## 4 Simulation Analysis
In the observation of \(x_{3}\), the initial maximum observation error of NDO reaches +250\(\sim\)\(--\)280 and gradually stabilizes to +15\(--\)15, while the error of GSTDO is almost 0. In the observation of \(d\), the initial maximum observation error of NDO reaches \(-\)1. It gradually stabilizes to +0.02\(--\)0.02 after 1.5 s, and the initial maximum observation error of GSTDO is +0.6\(\sim\)\(-\)1, but it converges to the actual value. In the observation of \(q\), the initial maximum observation error of NDO reaches \(-\)1 and gradually stabilizes to +0.07\(--\)0.07 after 0.5 s, and the initial maximum observation error of GSTDO is +0.6\(\sim\)\(-\)1 but converges to the actual value in 0.03 s. In summary, NDO has an obvious observation error at the beginning, it takes some time to approach the true value and there will always be an observation error. The GSTDOs proposed in this paper can observe the real value from the beginning and keep the observation error at almost zero, and the convergence time is lower. This provides great convenience for solving modeling uncertainties that cannot be directly obtained in practice and values that cannot be directly measured. In order to further verify the effectiveness of the controller and eliminate the influence of the observer on it. In the experiment, both controllers are compared based on the observer proposed in this paper. The results of GSTBSMC and SMC are shown in Figures 8 and 9. The initial maximum tracking error of SMC is +0.03\({}^{\circ}\), which gradually sta  
Figure 6: Comparison of the observational effects of GSTDO and NDO in Experiment 1.  
bilizes to +0.005\(-\)\(-\)0.005\({}^{\circ}\), and the initial maximum tracking error of GSTBSMC is \(\pm\)0.03\({}^{\circ}\), which in a shorter time of 0.5 s converges to the desired curve, and the error stabilizes at +0.0003\(-\)\(-\)0.0003\({}^{\circ}\). Obviously, GSTBSMC still has better tracking performance and can asymptotically expect the curve in a shorter time. Its error value is very small, with no significant fluctuations. Figure 8: Comparison of the tracking effect of GSTBSMC and SMC in Experiment 1. Figure 7: Comparison of the observation error of GSTDO and NDO in Experiment 1. Then, in order to verify the universal applicability of the control algorithm, the amplitude of the control target signal and disturbances is changed, and the two control methods are compared. The sinusoidal signal \(6\sin t\) is selected as the control target, the mismatched disturbance \(d\) is \(\cos t\) and the matched disturbance \(q\) is \(\cos t+1\). The tracking performance of the two controllers under the same conditions is shown in Figure 10, and the tracking error curve is shown in Figure 11. It is obvious that GSTDO-GSTSMC has better tracking performance. Compared with NDO-SMC, the maximum initial tracking error is \(+0.7\)\(\sim\)\(-1.9^{\circ}\), and the maximum initial tracking error of GSTDO-GSTSMC is \(-0.05^{\circ}\), which can approach the desired curve in a short time of 0.5 s. In the presence of disturbances, the error of NDO-SMC will increase significantly, and the proposed controller can still guarantee good tracking performance. The control input of GSTDO-GSTSMC is normalized as shown in Figure 12 below. Figure 10: Comparison of the tracking results of GSTDO-GSTBSMC and NDO-SMC in Experiment 2. Figure 9: Tracking error comparison between GSTBSMC and SMC in Experiment 1. The observation performance of the observer in the above two control methods is shown in Figures 13 and 14. In the experiment, \(x_{2}\), \(x_{3}\), mismatched perturbation \(d\) and matched perturbation \(q\) were observed, respectively. It can be seen from the observation results that the GSTDO proposed in this paper has better observation performance. In the observation of \(x_{2}\), the initial maximum observation error of NDO reaches +27\(\sim\)--15 and gradually stabilizes to +0.4\(\sim\)-0.1, and the GSTDO error is almost 0.