The riding conditions for a highspeed tracked vehicle are quite complex. To enhance the adaptability of suspension systems to different riding conditions, a semiactive and selfadaptive hybrid control strategy based on disturbance velocity and frequency identification was proposed. A mathematical model of the semiactive, selfadaptive hybrid suspension control system, along with a performance evaluation function, was established. Based on a twodegreeoffreedom (DOF) suspension system, the kinematic relations and frequency zerocrossing detection method were defined, and expressions for the disturbance velocity and disturbance frequency of the road were obtained. Optimal scheduling of the semiactive hybrid damping control gain (
The driving conditions for highspeed tracked vehicles are harsh and varied. With the adoption of a damping adjustable suspension system, not only can the vibration performance of a vehicle be improved, the average offroad speed can also be substantially improved, thereby enhancing the motility and effectiveness of the vehicle [
Many methodologies have been used to design semiactive suspension control systems. A controller based on the skyhook theory was developed by Emura [
For a multiwheel tracked vehicle, the track has a certain attenuation effect on highfrequency road excitations which can reduce the highfrequency vibration of the vehicle body. Therefore, in the mathematic analysis of ride comfort, the influence on ride comfort of the track can be ignored [
For all kinds of vehicle suspension systems, the input disturbance comes from the road. In order to enhance adaptability, the combination of suspension control and road excitation identification is key and a central theme in current research on damping tunable suspensions. This paper proposes a semiactive selfadaptive hybrid control strategy for a tracked vehicle with a hydropneumatic suspension. The proposed strategy takes advantage of the adaptability of the suspension control algorithm and damping control gain scheduling under different road excitations. First of all, the identification of the disturbance velocity and frequency was fulfilled based on the suspension kinematic analysis and frequency zerocrossing detection method. Different damping control gains were optimized offline by exploiting the PSO algorithm and then implemented online by lookup tables. Experimental study of typical control strategies was performed and the results showed that the proposed control strategy outperforms the others in achieving a good tradeoff between the ride comfort and safety under various riding conditions.
The structural framework of the semiactive selfadaptive hybrid control strategy for the suspension system based on disturbance identification is illustrated in Figure
Hybrid control strategy of the suspension based on disturbance identification.
The “quarter vehicle model” contains all the major characteristics of a suspension system. A singlewheel suspension system with a tunable damper was studied in this paper, as presented in Figure
The singlewheel suspension model.
The kinematic model of a singlewheeled suspension system (Figure
(1) When the disturbance frequency is smaller than onefifth of the damping control bandwidth [
(2) When the disturbance frequency is higher than or equivalent to onefifth of the damping control bandwidth, a time delay caused by tuning the damping accounts for a large proportion of the suspension vibration period and a selfadaptive control mode is adopted. The damping control gain is selftuned with respect to the statistical characteristics of the disturbances and no longer adjusted during the single vibration period of the suspension. The control algorithm is expressed as follows:
The performance evaluation indices of a vehicle suspension system mainly include the sprung mass acceleration, wheel dynamic load, and suspension stroke. Taking the vertical disturbance velocity from the road as input, the transfer function of the aforementioned indices can be solved as follows:
(1) The transfer function
(2) The transfer function
(3) The dynamic load
The transfer function
According to the kinematic relationship of the twodegreeoffreedom (DOF) suspension system, we have
Based on disturbance velocity, the zerocrossing method can be applied to estimate the main frequency of the disturbance signals [
In general, the damping of adjustable suspensions leads to an improvement in the performance of one index while worsening the performance of other indices; therefore, the adjustment of the damping control gain should follow the principle of achieving an optimal comprehensive index. For the suspension system, the control objective function of the overall performance can be expressed as
In the paper, the PSO algorithm is used to obtain optimal values for the semiactive hybrid control gains (
For the semiactive hydropneumatic suspension, during one vibration period the damping coefficient changes according to the vibration status of the suspension, such that the expression of the damping force is a multisection function. This results in difficulty for evaluating the overall performance of the suspension by using a mathematical modelling approach. The approach adopted herein integrates multibody dynamic software (RecurDynV8R3 [
Cosimulation model of singlewheel suspension.
To optimize the damping control gains, the input, output, sampling points, and parameters of the PSO algorithm of the control module need to be determined. The inputs are the statistical values of the suspension performance indices within one control period from AMESim and the output is the damping control gain.
The program diagram of the PSO is depicted in Figure
Flowchart of PSO algorithm.
Figure
Flowchart of Simulink model using the PSO algorithm and control algorithm.
To obtain the optimized damping control gains under different disturbances, sinusoidal disturbance signals of various frequencies and amplitudes were set up in the RecurDyn model. The periodic control signal in AMESim was adjusted according to the disturbance frequencies. Here, it was set as 5 times the cycle time of the disturbance to allow accurate statistical computing of the output performance and suspension status. In the Simulink model, there exist continuous and discretetime block. The sample time of the continuous block is infinitely small, but for the discretetime block it is definite. In order to make them work at identical step, the system running frequency was set as 100 Hz. The parameters of the twoDOF singlewheel suspension system model and initial parameter values of the PSO algorithm are displayed in Tables
Initial values of singlewheel suspension.
Variables  Symbol  Unit  Value 

