## 3 Stability Based Coordinated Control of Active Suspension and DYC
### Coordinated Controller  
The lateral force is affected by the tire cornering stiffness \(K\). While the tire cornering stiffness is not fixed, it will change with the tire pressure and vertical load. Among them, the vertical load is affected by the active suspension. So, the working of the active suspension will affect the lateral force by affecting the vertical load.  
When the active suspension creates an anti-roll torque, it also causes a load transfer between the left and right wheels. Figure 4 shows the influence of the vertical load on the tire cornering stiffness [26]. With the increase in the vertical load, the tire cornering stiffness increases at a decreasing speed. When the vertical load exceeds a certain limit, it decreases. Here, \(F_{N2}\) is the average of \(F_{N1}\) and \(F_{N3}\). However, the cornering stiffness of B is greater than the average of A and C. It indicates that the vertical load transfer leads to a decrease in the average cornering stiffness. Additionally, the larger the difference between left and right is, the smaller the average lateral force is.  
For the active suspension, if more anti-roll torque is allocated to the front suspension, the vertical load difference between the two front wheels will increase. Then, the total lateral force of the front wheels will decrease, which tends to reduce the vehicle yaw rate. If more anti-roll torque is allocated to the rear axle, the vertical load difference between the two rear wheels will increase. The total lateral force of the rear wheels will decrease, which tends to increase the vehicle yaw rate. So, while tracking the expected yaw rate, in addition  
Figure 4: The influence of vertical load on tire cornering stiffness.  
to the DYC, the active suspension can also play a role by adjusting the distribution of the anti-roll torque.  
Based on this, a coordinated controller, as shown in Figure 5, is proposed to adjust the active forces distribution of the active suspension according to the state feedback of the vehicle yaw stability. For the coordinated controller, the deviation between the actual and expected value of the yaw rate is taken as the input. Additionally, the distribution of the anti-roll torque weight is the output. When the actual yaw rate is greater than the expected value, the yaw rate needs to be reduced. So, the anti-roll torque distribution weight of the front suspension should be increased. When the actual yaw rate is less than the expected value, the yaw rate needs to be increased. So, the anti-roll torque distribution weight of the rear suspension should be increased.  
Based on the flow chart, Equation (36) is established for the coordinated controller as the distribution scheme of the anti-roll torque. Through the adaptive adjustment of the weight distribution coefficient, the active suspension can cooperate with the DYC controller which can further improve the yaw stability. The weight coefficients of the anti-roll torque distribution are defined as:  
\[\begin{cases}W_{f}=1+k\cdot r(r-r_{d})\\ W_{r}=1-k\cdot r(r-r_{d})\end{cases} \tag{36}\]  
where \(W_{f}\) and \(W_{r}\) are the weight coefficient of the anti-roll torque in the front and rear suspension. \(k\) is the control parameter.  
Different from the active suspension roll controller in Section 3.1, an anti-roll torque distribution is introduced. When the active suspension controller receives the \(W_{f}\) and \(W_{r}\) from the coordinated controller, the required anti-roll torque from the PI controller is distributed according to the weight coefficients.  
\[\begin{cases}T_{f}=\frac{W_{f}}{2}T_{req}\\ T_{r}=\frac{W_{r}}{2}T_{req}\end{cases} \tag{37}\]  
where \(T_{f}\) and \(T_{r}\) are the required anti-roll torque from the front and rear suspensions. \(T_{req}\) is the total required anti-roll torque.  
Figure 5: Principle framework of active suspension and DYC coordinated control.