csky⋅x˙2,−csky⋅x˙2−Fs,Fs<csky⋅x˙2.From equations (31)∼(33), when the electromagnetic damping force feedback adjustment is used, the Fk output by the MR damper decreases, and when Fk decreases, it can be known from equations (8) and (9) that the energy consumption of the MR damper decreases with it.The comparison of the semiactive control force of the hybrid suspension with or without the electromagnetic damping force feedback adjustment is shown in Figure15.Figure 15
Semiactive force of the hybrid suspension.From Figure15, the RMS of the ideal semiactive control force of the hybrid suspension is 327.6 N, and when there is no electromagnetic damping force feedback adjustment, the RMS of the actual semiactive control force of the suspension is 404.1 N, and the difference between the actual semiactive force of the suspension and the ideal semiactive force is 23.35%. When there is electromagnetic damping force feedback adjustment, the RMS of the actual semiactive control force of the suspension is 359.3 N, and the difference between the actual semiactive force of the suspension and the ideal semiactive force is 9.68%. Therefore, when there is electromagnetic damping force feedback adjustment, the actual semiactive control force of the suspension has a smaller fluctuation amplitude, which helps to improve the semiactive control effect of the hybrid suspension.The dynamic responses of the hybrid suspension with or without electromagnetic damping force feedback adjustment are shown in Figure16. Among them, the damper of the passive suspension is the original damper of the vehicle, and its damping value is 1600 N·s/m.Figure 16
The dynamic responses of the hybrid suspension in semiactive control. (a) The response curves of sprung mass acceleration. (b)The response curves of suspension working space. (c) The response curves of dynamic tire load.
(a)
(b)
(c)Table2 shows the response RMS values of the hybrid suspension in semiactive control.Table 2
The response root mean square values of the hybrid suspension in semiactive control.
Indicators
Passive suspension
Without feedback semiactive control
With feedback semiactive control
a
w (m/s2)
2.3638
2.0133
1.9625
SWSrms (m)
0.0185
0.0194
0.0177
DTLrms (N)
505.0077
481.3326
451.0680From Table2, compared with the passive suspension, when there is electromagnetic damping force feedback adjustment, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 16.98%, 4.32%, and 10.68%, respectively, and compared with the nonfeedback semiactive control, when the feedback semiactive control is performed, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 2.52%, 8.63%, and 6.71%, respectively.From equations (9) and (29), the total system energy of the hybrid suspension in semiactive control is(34)W1=Wk−Wb,where W1 is the total system energy of the hybrid suspension in semiactive control.From equation (33), when the hybrid suspension semiactive controlled, the curves of the total system energy change over time are shown in Figure 17.Figure 17
The system energy of the hybrid suspension in semiactive control.From Figure17, when there is the nonfeedback semiactive control, the total system energy of the hybrid suspension is 60 J. And when there is the feedback semiactive control, the total system energy of the hybrid suspension is 307 J.


