{'fraction_non_alphanumeric': 0.012838801711840228, 'fraction_numerical': 0.0, 'mean_word_length': 5.104347826086957, '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}}
Energy-Based Approach for Controller Design of Overhead Cranes: A Comparative Study

In this paper, five controllers including linear and nonlinear ones for an underactuated overhead crane are derived based on the passivity of the system. The total energy of the system and its square are used in Lyapunov candidate function to design controllers. The equilibrium point of the closed loop is proven to be asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. In addition, the optimal linear controller is also combined to force the swing angle to converge fast to zero by reaching destination of the trolley. Numerical simulations are carried out to evaluate the controllers.