Sprung mass 

kg  2.4 × 10^{3} 
Unsprung mass 

kg  85 
Initial charge pressure of the accumulator 

Pa  6.8 × 10^{6} 
Volume of the accumulator 

m^{3}  0.85 × 10^{−3} 
Section area of the actuation cylinder 

m^{2}  4.4 × 10^{−3} 
Lower limit of the damping coefficient 

kNs/m  0.6 
Higher limit of the damping coefficient 

kNs/m  25.0 
Bandwidth of the damping control system 

Hz  42 
Initial parameter settings of PSO algorithm.
Variables  Symbol  Unit  Value 

Number of particles 

—  4 
Particle dimensions 

—  3/1 
Acceleration factor 1 

—  2 
Acceleration factor 2 

—  2 
Inertia factor 

—  0.7 
Iteration steps 

—  20 
The damping coefficients are optimized based on the weighting of the suspension evaluation indices which are set according to the frequency regions and velocity grades of the road disturbance, such that the suspension can achieve a good tradeoff between ride comfort and safety.
To improve ride comfort, it is important to suppress the resonant peak to within 1 Hz of the sprung mass acceleration because this frequency region contains the natural frequency of the sprung mass. On the other hand, it has been proven that some parts of the body, such as the stomach and eyeball, have a natural frequency between 4 and 8 Hz [
Using the values listed in Table
The rules for weight allocation are as follows: under the same disturbance velocity grade, when the frequency is close to the natural frequency of the vehicle body great attention should be paid to the improvement of ride comfort; when the frequency approaches the natural frequency of the wheel, the emphasis should be on suppression of the wheel dynamic load and suspension stroke [
The results of incorporating weighting factors with respect to the disturbance frequencies and velocity grades are displayed in Table
Weighting factors for different disturbances.
Velocity grades ( 
Weighting factor ( 




 
0–4 Hz  4–6 Hz  6–8 Hz  8–16 Hz  
Good ( 




Average ( 




Poor ( 




Very poor ( 




The optimized results of damping control gain.
A test rig for the hydropneumatic suspension was used to perform an experimental study of the proposed control strategy and thus verify its feasibility. The test rig was structured with a hydraulic vibration exciter, road wheel, actuation cylinder, proportional throttle valve, and accumulator, as illustrated in Figure
Test rig of hydropneumatic suspension.
The input disturbance is determined by the road class and vehicle speed. Road roughness coefficient is an evaluation index which determines the road class. The following formula is used as the fitting expression of the power spectral density function of the international standard road:
According to the international standard, the classification of different roads is shown in Table
Different roads classification.
Road class 



Lower limit  Geometric mean value  Upper limit  
A  8  16  32 
B  32  64  128 
C  128  256  512 
D  512  1024  2048 
E  2048  4096  8192 
F  8192  16384  32768 
G  32768  65536  131072 
H  131072  262144  524228 
Since most driving conditions of tracked vehicle are relatively harsh, the vibration exciter is actuated to simulate the excitations of driving on D, F, and H road at different speeds. The imposed disturbance signals and their estimated values are displayed in Figure
The input disturbances estimation and the optimization results.
Driving conditions  Periods  

