# Adaptive Semi-Active Suspension and Cruise Control through LPV Technique
## 4 System and Decision Integration Method  
In this section, the system integration and decision layer with the method of selecting scheduling variable \(\rho\) depending on GPS-based road data and look-ahead cruise control are described. The integration of the vertical and longitudinal control system is shown in Figure 6. There are various outputs that the controlled vehicle provides, however suspension deflection, GPS position, and prehistoric road data from these outputs are used in the integration of this system. GPS based road database consists of information about road conditions for each coordinate. According to GPS data, current oncoming road conditions can be known by using a GPS based road database. This information on road conditions is used for the decision layer and look-ahead cruise control. The look-ahead cruise control algorithm generates optimal velocity for the decision layer and longitudinal force(\(F_{lon}\)) for the controlled vehicle, while a semi-active LPV controller generates damping force(\(F_{i,pert}\)) for each wheel of the controlled vehicle by using suspension deflection measurement input and the value of the scheduling variable \(\rho\). Here, the decision logic layer is responsible for selecting \(\rho\) based on road data, previous measurements and the calculated optimal velocity \(\lambda\). Multiple passive suspension simulations have been evaluated with different road types, velocities and \(\rho\) values to analyze the performance results. The root mean square (RMS) value of these performances are calculated as below:  
\[ \begin{split}\mathcal{P}^{ua}=\sqrt{\frac{1}{T_{a}}\int_{0}^{T_{a }}a^{2}(t)dt}\\ \mathcal{P}^{td}=\sqrt{\frac{1}{T_{t}}\int_{0}^{T_{t}}t_{d}^{2}( t)dt},\end{split}  \tag{18}\]  
where \(a(t)\) is the time-weighted acceleration, \(t_{d}(t)\) is the time-weighted tire deformation, \(T_{a}\) and \(T_{t}\) is the number of acceleration and tire deformation values. Table 2 shows the RMS values of vertical accelerations and tire deformations of passive suspension simulations for 10 cm bump, multiple bumps, sine-sweep road types with different vehicle velocities. Note, that scaled vertical acceleration and tire deformation values are also calculated. These scaled performance values are calculated as follows:  
\[\xi_{i,j}^{k}=\frac{\mathcal{P}_{i,j}^{k}}{\mathcal{P}_{max}^{k}}, \tag{19}\]  
Figure 6: Integration of the system. where \(\zeta\) is the scaled value, \(\mathcal{P}\) states RMS value of the performance, \(k\in[va,td]\), where \(va\) is the vertical acceleration performance, \(td\) is the tire deformation performance, \(i\) denotes the road type, \(j\) expresses the velocity of the vehicle. It is assumed that the speed limit is 80 km/h for the vehicle, thus maximum velocity is 80 km/h in these passive suspension simulations. The selection of the scheduling variable depends on the results of performances with the passive suspension system. The scaled performance value is compared to each velocity and road type. Equation (20) calculates the scheduling variable according to the relationship between performances as follows:  
\[\rho= \begin{cases}\frac{\zeta_{ij}^{va}}{\zeta_{ij}^{va}+\zeta_{ij}^{td}}&\text {if }\zeta_{ij}^{va}>\zeta_{ij}^{td}\\ 1-\frac{\zeta_{ij}^{td}}{\zeta_{ij}^{td}+\zeta_{ij}^{td}}&\text{if }\zeta_{ij}^{td}> \zeta_{ij}^{va}\\ 0.5&\text{if }\zeta_{ij}^{td}=\zeta_{ij}^{va}.\end{cases}  \tag{20}\]  
Here, the magnitude of the scaled values of vertical acceleration and tire deformation have significant importance to select the corresponding formula for the scheduling variable. As described in Section 3, the scheduling variable, \(\rho=1\) stands where passenger comfort is preferred, whereas \(\rho=0\) represents a controller considering stability and road holding of the vehicle. Thus, formulation of the scheduling variable is different for the case where \(\zeta_{ij}^{td}\) is greater than \(\zeta_{ij}^{va}\) and for the case where \(\zeta_{ij}^{va}\) is greater than \(\zeta_{ij}^{td}\).