# Ground Simulation Tests in Two-Dimensional Dynamic Acceleration Environment
## 3 Simulation of Impact Overload Environment
### Speed Control System Based on Active Disturbance Rejection Control
\right.. \tag{10}\]  
The control quantity \(i_{Ts}\) obtained by the nonlinear state error feedback control can be written as  
\[i_{Ts}=i_{Ts0}-\frac{JL_{r}}{\rho L_{m}\psi_{r}}\delta_{3}(t). \tag{11}\]  
Substituting Equation (11) into Equation (7) yields the following formula  
\[\left\{ \begin{array}{l}\dot{\omega}=\frac{\rho L_{m}}{JL_{r}}\psi_{r}i_{Ts0} \\ y=\omega\end{array} \right.. \tag{12}\]  
After the ADRC is adjusted, the coupling term is no longer included in the speed state equation and the total disturbance of the system is canceled. The structure of the speed outer loop ADRC system is illustrated in Figure 7.  
Similarly, the first-order ADRC regulations for the excitation current loop and the torque current loop can also be obtained. The differential equation for the rotor flux is shown as follows:  
\[\dot{\psi}_{r}=-\frac{R_{r}}{L_{r}}\psi_{r}+\frac{L_{m}R_{r}}{L_{r}}i_{Ms}, \tag{13}\]  
where \(R_{r}\) is the rotor resistance and \(i_{Ms}\) is the excitation component of the stator current. Equation (13) does not contain a coupling term, and the rotor flux outer loop can be regulated by a PI controller. The first-order ADRC regulators are applied to the speed outer loop, the excitation current loop, and the torque current loop. Thus, the asynchronous motor speed control system based on the ADRC is designed. Simulation and analysis of the speed control system based on ADRC are conducted. The parameters of the asynchronous motor are shown in Table 1. The appropriate parameters of the speed control system should be set before the simulation. The discretization time values are all set to 100 ms in this system. The regulator coefficients of the speed outer loop are: \(\beta_{21}\) = 1000, \(\beta_{22}\) = 16,000, \(\alpha_{3}\) = 0.5, \(\delta_{3}\) = 0.01, \(\beta_{3}\) = 10. The regulator coefficients of the excitation current loop are: \(\beta_{01}\) = 10,000, \(\beta_{02}\) = 120,000, \(\alpha_{1}\) = 0.5, \(\delta_{1}\) = 0.01, \(\beta_{1}\) = 100. The regulator coefficients of the torque current loop are: \(\beta_{11}\) = 10,000, \(\beta_{12}\) = 120,000, \(\alpha_{2}\) = 0.5, \(\delta_{2}\) = 0.01, \(\beta_{2}\) = 100. The regulator coefficients of the rotor flux outer loop are: \(\text{K}_{\text{p}}\) = 2, \(\text{T}_{\text{I}}\) = 10. In the simulation test of the system operation, the motor is started without a load. When the clutch is engaged, the load disturbance is produced, and the torque transmitted depends on the speed difference between the driving plate and the driven plate. The load torque is shown as follows:  
\[T_{f}=J_{d}\cdot\alpha=10\times 3=30\text{ Nm}, \tag{14}\] \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Polar logarithm (pn) & 2 \\ Rated voltage (Vn) [V] & 380 \\ stator resistance (Rs) [\(\Omega\)] & 0.68 \\ Rotor resistance (Rr) [\(\Omega\)] & 0.45 \\ Stator leakage inductance (Lis) [H] & 0.0042 \\ Rotor leakage inductance (Lir) [H] & 0.0042 \\ Mutual inductance between stator and rotor (Lm) [H] & 0.01486 \\ Motor inertia (Jm) [kg-m\({}^{2}\)] & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the asynchronous motor. Figure 7: Structure of the active disturbance rejection system of the speed outer loop. where \(J_{d}\) = 10 Kgm\({}^{2}\), which is the load moment of inertia, \(\alpha\) = 3 rad/s\({}^{2}\), which is the load angular acceleration. The set motor speed is 200 rpm, and the motor relay is set as 0.4 s with a load of 30 Nm added abruptly. The simulation results of the motor speed controlled by ADRC are shown in Figures 8 and 9. As can be observed, the system response does not exhibit overshoot and the rise time is 0.037 s. When the load is suddenly applied at 0.4 s, the motor speed drops to 196.9 rpm. After 0.01 s, the speed quickly returns to a stable state. The load is driven by the air cannon before the clutch is engaged, and it is driven by the motor after the clutch is engaged.