## 4.3. The Design of Multimode Coordination Controller

When the hybrid suspension is actively controlled, the suspension has good vibration isolation performance but high energy consumption. And when the hybrid suspension is semiactively controlled, the suspension has good economic performance but the control has limitations. Considering that the ball screw actuator can realize active control of the hybrid suspension in any suspension state, a multimode coordinated control strategy of the hybrid suspension is designed:(35)F=Fb=Fs,Fs≥csky⋅x˙2,−csky⋅x˙2,Fs>csky⋅x˙2,cs=c0,x˙2−x˙1x˙2>0,F=Fz=−csky⋅x˙2,cs=c0+ck,x˙2−x˙1x˙2≤0,The frame diagram of the multimode coordinated control strategy of the hybrid suspension is shown in Figure18.Figure 18
The frame diagram of the multimode coordinated control strategy of the hybrid suspension.From equations (9), (12), (26), and (29), the total system energy of the hybrid suspension in multimode coordinated control is(36)W2=Wk−Wb−WZ−Wc,where W2 is the total system energy of the hybrid suspension in multimode coordinated control.A hybrid active suspension simulation model is established by using MATLAB/Simulink software. From Figure11, when the hybrid suspension is actively controlled, the energy consumption of the MR damper is mainly affected by the vehicle speed. In order to verify the vibration isolation performance and energy consumption performance of the hybrid active suspension in the cyclic driving conditions, this article simulates vehicle urban and suburban conditions which is based on GB/T 19233-2003 “Light Vehicle Fuel Consumption Test Method”; among them, the urban conditions include four cycle units, each cycle time is 195 s; the suburban conditions include one cycle unit, and the cycle time is 400 s [26]. And the schematic diagram of the urban conditions unit is shown in Figure 19.Figure 19
The schematic diagram of the urban conditions unit.In order to simulate the vehicle acceleration signal, a vehicle speed variation model in different cycle units is established by using the signal builder function module in Simulink software. On this basis, the vehicle acceleration model in different cycle units is obtained, and the vehicle acceleration model can be used as the switching control model for the variable damping when the hybrid suspension is actively controlled. The shock absorbers of active suspension and passive suspension adopt the original damper of vehicle, and the damping valuec1 is 1600 N·s/m. However, because of the long simulation time, the dynamic response curves of the hybrid active suspension in urban and suburban conditions cannot be displayed. Figure 20 shows the dynamic response curve of the hybrid active suspension in the 145–175 s in the urban circulation unit; among them, vehicle in the 145–155 s is in a constant speed, vehicle in the 155–163 s is in the deceleration state, and vehicle in the 163–175 s is in other constant speed.Figure 20
The dynamic responses of the hybrid suspension. (a) The response curves of sprung mass acceleration. (b) The response curves of suspension working space. (c) The response curves of dynamic tire load.
(a)
(b)
(c)The dynamic response RMS values of the hybrid suspension in urban and suburban circulation units are shown in Tables3 and 4, respectively.Table 3
The dynamic response root mean square values of the hybrid suspension in urban circulation unit.
Indicators
Passive suspension
Active suspension
Hybrid suspension
a
w (m/s2)
1.4440
1.0078
0.8746
SWSrms (m)
0.0089
0.0080
0.0087
DTLrms (N)
334.4223
289.1024
264.8285Table 4
The dynamic response root mean square values of the hybrid suspension in suburban circulation unit.
Indicators
Passive suspension
Active suspension
Hybrid suspension
a
w (m/s2)
2.5204
1.7422
1.5333
SWSrms (m)
0.0159
0.0142
0.0154
DTLrms (N)
585.4460
508.2344
470.9650From Figure20 and Tables 3 and 4, the dynamic responses are good when the hybrid suspension is multimode coordinated control. When in the urban circulation unit, compared with the passive suspension, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 39.43%, 2.25%, and 20.81%, respectively. Compared with the active suspension, aw and DTLrms of the hybrid suspension are reduced by 13.22% and 8.40%, respectively, but SWSrms is increased by 8.05%. When in the suburban circulation unit, compared with the passive suspension, aw, SWSrms, and DTLrms of the hybrid suspension are reduced by 39.16%, 3.14%, and 19.55%, respectively. Compared with the active suspension, aw and DTLrms of the hybrid suspension are reduced by 11.99% and 7.32%, respectively, but SWSrms is increased by 8.45%.The system energy of the hybrid suspension in urban and suburban circulation units are shown in Figures21 and 22, respectively.Figure 21
The system energy of the hybrid suspension in urban circulation units.Figure 22
The system energy of the hybrid suspension in suburban circulation units.Then, the system energy values of the hybrid suspension in urban and suburban circulation units are shown in Table5.Table 5
The system energy values of the hybrid suspension (J).
Cycle unit
Active suspension
Hybrid suspension
Urban
−2165
38
Suburban
−15071
−122From Table5, when in the urban circulation unit, the system energy of the active suspension and hybrid suspension is −2165 J and 38 J, respectively. And when in the suburban circulation unit, the system energy of the active suspension and hybrid suspension is −15071 J and −122 J, respectively. The entire operation cycle includes 4 urban cycle units and 1 suburban cycle unit, so the pure energy of the active suspension system during the entire operation cycle is −23731 J, while the pure energy of the hybrid suspension system is 38 J. Therefore, the hybrid suspension system basically realizes energy self-powered in theory.