0~5 s  5~10 s  10~15 s  
Road class  D class  F class  H class 
Speed 
60  30  5 
RMS value of disturbance (measured/estimated)/(m⋅s^{−1})  0.48/0.46  0.39/0.38  0.27/0.26 
Estimated frequency (Hz)  9.5  1.8  0.8 
Control mode  Adaptive  Semiactive  Semiactive 
Weighting factor ( 



Damping coefficient (kNs/m) 








The typical disturbance input and its estimation.
Figures
Comparison of suspension performances of different control strategies (hybrid/skyhook/ground hook/passive).
Performances  Driving conditions  

D road, 60 kmph 
F road, 30 kmph 
H road, 5 kmph  

4.92/5.35/5.72/4.65  4.85/4.44/7.63/6.47  2.86/2.59/4.49/4.0 

6.57/9.28/8.76/7.87  4.96/5.13/3.63/4.7  3.22/3.27/2.42/2.92 

13.1/20.1/19.8/15.1  29.8/30.6/22.6/27.9  46.1/47.1/37.7/42.4 
The sprung mass acceleration comparison.
Comparison of the dynamic load of the wheel.
Comparison of the suspension stroke.
Comparison of normalized performances of different control strategies.
D road, 60 kmph
F road, 30 kmph
H road, 5 kmph
In the time interval of 0~5 s, as the disturbance frequency exceeded the adjustment bandwidth of the suspension damping, the selfadaptive control mode was adopted. Furthermore, since the disturbance frequency was relatively close to the natural frequency of the road wheel and the disturbance velocity was relatively large, greater emphasis was placed on suppressing the dynamic load on the wheel and suspension stroke. As seen from Figure
In the time intervals of 5~10 s and 10~15 s, since the disturbance frequency was relatively low, close to the resonant frequency of the sprung mass, and the disturbance velocities were in the mid to low range, the emphasis was on the improvement of ride comfort. The adopted control strategy was therefore the semiactive control. It was found that the sprung mass acceleration was significantly improved by about 25.1% (5~10 s) and 28.5% (10~15 s) in comparison to passive suspension systems, while the wheel dynamic load as well the suspension stroke became slightly worse. The wheel dynamic load increased by about 5.5% (5~10 s) and 10.2% (10~15 s) and the suspension stroke increased by about 6.8% (5~10 s) and 8.7% (10~15 s), respectively. In the test of the above low frequency (0~2 Hz) excitations, as seen from Figures
In summary, the semiactive hybrid control strategy is unable to achieve the same effect as skyhook control alone with respect to ride comfort, nor the same ride safety features as groundhook alone. However, for the real driving condition which contains different kinds of disturbances, the hybrid strategy outperforms the others with respect to the overall performances by taking advantage of the adaptability of the suspension control algorithm and damping control gain scheduling under different road excitations.
This paper proposed a semiactive and selfadaptive hybrid control strategy for hydropneumatic suspensions for tracked vehicles based on road disturbance identification, and presented an experimental study using a test rig. The conclusions are as follows.
(1) Using an offline PSO algorithm, the optimized damping control gains of the hydropneumatic suspension under various disturbances can be obtained.
(2) Based on the twoDOF kinematic relations of the orderreduced suspension model and frequency zerocrossing detection method, the comprehensive index of the suspension performances and expressions of disturbance velocity and frequency can be established, and accurate identification of the disturbance can be realized.
(3) The results of the test rig experimental study based on four typical control strategies indicates that the proposed semiactive selfadaptive hybrid control strategy is capable of performing adjustments on the control mode and control gain according to the disturbance characteristics. Moreover, the strategy is capable of enhancing the adaptability of the suspension system under different riding conditions and achieves a good tradeoff between ride comfort and ride safety.
The authors declare that there are no conflicts of interest regarding the publication of this manuscript.