{'fraction_non_alphanumeric': 0.018633540372670808, 'fraction_numerical': 0.0, 'mean_word_length': 5.331877729257642, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Stable Direct Adaptive Neural Control of an Electrically Driven Dual-Axis Motion Platform Using Backstepping Technique

Abstract In this paper, the adaptive backstepping neural control (ABNC) is applied to an electrically driven dual-axis motion platform. The Dynamic model of the electrically driven dual-axis motion is obtained by coupling the dynamics of the dual-axis motion platform with the actuators (DC motors) dynamics. Thus, it is more realistic to select the actuators input voltages to be the control inputs instead of input torques, unlike the case when the actuators dynamics are not included. Unlike the existing ABNC techniques, single hidden layer feedforward neural networks with additive hidden nodes (SLFNN) are used to approximate the unknown nonlinear functions in the actual and virtual control laws where the networks parameters are adjusted based on extreme learning machine (ELM) algorithm. In ELM-based SLFNN, the hidden layer parameters are randomly selected and only the output layer weights linking the hidden layer with the output layer are needed to be updated. The adaptive update laws for the output layer weights are derived based on Lyapounov stability theory for guaranteeing semi-global boundedness of all signals in the closed-loop system. The simulation study illustrates the effectiveness of the proposed controller and shows that the system outputs track the desired trajectories with small tracking errors.