# Design of Constant Speed Controller for Hydraulic Retarder Based on Robust Control
## 4 Simulation Results and Analysis
### Simulation Results
The root-mean-square of the speed errors for the three controllers, under varying vehicle mass and specific slope conditions, exhibits minimal variation, indicating commendable speed tracking performance. The sliding mode controller with saturation function and high-frequency controller has smaller speed fluctuation when the vehicle mass changes, and the maximum absolute speed error is not more than 0.079 km/h. The fuzzy controller has a maximum absolute speed error of 0.113 km/h, and the speed variation is rather considerable. At the same time, when the vehicle mass changes, although the sliding mode controller can achieve rapid and stable regulation of vehicle speed, its control output of the hydraulic retarder filling rate signal will appear to have obvious chattering, which makes it difficult to adjust the filling rate of the hydraulic retarder in reality. The reaction time of the fuzzy controller is slow, and it normally takes about 2 s to output the appropriate retarder filling rate to stabilize the vehicle speed. Figure 12: Simulation results under C2 conditions: (**a**) Vehicle speed, (**b**) Hydraulic retarder filling rate, (**c**) Vehicle speed error and (**d**) Braking power of hydraulic retarder. Figure 13a,b show the simulation results of the three controllers for the C3 condition. The root-mean-square error of the vehicle speed of the fuzzy controller under the C3 condition is 0.184 km/h, and the maximum absolute error is 0.37 km/h. Compared with the other two controllers, the fuzzy controller has a larger fluctuation of the vehicle speed, and the speed tracking performance is poor. In terms of controller control output, the retarder filling rate signal output from the high-frequency controller shows the best smoothing when the vehicle mass changes in steps and fluctuates only for a short period of time after the mass has changed. Sliding mode controllers with saturation functions exhibit high-frequency chatter. The retarder filling rate signal from the fuzzy controller shows poor smoothing. Figures 11-13 show that while the vehicle descends at its initial speed, the hydraulic retarder performs a dynamic filling process for about 1 s, and the vehicle's speed gradually increases. After the first filling process concludes, as the vehicle's speed is rather high at this time, the braking power of the hydraulic retarder will be limited by the cooling power of the radiator, remaining at a constant value of 500 kW, and the volume of working fluid in the working cavity of the retarder increases with the slowing down of the vehicle's speed until the working cavity is full of the working fluid, while the hydraulic retarder filling rate achieves the maximum value. At around 20 s, the vehicle speed decreases to near the target speed, and the speed controller begins to operate. It calculates the required hydraulic retarder filling rate under the present working conditions based on the speed error or speed error rate, allowing the vehicle to continue descending at the target speed. The braking power output of the hydraulic retarder does not exceed the maximum cooling power of the radiator in the cooling system during the whole process. In conclusion, when a vehicle with constant mass is traveling downhill at a set gradient of 6%, all three controllers can effectively meet the requirement of maintaining a constant speed during downhill travel, with the fuzzy controller showing stronger speed tracking  
Figure 13: Simulation results under C3 conditions: (**a**) Vehicle speed, (**b**) Hydraulic retarder filling rate, (**c**) Vehicle speed error and (**d**) Braking power of hydraulic retarder. performance and smoother control output than the other two controllers.