# Finite-Time Height Control of Quadrotor UAVs
## 5 Simulation and Experiment Results
The parameters of the integral sliding mode controller are \(k_{1}=55\), \(k_{2}=0.5\) and \(k_{3}=0.5\). Figure 7 shows the simulation results of tracking the periodic signal. Figure 5: Tracking curves for the fixed signal in the inner loop. Figure 6: Disturbance observation curve for the fixed signal by the finite-time ESO. As can be seen from Figure 7, when tracking the periodic signal \(z_{d}(t)=2+0.5 sin(0.01t)[\text{m}]\), the actual height \(z(t)\) also converges to the expected height \(z_{d}(t)\) quickly and accurately. Figure 8 shows the tracking error for the period signal. As can be seen from Figure 8, the tracking error \(e(t)\) quickly converges to a small neighborhood around zero and then remains within an error range of a neighborhood radius 0.034 m. Figure 9 shows the curve of the inner-loop control system for tracking the periodic signal. As can be seen from Figure 9, when tracking periodic signals, \(\tau(t)\) can also be tracked stably and quickly by \(x_{1}(t)\), state \(x_{1}(t)\) can be estimated by \(z_{1}(t)\) in real time, and the error converges to small enough within a finite time. Figure 10 shows the disturbance observation curve of the finite-time ESO when tracking the periodic signal. Figure 10 shows the tracking of the external disturbance \(\tilde{\xi}(t)\) by the finite-time ESO. Also, after a period of convergence time, the estimated value \(z_{2}(t)\) is simulated for the external disturbance \(\tilde{\xi}(t)\), and the peak value is almost the same as the trend. Figure 8: Tracking error for the period signal. Figure 7: Simulation result of tracking the period signal. Therefore, through the above two simulations, it can be proved that the dual closed-loop control scheme designed in this paper is effective for the height control of the quadrotor UAV. To highlight the advantages of the proposed control strategy in this paper, experiments are carried out by comparing both method one in [30] and method two in [31]. Note that there is also a super-twisting ESO and a super-twisting controller proposed in [30] for a quadrotor UAV. The main different between [30] and this paper is that there is a dual closed-loop control frame in this paper. Similarly, [31] introduces a dual closed-loop control frame, but there are active disturbance rejection controls and proportional-derivative controls in the inner and outer loops, respectively. The experiment results are shown with a quadrotor UAV in Figure 11.  
Figure 11: Performance comparison of the height control methods. Figure 9: Tracking curves for the periodic signal in the inner loop. In Figure 11, it is obtained that the proposed dual closed-loop control frame shows better effects on a characteristic of zero overshoot than method one in [30]. In addition, compared with method two from [31], it is obvious to see that the proposed control strategy in this paper achieves a more desired result. Also, existence of the proportional-derivative controller in the outer loop weakens stability performances of the quadrotor UAV. By replacing the proportional-derivative controller with an integral sliding mode controller, the experiment results show greater robustness, as shown in Figure 4:0