# Ground Simulation Tests in Two-Dimensional Dynamic Acceleration Environment
## 3 Simulation of Impact Overload Environment
### Speed Control System Based on Active Disturbance Rejection Control  
When the clutch is engaged, the output torque of the motor is increased rapidly, and the serious load disturbance is produced. In order to improve the precision of the speed control system, it becomes necessary to compensate for the disturbance. Active disturbance rejection control (ADRC) considers perturbations to the model and parameters and unmeasurable external disturbances as the total disturbance of the system. Based on the feedback control of the system error, the total disturbance is observed and corrected, which alleviates the conflict between the response speed and overshoot in the PID controls. ADRC does not rely on any precise mathematical model of a system, and it significantly improves the dynamic response characteristics of the controller through a proper nonlinear combination. The load disturbance can be estimated and compensated by a speed controller based on active disturbance rejection control (ADRC). Many researchers have studied the application of the speed controller based on ADRC. In order to improve pointing accuracy and rotation speed, [PERSON] et al. [16]  
Figure 6: Plots of the revolution speeds when the clutch is engaged. designed the inner and outer loops of an ADRC for the antenna pointing control of a large flexible satellite system. [PERSON] et al. [17] designed an idle speed controller based on ADRC to compensate for varying engine load and friction torque in passenger car diesel engines. ADRC consists of three main components: a tracking differentiator (TD), an extended state observer (ESO), and a nonlinear state error feedback law (NSEFL). The TD arranges the transition process for the system and extracts the differential signal. ESO is the core of ADRC and can estimate the total disturbance of the system in real time and compensate for it. The outputs of the TD and ESO are compared to obtain the systematic error. Based on the error signal, the NSEFL produces a control strategy for the controlled object. Based on the torque and motion equations of the three-phase asynchronous motor, the differential equation of the speed loop can be obtained as follows:  
\[\dot{\omega}=\frac{\rho L_{m}}{JL_{r}}\psi_{r}i_{Ts}-\frac{1}{J}T_{L}, \tag{6}\]  
where \(\omega\) is the rotor speed, \(\rho\) is the number of the pole pairs of the motor, \(L_{m}\) is the stator-rotor mutual inductance, \(J\) is the system moment of inertia converted to the motor shaft, \(L_{r}\) is the rotor inductance, \(\psi_{r}\) is the rotor magnetic flux, \(i_{Ts}\) is the torque component of the stator current, and \(T_{L}\) is the load torque. There is a coupling term in Equation (6). When the load disturbance is considered, \(g_{3}(t)\), the equation of state of the revolution speed becomes  
\[\left\{ \begin{array}{l}\dot{\omega}=\frac{\rho L_{m}}{JL_{r}}\psi_{r}i_{Ts} +g_{3}(t)\\ y=\omega\\ g_{3}(t)=-\frac{T_{L}}{J}\end{array} \right.. \tag{7}\]  
The corresponding second-order ESO is as follows:  
\[\left\{ \begin{array}{l}\varepsilon_{3}=\dot{\omega}-\omega\\ \dot{\omega}=\frac{\rho L_{m}}{JL_{r}}\psi_{r}i_{Ts}+\delta_{3}(t)-\beta_{21} \varepsilon_{3}\\ \dot{\delta}_{3}(t)=-\beta_{22}fal(\varepsilon_{3},a_{3},\delta_{3})\end{array} \right. \tag{8}\]  
where \(\alpha_{3}\), \(\beta_{21}\), \(\beta_{22}\), \(\delta_{3}\) are four adjustable parameters, \(fal()\) is a nonlinear function, and it can be defined as follows:  
\[fal(\varepsilon,\alpha,\delta)=\left\{ \begin{array}{l}|\epsilon|^{\alpha}{ \rm sgn}(\varepsilon),|\epsilon|>\delta\\ \varepsilon\delta^{\alpha-1},|\epsilon|\leq\delta\end{array} \right.. \tag{9}\]  
The nonlinear state error feedback control law is  
\[\left\{ \begin{array}{l}e_{3}=\omega^{*}-\dot{\omega}\\ i_{Ts0}=\beta_{3}fal(\varepsilon_{3},a_{3},\delta_{3})\end{array}