## 1 Introduction  
Magnetorheological fluid (MRF) with rheological properties is regarded as one of the most promising intelligent materials. When exposed to magnetic field, MRF can change from a free-fluid state to a solid-like state within a few milliseconds, resulting in shear yield stress, which is applied to many fields [1; 2; 3]. The magnetorheological fluid brake (MRB), as a new type of semi-active control device, has attracted more and more of researchers' attention because of its quick response, easy control, strong controllability, simple structure, and low power consumption [4; 5]. However, MRB has a high degree of nonlinearity, time delay and uncertainty in its working process, and it is difficult to control it accurately because of the interaction between current, magnetic field, magnetorheological fluid and structure [6; 7]. The braking force of MRB depends on the shear stress in the magnetorheological fluid between the brake discs, which continuously changes by controlling the intensity of the external magnetic field. Therefore, by controlling the external magnetic fields and related temperature devices in real time, torque transferred can be easily and continually adjusted. Due to its rapid and reliable response, simple control, low energy consumption and strong anti-interference ability, MRB has attracted extensive research attention [8]. In order to realize the optimal control of MRB, many researchers improved the PID controller according to the characteristics of the equipment. [PERSON] et al. proposed a strategy of DC motor speed control using an MR clutch, and designed a PID controller to adjust the output speed [9]. In order to analyze the braking performance, [PERSON] et al. developed a magnetorheological brake implemented by a PID controller, and it showed that the designed MR brake system had smaller overshoot than the traditional hydraulic brake [10]. To improve the security and adaptability of this device, [PERSON] et al. proposeda welding teaching device with an MRB, and a PID control strategy was adopted in a feedback system [11]. To eliminate the viscous torque of MRB, [PERSON] et al. designed a PID controller in combination with a novel magnetorheological brake, and the closed-loop braking performance of the innovative MRB was demonstrated, which provided good braking torque capacity and had no residual viscous torque [12]. To investigate the motion characteristics of the prosthetic limbs used by MRF dampers, [PERSON] et al. proposed a fuzzy-PID controller to realize an energy-efficient MRF damper [13]. [PERSON] et al. used a fuzzy PID control method to simulate the dynamic performance of mount, and the results showed that this method was effective in reducing the acceleration of the vehicle body [14]. [PERSON] et al. proposed a haptic master activated by an MR clutch and MR brake, and the designed fuzzy plus PID controller had an excellent track control performances [15]. [PERSON] et al. proposed a type of antilock braking system (ABS) using MRB, and it was proved that the ABS with the fuzzy logic sliding mode controller had a great braking control effect [16]. [PERSON] et al. designed a hybrid ABS with a multipole MRB, showing that the hybrid ABS is feasible in practical applications, which can effectively improve the braking performance and ensure driving stability [17]. [PERSON] et al. proposed an adaptive approach for MRB feedback control and confirmed the effectiveness of the proposed adaptive controller [18]. In order to obtain higher control precision, optimizing intelligent algorithms is the main method of some researchers. Due to the nonlinear dynamic and hysteresis characteristics of MRFA, [PERSON] et al. proposed a self-turning fuzzy controller used the fuzzy logic algorithm, and the experiment results showed that the designed controller had better control performance than PID controller and the open-loop control method [19]. [PERSON] et al. designed a magnetorheological brake with a fuzzy-PID control algorithm to investigate control performance [20]. [PERSON] et al.