# Design of Constant Speed Controller for Hydraulic Retarder Based on Robust Control
## 1 Introduction  
In recent years, the rapid advancement of modern transportation has led to a trend toward high power and substantial load capacity in both passenger vehicles and trucks. This trend causes the issue of automobile travel safety and imposes greater demands on the braking efficiency and reliability of vehicle braking systems. The braking system isessential for ensuring vehicle safety; it can be categorized into three types based on its function: service brake, parking brake, and auxiliary brake [1]. The primary brake is mainly used to decelerate the vehicle, halt it, or maintain its stationary position, while the auxiliary brake is generally employed to ensure that the vehicle drives downhill at a constant speed. When heavy-duty vehicles are travelling downhill, the continuous use of the service brakes will lead to overheating of the brake pads, reducing braking efficiency and even causing failure [2]. For this reason, modern heavy-duty vehicles usually use auxiliary brakes combined with mechanical brakes [3]; through the auxiliary brake without wear to bear the main braking force, not only to reduce the mechanical brake wear, but also to improve the braking safety and efficiency, this has become the mainstream development direction of long downhill braking technology. Hydraulic retarders and electromagnetic retarders are the principal auxiliary braking devices installed and used in the present market for heavy-duty vehicles [4]. These two types of auxiliary braking devices occupy the majority of the market share [5]. In recent years, the ongoing advancement of hydraulic technology has rendered hydraulic retarders superior to electromagnetic retarders due to their minimal inertia, ease of initiation, smooth operation, rapid response, and additional benefits, facilitating automatic control. Furthermore, the integration of hydraulic valves with various electronic components simplifies the execution of intricate control operations [6]. The above features make the hydraulic retarder particularly suited for vehicles traveling down a long slope under continuous braking conditions, and has been widely used in heavy-duty vehicles. Therefore, it is necessary to carry out in-depth research on the auxiliary braking of the hydraulic retarder for heavy-duty vehicles under long downhill working conditions. Heavy vehicles need to continuously consume gravitational potential energy when going downhill at a constant speed, which requires the hydraulic retarder to provide stable high-torque braking [7]. Existing hydraulic retarders are mainly designed based on the hydraulic coupling principle: compressed air presses oil into the working chamber during startup, and the rotor blades push the oil to impact the stator to generate a reverse torque, which achieves continuous decelerating braking through the circulating flow of oil [8]. The hydraulic retarder control mainly includes two modes: constant speed and constant torque [9]. Constant-speed control changes the braking torque by adjusting the oil filling rate to keep the vehicle going downhill at a constant speed; constant torque control outputs a fixed braking force according to the vehicle speed. This technology can avoid overheating and excessive wear of mechanical brakes and also improve driving safety and efficiency [10]. Since the braking torque output from the retarder mainly depends on the oil filling rate of the working chamber and the rotor speed (related to the vehicle speed), the actual control is mainly through the adjustment of the oil filling rate to achieve the precise regulation of braking force [11]. The control accuracy of the hydraulic retarder's filling rate directly affects its output braking torque. When driving downhill in practice, the vehicle load and the angle of the ramp change constantly, resulting in continuous fluctuations in the required braking torque.