2.2 Semi-active Suspension Control for Passenger Comfort and Road Holding 18
2.2.4 Road Adaptivity Methods
One of the main contributions of this thesis is making the proposed system road adaptive.
This road adaptivity must be provided by considering both the vertical and longitudi- nal dynamics of the vehicle. Therefore, different road adaptivity methods have been introduced and integrated into the control systems.
2.2.4.1 Road Adaptivity Method I - ISO-2631-Based Adaptation
As introduced earlier, road adaptivity can be applied by changing the scheduling vari- able ρ according to different road irregularities and velocities. The first method in
designing the scheduling variable depends on the Frequency-weighted vibration magni- tude(FWVM) value of the ISO 2631-1 standard. This value and its likely reaction in public transport are shown in Table 2.5.
The algorithm is based on the look-ahead estimation algorithm that considers pre- historic simulation of passive suspension, which was performed in order to calculate the RMS values of tire deformation and FWVM value with different road irregularities and vehicle velocities. One of the designed databases for this thesis consists of the passive suspension simulations due to the availability of this suspension system in many vehicles and the ease of measuring and storage the data of passive suspension.
The architecture of the algorithm is shown in Figure 2.9. The algorithm’s input is velocity and road category, while it has a real-time connection with the database. The calculated scheduling variable is sent to the database to store it for a further scenario to avoid repetitive calculations for the same scenario; thus, the system works faster and more efficiently.
Figure 2.9: Architecture of an adaptivity algorithm.
Algorithm 1 shows the selection procedure of the scheduling variable according to road categoryRin theRoadDatabase. Here,f wvmis the frequency-weighted vibration magnitude, and ν is the vehicle’s velocity. If thef wvm value of the road category and dedicated velocity is nearly zero, in that case, there is no comfort-related issue, thus scheduling variable can be selected as ρ = 0 to ensure vehicle stability. In case of the f wvmvalue is nearly under the "a little comfortable" level, then the scheduling variable can be selected as ρ = 1 in order to ensure the driving comfort because there is no vehicle-stability related issue with a lowf wvmvalue. In other cases, bothf wvmand the RMS value of tire deformation are high; in that case, the scheduling variable is selected asρ = 0.5 to consider both driving comfort and vehicle stability simultaneously. These comfort levels are defined by ISO and they are shown in Table2.5.
The algorithm works for the different road categories which exist in the database, while if the velocity differs from the database, then the interpolation method can be used in order to calculate the dedicated velocity and itsf wvm value.
Data: RoadDatabase Result: Export ρ R ← input
ν ← input
find: Rνf wvm inR if Rνf wvm≤ 0.01 then
ρ = 0 else
if 0.01≤Rνf wvm≤ 0.37 then ρ = 1
else ρ = 0.5 end end
Algorithm 1:Adaptivity algorithm.
2.2.4.2 Road Adaptivity Method II - Mathematical Approach I
The basic mathematical approach is proposed for road adaptivity of the system in this section. This mathematical approach is based on the performance comparison and its effect on the system.
According to GPS data, current and oncoming road conditions can be known by using a GPS-based road database. This information on road conditions is used for this method.
This database is based on the historical travel data and measurements of the vehicle.
Multiple passive suspension simulations have been evaluated with different road types, velocities, and ρ values to analyze the performance results. The RMS value of these performances is calculated. The architecture of this method is shown in Figure2.10.
Note that normalized vertical acceleration and tire deformation values are also cal- culated. These normalized performance values are calculated as follows:
ζi,jk = Pki,j
Pkmax. (2.18)
whereζ is the normalized value,Pstates RMS value of the performance,k∈[va, td], wherevais the vertical acceleration performance,tdis the tire deformation performance, idenotes the road type,j expresses the velocity of the vehicle.
The selection of the scheduling variable depends on the results of performances with the passive suspension system. The normalized performance value is compared to each velocity and road type. Equation (2.19) calculates the scheduling variable according to the relationship between performances as follows:
ρ=
ζi,jva
ζi,jva+ζi,jtd ifζi,jva > ζi,jtd, 1− ζ
td i,j
ζi,jva+ζi,jtd ifζi,jtd > ζi,jva, 0.5 ifζi,jtd =ζi,jva.
(2.19)
Figure 2.10: Architecture of mathematical method I.
Here, the magnitude of the normalized values of vertical acceleration and tire de- formation have significant importance in selecting the corresponding formula for the scheduling variable. Therefore, the formulation of scheduling variable is different for the case whereζi,jtd is greater thanζi,jva and for the case whereζi,jva is greater thanζi,jtd. As de- scribed earlier, in the latter case scheduling variable is closer to ’1’, where the controller works comfort-oriented. In the former case, the scheduling variable is closer to the ’0’, where the controller works safety-oriented.
2.2.4.3 Road Adaptivity Method III - Mathematical Approach II
This section presents another mathematical approach to the road adaptivity method.
This method is based on the comparison of the performance results in the corresponding velocity and road category in the database. The difference between this method and previous mathematical approaches is the sensitivity of the calculation. This method defines the scheduling variable as more sensitive.
There are four steps for this method: First, the performance index must be defined according to the cloud database and previous measurement of the passive suspension.
This performance index defines the importance and relationship between driving comfort and road holding. In the second step, the shifting index is calculated, while in the third step, the rate index is defined. Finally, the scheduling variable is calculated according to the performance and shifting index.