## 5. Test and Analysis

In order to verify the damping effect of the hybrid suspension system in active mode and semiactive mode, a hybrid suspension vibration test system is designed, as shown in Figure23. During the test, the MR damper has no controllable current input in the active control mode of the hybrid suspension, and its damping value is always 800 N·s/m. The passive suspension, semiactive suspension, and active suspension all adopt the original damper of the vehicle, and the damping value c1 is 1600 N·s/m.Figure 23
The test system of the hybrid active suspension.Because of the limitation of test conditions, only the sprung mass acceleration dynamic response of the hybrid suspension is measured in this test. The dynamic response of the sprung mass acceleration of the hybrid suspension in active mode under random road is shown in Figure24. The power spectrum of the sprung mass acceleration of the hybrid suspension in active mode is shown in Figure 25.Figure 24
The dynamic response of the sprung mass acceleration of the hybrid suspension in active mode.Figure 25
The power spectrum of the sprung mass acceleration of the hybrid suspension in active mode.Table6 shows the sprung mass acceleration RMS test values of the hybrid suspension in active mode.Table 6
The sprung mass acceleration RMS of the hybrid suspension in active mode.
Indicators
Passive suspension
Active suspension
Hybrid suspension
a
w (m/s2)
1.3378
0.9423
0.8074From Table6, compared with passive suspension, aw of the hybrid suspension in active mode is reduced by 39.45%, and compared with active suspension, aw of the hybrid suspension in active mode is reduced by 14.32%. And from Figure 25, when the hybrid suspension is actively controlled, compared with passive suspension, the vibration isolation performance of the suspension in the low frequency and low-frequency resonance areas is similar to that of the passive suspension, and the vibration isolation performance in the high frequency and high-frequency resonance areas is better than that of the passive suspension. Compared with active suspension, the vibration isolation performance of the suspension in the low frequency, high frequency, and resonance regions is slightly better.The dynamic response of the sprung mass acceleration of the hybrid suspension in semiactive mode under random road is shown in Figure26. The power spectrum of the sprung mass acceleration of the hybrid suspension in semiactive mode is shown in Figure 27.Figure 26
The dynamic responses of the sprung mass acceleration of the hybrid suspension in semiactive mode.Figure 27
The power spectrums of the sprung mass acceleration of the hybrid suspension in semiactive mode.Table7 shows the sprung mass acceleration RMS test values of the hybrid suspension in semiactive mode.Table 7
The sprung mass acceleration RMS of the hybrid suspension in semiactive mode.
Indicators
Passive suspension
Semiactive suspension
Hybrid suspension
a
w (m/s2)
1.3378
1.1536
1.1182From Table7, compared with passive suspension, aw of the hybrid suspension in semiactive mode is reduced by 16.42%. Compared with semiactive suspension, aw of the hybrid suspension in active mode is reduced by 3.07%. And from Figure 27, when the hybrid suspension is semiactively controlled, compared with passive suspension, the vibration isolation performance of the suspension in the low frequency and low-frequency resonance areas is worse than that of the passive suspension, and the vibration isolation performance in the high frequency and high-frequency resonance areas is better than that of the passive suspension. Compared with semiactive suspension, the vibration isolation performance of the suspension in the low frequency, high frequency, and resonance regions is slightly better.The energy consumption power and energy-regenerative power of the hybrid suspension are shown in Figure28.Figure 28
The energy consumption power and energy-regenerative power of the hybrid suspension.From Figure28, in the active mode, the average power consumption of the ball screw actuator is 25.61 W. In the semiactive mode, the average regenerative power of the ball screw actuator is 26.96 W, and the average of the MR damper energy consumption power is 1.78 W. Therefore, the pure average power consumption of the hybrid suspension is −0.43 W, and the test results are basically consistent with the simulation.


## 6. Conclusion

(1)
A ball screw actuator and MR damper are introduced into vehicle suspension system and a new kind of hybrid active suspension structure is put forward. The ball screw actuator is prototyped, and the functional relationship between the back-EMF coefficient, the electromagnetic torque coefficient of the motor, and the suspension vibration speed is obtained by test analyses. And the active output mechanical properties of the ball screw actuator are tested, and the results show that the actuator has good active output force characteristics.
(2)
The influences of the variable damping value of the suspension system on the riding comfort, handling and stability, and energy consumption characteristics of the hybrid suspension in the active control mode are analyzed. Then, the optimal damping values of the hybrid suspension at different vehicle speeds are designed. The effects of electromagnetic damping force on the actual semiactive force and the system energy of the suspension in the semiactive control mode are analyzed, and then, the hybrid suspension with semiactive mode which has electromagnetic damping force feedback adjustment is designed. On this basis, a multimode coordinated control strategy for the hybrid suspension is designed.
(3)
The damping performance and energy consumption characteristics of the hybrid suspension under cyclic driving condition are simulated by MATLAB/Simulink software, and the results show that when in the urban circulation unit, compared with active suspension,aw and DTLrms of the hybrid suspension are reduced by 13.22% and 8.40%, respectively. And when in the suburban circulation unit, compared with the active suspension, aw and DTLrms of the hybrid suspension are reduced by 11.99% and 7.32%, respectively. The pure energy of the active suspension system during the entire operation cycle is −23731 J, while the pure energy of the hybrid suspension system is 38 J. Therefore, the hybrid suspension system basically realizes energy self-powered in theory.
(4)
The effectiveness verification test of the hybrid suspension in active mode and semiactive mode control is carried out, and the results show that when the hybrid suspension is actively controlled, compared with active suspension,aw of the hybrid suspension in active mode is reduced by 14.32%. When the hybrid suspension is semiactively controlled, compared with semiactive suspension, aw of the hybrid suspension in active mode is reduced by 3.07%. The test and simulation results are basically consistent, and the test verifies the correctness of the simulation.



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*Source: 6378023-2018-12-16.xml*