## 3 Results and Discussion
### Test Verification of HMCVT
#### 3.1.2 Test Verification of Variable Pump-Fixed Motor Control System  
The variable pump-fixed motor hydraulic test platform was designed and fabricated (Figure 11a). The MPC method is used for experimental verification and simulation comparison, as shown in Figure 11b. It is very obvious that the simulated speed change is consistent with the experimental speed change, which proves the correctness of the designed variable pump-fixed motor hydraulic system model. In this study, some control methods were used to analyze two operating conditions (constant displacement ratio and variable displacement ratio), which are shown in Figures 12 and 13. Figure 12 shows the simulation test result of the constant speed control under the state of constant displacement ratio. The variable pump-constant motor hydraulic system is controlled by the PID-MPC dual-loop control method. In the constant displacement ratio working condition, the 1s step signal is used for test, and the sinusoidal interference signal is added at 6s as a disturbance, which can observe the signal tracking performance and anti-interference performance of several control methods. Figure 12 shows that the PID-MPC dual-loop control method has a small overshoot compared to the PID control. Moreover, the control time for stable rotation speed is similar to PID. Compared with MPC, the PID-MPC dual-loop control method has a faster response speed. When interference signals are inserted, this control method shows excellent anti-interference ability. Therefore, the PID-MPC double-loop control inherits the advantages of fast PID response speed and a small MPC overshoot range in the speed control state. The constant displacement ratio torque change is shown in Figure 13. Under the PID-MPC double-loop control method, the PID-MPC dual-loop control method has a faster response speed. When interference signals are inserted, this control method shows excellent anti-interference ability. Therefore, the PID-MPC double-loop control inherits the advantages of fast PID response speed and a small MPC overshoot range in the speed control state. The constant displacement ratio torque change is shown in Figure 13. Under the PID-MPC double-loop control method, the PID-MPC double-loop control method has a faster response speed. When interference signals are inserted, this control method shows excellent anti-interference ability. Therefore, the PID-MPC double-loop control inherits the advantages of fast PID response speed and a small MPC overshoot range in the speed control state. The constant displacement ratio torque change  
control, the torque of the pump-motor hydraulic system has the smallest fluctuation range and impact degree compared to PID and MPC independent control. The above shows that the control method has superior torque characteristics. When the pump-motor hydraulic system is in variable displacement ratio, the performance of speed and torque are shown in Figure 14. Due to the predictive characteristics of MPC, the speed tracking performance has a certain delay in the first stage. Therefore, the speed tracking characteristics are poor in the starting stage of the pump-motor hydraulic system (Figure 14a). Although the speed tracking effect of PID control is good, its speed fluctuates wildly at 0 displacement ratio, and the speed stability is poor, which may exacerbate the instability of speed and the degree of loss in mechanical components. The PID-MPC double-loop control not only has a slight speed tracking error but also has the smallest speed fluctuation and impact at 0 displacement ratio. As shown in Figure 14b, the torque controlled by PID-MPC has the shortest time and the smallest amplitude change in the time domain, which results in the smallest torque impact. Therefore, PID-MPC dual-loop control has excellent tracking characteristics and stability. In summary, the PID-MPC control designed in this study is more suitable for the comprehensive control of the speed and torque of the pump-motor hydraulic system. Figure 10: Results of clutch control test.