The database consists of several measurements and historical data with different road irregularities and velocities. The measurement data have the size and type of the road irregularity, location of the road irregularity, velocity,f wvm, and RMS value of the tire deformation value. Categorization and grouping of these data are important when the new data arrives from the on-board computer.
The normalized value ζ calculation has been introduced in the previous section.
When the velocity of the simulated vehicle differs from the cloud, the interpolation method is used to find corresponding performance values for different road irregularities and velocities. The performance index calculation results give us the mode of perfor-
Figure 2.11: Architecture of mathematical method II.
mance. This calculation is based on the comparison of the performance’s normalized value.
Here, Υ = 1 stands for the driving comfort mode, Υ = 0 stands for road holding mode and both performance consideration is defined as Υ = 0.5. This consideration can be defined as the distance of the scheduling variable from 0.5. The driving comfort mode means that the effect of vertical acceleration of the vehicle is higher than the effect of the tire deformation, and the focus should be minimizing the vertical acceleration.
The mode of road holding focuses the minimizing tire deformation due to its effect being higher than the vertical acceleration for the vehicle. In the case of the performance index being in the driving comfort mode, then the scheduling variable must be close to the one due to the characteristics of the semi-active controller. In another case, where this mode is road holding, the scheduling variable must be close to zero. The definition of performance index is shown in Eq. 2.20.
Υ =
0, if ζtd> ζva, 1, if ζtd< ζva, 0.5, if ζtd =ζva.
(2.20)
Next, shifting index κ must be found. This index defines the distance of the corre- sponding scheduling variable from the middle range(0.5). The shifting index is calculated according to rate indexχ, which is computed by the average rate between the normalized value of tire deformation andf wvmin the database, while this value is calculated as two according to data in the cloud. It means that if the rate of the corresponding normalized performance value is greater than two, the shifting index κ is 0.5. Because, κ cannot be greater than 0.5 due to scheduling variable limitation(ρ ∈ [0.01,0.99]). In the case normalized tire deformation is greater than normalized vertical acceleration, the rate of
normalized tire deformation and vertical acceleration has been used to calculateκ. The value of 0.25 restricts the κvalue between 0 and 0.5.
κ=
0.5, if ζζvatd ∨ζζvatd >=χ,
ζtd
ζva0.25, if ζtd> ζva,
ζva
ζtd0.25, if ζva > ζtd.
(2.21)
Finally, the scheduling variable ρ is calculated according to the performance index, shifting index, and rate index by Equation2.22.
ρ=
0.5−κ, if Υ = 0, 0.5 +κ, if Υ = 1, 0.5, if Υ = 0.5.
(2.22)
The architecture of this method is shown in Figure 2.11. The normalization value is provided by a cloud-based database to the performance index design algorithm and shifting index algorithm. The computed performance index is used in the calculation of the shifting index. The scheduling variable is designed with the calculated shifting index and performance index.
2.2.4.4 Road Adaptivity Method IV - Fuzzy Logic Control
This method finds the dedicated scheduling variable for road adaptation with Fuzzy Logic Control (FLC) method. In the FLC, the dynamic behavior of a fuzzy system is characterized by a set of linguistic description rules based on expert knowledge. The fuzzy control rule is a fuzzy conditional statement in which the antecedent is a condition in its application domain, and the consequent is a control action for the system under control.
Matlab Fuzzy Logic Designer has been used to design the fuzzy controller. The fuzzification is composed of the process of transforming crisp values into grades of mem- bership for linguistic terms of fuzzy sets. The membership function is used to associate a rate to each linguistic term. FLC has four variables for fuzzification: three inputs (performance, velocity, and road irregularity) and one output (scheduling variable). In- puts have a beta shape membership function, while output has a triangle membership function. The interval input of the membership function is set at [−1 1].
The first input for the FLC is the type of road irregularity, where χ ∈[1,2,3,4,5].
Five different road types, where four irregularities and flat road have been considered in the following order: 10 cm bumps, several bumps, sine-sweep irregularity, 7 cm pothole, and flat road. These road irregularities have been simulated with multiple scheduling variables and velocity. The second input is the velocity of the vehicle,υwith the following boundary: χ∈[0 110]. Note that the lowest velocity of the simulated vehicle is 5km/h.
Figure 2.12: Block diagram of a fuzzy logic controller.
The third input is the performance mode with ϵ ∈ [1,2]. The performance mode is defined like the introduced Υ in the previous section. Here, the normalized value of the two performances is compared, and the mode of the performance is clarified. The architecture of the FLC method is shown in Figure 2.14.
The degree of membership of the inputs is shown in Figure 2.13. The output of the FLC is scheduling variableρ, which is used for the LPV controller in order to trade-off between driving comfort and vehicle stability.
The fuzzy control rules are based on historical simulations. Unlike passive suspen- sion databases, multiple simulations have been run with semi-active suspension. These simulations have been held with different road irregularities, velocity, and scheduling variables.
Surfaces of the FLC model with inputs and output are seen in Figure 2.15. Accord- ing to the surfaces, the output of the FLC varies with different inputs. The desired output can be found on these surfaces, while the FLC method can be used in real-time simulation. The performance mode is defined according to the normalized value of the simulation performances. The corresponding minimum performance result is chosen in the dedicated velocity then its scheduling variable interval is selected as output depend- ing on the defined performance mode.
Figure 2.13: Degree of membership for inputs and output.
Figure 2.14: The architecture of FLC.
Figure 2.15: Surfaces of FLC model.