# Quadrotor Cascade Control System Design Based on Linear Active Disturbance Rejection Control
## 4 Simulation
: _The step input is the most severe operating condition for the system, whose rise time is almost zero, and the frequency band of the signal is inversely proportional to the rise time. In this test, we give the step expectation signal and add the step signal perturbation in the 12 th second of the simulation as a way to test the tracking performance and interference immunity of SMC&A-LADRC, giving the step expectation signal as shown in Equation (39):_  
\[\mathrm{N}(t)= \begin{cases}1.2&0\leq t<5\\ 0.2&5\leq t<10\\ 3.7&10\leq t<15\end{cases}  \tag{39}\]  
The tracking graph of the position control channel is shown in Figure 9.  
Figure 9: Tracking trajectory of the quadrotor in severe working condition. (**a–c**) are the tracking curves for each of the three position control channels. **Remark 3**. : _Reference [22] proposed a LADRC attitude control scheme with improved fal function; after simulation study, this scheme has less errors than the classical ADRC. Ideally without external disturbances, LADRC can achieve the same smooth curve as SMC&A-LADRC, but the quadrotor UAV will definitely be subject to external disturbances such as air drag and wind disturbances in operation, so comparing SMC&A-LADRC with LADRC can adequately reflect the superiority of the proposed control scheme._  
Simulation case 3 is to test the control performance of SMC&A-LADRC under severe working conditions. Figure 9a-c indicate the tracking state of \(x\), \(y\) and \(z\) channels, respectively; thus, it is obvious that the SMC&A-LADRC controller has reached smoothness at 0.1 s, which is 0.2 s faster than the response under LADRC control, and there is no obvious fluctuation. At 5 s and 10 s, the input signal is in the form of a step signal, changing the desired value, and it is obvious from the graph that there is a significant vibration in LADRC, while the curve of SMC&A-LADRC fluctuates less and is smoother. To verify that SMC&A-LADRC has good robustness, we introduce severe step disturbance at the 12 th s. It is obvious from the figure that the proposed control scheme has good anti-disturbance performance. Figure 10 shows the comparison of LADRC and SMC&A-LADRC errors in the saving state. From the figure, it can be seen that the errors of SMC&A-LADRC converge faster than LADRC when subjected to step perturbation and can converge to zero better, which proves that the control scheme proposed in this paper is reasonable and effective. The above shows that SMC&A-LADRC is able to respond quickly to the changes in the input signal, which allows the quadrotor UAV to work with the shortest path and energy optimization to achieve a long-endurance operating mode. **Remark 4**. : _In the comprehensive simulation cases 2 and 3, we designed two different external disturbances to verify the robustness of the control system; one is the gusty wind disturbance that the quadrotor UAV must be subjected to in flight, and the other is a step signal to simulate the uncertain strong external disturbance. Figures 8 and 10 illustrate that if the external noise disturbance is large, the upper bound of the disturbance also needs to be increased, but too large an upper bound may cause jitter or system runaway, which does not guarantee good tracking performance. The introduction of SMC&A-LADRC can reconcile the conflicts between the coupling and immunity performance of each channel of the quadrotor UAV and make the control system more robust, which is a practical control algorithm for quadrotor UAVs with strong external disturbances._  
Combining all the above simulation cases, simulation case 1 is to verify whether the SMC&A-LADRC control strategy proposed in this paper has good trajectory tracking performance, and simulation cases 2 and 3 are designed with wind disturbance and step disturbance to verify whether the SMC&A-LADRC control strategy has good robustness.