ABSTRACT
This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS) method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on an MSV verify the effectiveness of the proposed control scheme.
ABSTRACT
In this study, 11 core coal samples were collected from deep-buried coalbed methane (CBM) reservoirs with burial depth intervals of 900-1500 m for gas estimation content by a direct method. In desorption experiments, the cumulative gas desorption data were recorded within 2 h in the field on the basis of the China National Standard method. For accuracy, two improved methods were proposed. The results show that the gas contents of deep-buried coal samples based on the China National Standard and mud methods are 3.58-9.89 m3/t (average of 6.03 m3/t) and 3.74-10.05 m3/t (average of 6.20 m3/t), respectively. The proposed Langmuir equation and logarithmic equation methods exhibited nonlinear relationships between the cumulative desorption volume and desorption time, which yield values of 6.33-13.34 m3/t (average of 9.36 m3/t) and 6.15-13.86 m3/t (average of 10.37 m3/t), respectively. In addition, the two proposed methods combine the raw data within 2 h by the China National Standard method and additional desorption points during extra time, which are helpful for the ability of the hypothetical methods to calculate the gas content. The Langmuir equation method is a relatively more accurate method to estimate the gas content in comparison with the proposed logarithmic method, which is based on the relative error and comparison plots of actual data and simulated results. From the perspective of numerical value, the Langmuir equation method gives values 1.06-3.39 times (average of 1.86 times) those of the China National Standard method. These analyses show that the proposed Langmuir equation method with extra desorption points is an effective method to determine the gas content of deep-buried CBM reservoirs.
