## 4 Calibration of Electrical Inertia Simulation Accuracy
### Calibration of Electrical Inertia Response Time  
When the motor is used to simulate mechanical inertia, there must be a delay problem, so the response time of the system needs to be measured [40; 41]. According to \(T_{t}-T_{d}=J\alpha\), it can be seen that when the driving torque \(T_{t}\) of the system is set as a constant value and the resistance moment \(T_{d}\) of the system is basically stable, the angular acceleration \(\alpha\) is a constant value. The corresponding angular acceleration curve can be obtained by measuring the rotational speed of the system. When the angular acceleration of the system is stable, the electrical inertia simulated by the system is stable. Therefore, the response time of the electrical inertia simulation of the measurement system can be obtained by observing the angular acceleration (or torque) curve. As shown in Figure 25, the electric inertia is calibrated by the steady acceleration test. Under the stable torque condition, the system uses the motor to follow the target speed through the step acceleration test. In the dotted line amplification area of Figure 25a (i.e., Figure 25b), the target velocity jumps from step to 10 r/min at 20.950 s, and then the acceleration of the system starts to respond at 20.952 s, and returns to stability at 21.022 s. By evaluating the acceleration response, the system response time of electrical inertia simulation is 72 ms. The above calibration method can be used to calibrate the response time of electric inertia under steady state conditions. However, in the process of driving load simulation, the speed and torque of the system are often unsteady, so the above calibration results cannot express the response rate of electric inertia in a real vehicle simulation environment. According to the speed tracking method, the system deduces the target speed \(\omega_{em}(s)\) of the system through the actual system model \(G_{em}(s)\), and then calculates the required motor torque \(T_{t}(s)\) by the speed closed loop. According to a series of standard inertia tests, the change of \(T_{d}\) in a continuous speed range can be neglected. When the output of load torque is accurate, the response time of the system can be evaluated by comparing the target acceleration \(\alpha_{t}\) with the measured acceleration \(\alpha_{r}\)  
Figure 23: Calibration test results under equivalent inertia of 4157.69 kg\(\cdot\)m\({}^{2}\) and 10,522.34 kg\(\cdot\)m\({}^{2}\). Figure 24: Simulated deviation of electrical inertia. At the moment \(t_{0}\) of a continuous torque fluctuation curve, the target acceleration of the system is \(\alpha_{t}\), assuming that after t seconds \(\left|\frac{\alpha_{r}-\alpha_{t}}{\alpha_{r}}\right|<1\%\), the response time of the signal is considered to be \(t\). In the actual operation process, because the sampling rate of the system is much higher than the response time of the system, the single response time adopts the following logical judgment method, in which \(\Delta t\) is the sampling frequency of the system. After counting m times, the average response time of the system is \(\frac{1}{m}\sum_{i=1}^{m}t_{i}\), as shown in Figure 26.  
As can be seen in Figure 27, the response time is represented by a gray histogram. According to the logical judgment of a single response time, the average response time of the system is 25.40 ms in a preset spectrum test with continuous load variation. The slowest response of system torque occurs in several periods when the torque fluctuates greatly. At this time, the system speed fluctuates repeatedly. Because of the system lag, it is difficult for the system to respond in time, and the maximum response time is 68 ms. Using the above methods, the response time of the control system can be calibrated in the simulation process. At present, in order to speed up the response of the system, lag compensation (such as Smith prediction), auto-disturbance rejection (ADRC), and several intelligence algorithms (such as the model reference adaptive algorithm) are generally used in the control system.