## 5 Hardware-in-the-Loop Experiments  
A rear wheel electrohydraulic system model was constructed to study the effect of the rear wheel electrohydraulic system on the handing stability of the 4 WS vehicle. However, the mathematical model of the rear wheel electrohydraulic system is more ideal for practical steering mechanisms. An actual hydraulic steering system is highly non-linear and complex, and has a large number of interferences. That is to say, the modeling of the rear wheel electrohydraulic system involves uncertainties. The designed H2/H\(\infty\) controller considers the modeling uncertainties to enhance the robustness of the 4 WS control system. The step steering maneuver was used to verify the H2/H\(\infty\) controller's robust stability against modeling uncertainties. In order to further demonstrate the H2/H\(\infty\) controller's robustness against modeling uncertainties, a real rear wheel electrohydraulic system was established to conduct hardware-in-the-loop experiments. The experimental control block diagram is shown in Figure 27, and the experimental platform is displayed in Figure 28.  
The experimental platform mainly consisted of four parts: the steering wheel module, the electrohydraulic control unit, the Simulink model in the computer, and the hydraulic steering execution module. The video game steering wheel, which is a Keteng brand device, was used as the steering wheel module, which was equipped with the steering angle sensor. The STM32f407 development board was used to design the electrohydraulic control unit. The Simulink model contained the nonlinear 8 DOF vehicle model, the reference model, and the robust controller model. The rear  
Figure 28: The experimental platform. Figure 27: The experimental control block diagram. wheel electrohydraulic system was composed of the hydraulic steering execution module and the electrohydraulic control unit. The hydraulic steering execution module was mainly made up of the proportional electromagnetic valve, the steering cylinder, the hydraulic pump, the hydraulic oil tank, the pressure compensated valve, and the relief valve. The schematic diagram of the hydraulic steering execution module is shown in Figure 29.  
The steering wheel module was operated, and the steering wheel angle was then obtained, as shown in Figure 30. The front wheel angle was then calculated by the electrohydraulic control unit based on the transmission ratio of the steering system, which is shown in Figure 31.  
Figure 30: The steering wheel angle. Figure 29: The schematic diagram of hydraulic steering execution module (1—hydraulic pump; 2,5—pressure compensated valve; 3,6—proportional electromagnetic valve; 4,7—steering cylinder; 8,9—relief valve; 10—hydraulic oil tank). Hardware-in-the-loop experiments under the H2/H\(\infty\), H\(\infty\), and proportional control methods were conducted. The experimental results are shown in Figure 32.  
As can be seen in Figure 32, throughout the simulation time, the yaw rate and sideslip angle responses of the 4 WS vehicle with the proportional controller showed a large number of slight oscillations, and large-amplitude vibrations occurred over a 5-8 period. These two phenomena may be caused by errors (such as oil temperature change and internal leakage) in the hydraulic steering system and by the sudden pressure shock. However, we can see that the H2/H\(\infty\) and H\(\infty\) controllers made the 4 WS vehicle response stable in terms of yaw rate and sideslip angle, which illustrates that  
Figure 31: The front wheel angle. Figure 28:0 Experimental results: (**a**) sideslip angle; (**b**) yaw rate. the H2/H\(\infty\) and Ho\(\infty\) controllers, compared with the proportional controller, were more robust against the modeling uncertainties of the rear wheel electrohydraulic system. The experimental results are consistent with the step steering maneuver simulation about the H2/H\(\infty\) controller's robust stability against modeling uncertainties.