Hierarchical Self-organizing Control Method Research For Under-actuated And Full-actuated Mechanical Systems

Mechanical Systems can be divided in three categories according to the relative conditions between the number of their actuators and the dimension of degrees of freedom (DOFs): under-actuated system, full-actuated system and redundant-actuated system. The control research for under-actuated and full-actuated systems has extensive application prospect, profound theoretical significance and important research value. Focusing on the general and crucial control problems for under-actuated and full-actuated mechanical systems, this paper presents the development of a novel type of hierarchical self-organizing control method based on the integration of fuzzy logic technology and optimal control theory. Our study aims to promote and facilitate the development of relevant control theory and control method, while improving the automation and intelligence level of mechanical control systems in industrial applications. Considering the variety of mechanical systems, this study chooses under-actuated gantry crane system and full-actuated two-DOFs robot system as the typical representatives and research objectives for under-actuated and full-actuated mechanical systems respectively, and carries out the research work as following:(1) Applying the Lagrangian modeling approach, the dynamic models of the gantry crane system and the two-DOFs robot system are first constructed. Through the analysis of their dynamics and common characteristics, the canonical dynamic model form for under-actuated and full-actuated mechanical systems is derived and presented. The dynamic models are then transforms into the state-space model type as the foundation of control research and design in following sections.(2) A hierarchical fuzzy optimal control method is proposed for the under-actuated gantry crane system. Initially, the control issue of gantry crane system is analyzed and transferred as a multi-objective optimization problem during the state-track process, and the corresponding optimal controller is designed according to the LQR theory. Then, the relationships between the optimal control strategy and the weighting matrixes in the cost function are analyzed and discussed, and the fuzzy logic regulator is designed for the weighting matrix configuration. After that, the hierarchical control architecture is proposed to combine the optimal control method and fuzzy logic technology, and finally presents the entire hierarchical fuzzy optimal control scheme.(3) A self-organizing fuzzy optimal control method is proposed for the full-actuated two-DOFs robot system. Due to the complexity of nonlinearity of robot dynamics, the fuzzy learning algorithm is introduced and presented for weighting matrix configuration. Based on that, the self-organizing fuzzy regulator is built to eliminate the difficulty in control rule base design and improve the precision of strategy regulation. Based on the Maximum principle for optimal control, the form of Riccati-like equation and new optimal control law are derived in the constraint of high-order nonlinear cost function, and the corresponding optimal controller is designed. In final, adapting the hierarchical architecture, the self-organizing fuzzy optimal control scheme is presented and completed.(4) Based on the Lyapunov stability theorem and its direct stability analysis method, the generalized stability of the hierarchical fuzzy optimal control is analyzed and proved; then the sufficient condition for Lyapunov stability for the nonlinear high-order optimal control system is derived; in further, asymptotical stability of the self-organizing fuzzy optimal control is proved and discussed.(5) According to the control designs above, a series of simulation research are carried out to testify the control performances, principles and properties of the hierarchical fuzzy optimal control method and self-organizing fuzzy optimal control method. Through these simulations, their effectiveness and advances in multiple control objectives optimization, dealing with dynamic coupling effects and other perspectives are verified and analyzed.