Motion Control For Underactuated Mechanical Systems

The underactuated mechanical systems are characterized by the fact that they have fewer actuators than the number of system state dimensions .The study is a top issue belongs to the control area. The reason why underactuated mechanical systems has widespread attention by researchers was because it's have incomparable advantages than those with full-drive systems in saving energy, enhancing system flexibility, reducing weight and costs and so on. The underactuated characteristics made the controller design more difficult. The control of underactuated mechanical systems has important application value and theoretical value. The main objects includes spacecraft, marine vessels, robots, transport and reference systems. Underactuated characteristics of the system were mainly due to the dynamics of the system itself, saving money or drive failure and other causes. In this thesis, we take overhead crane, Acrobot robot, ball and beam system as the research object of the underactuated system controller design and stability analysis. The work accomplished includes the following:Firstly, by a large number of readings, summarized the reasons causing the system to underactuated characteristics, analyzed the significance of underactuated systems research, outlined the main object of the study, for different research object illustrated its system model transformation, controller design and stability analysis, Then, the objective of this dissertation is proposed.Secondly, based on Euler - Lagrange method, we established the dynamic model of underactuated systems. Established overhead crane, Acrobot robot and the ball and beam typical underactuated mechanical systems'models. The structural characteristics of the under-actuated mechanical system model were analyzed. Propose cascade norm forms of underactuated system and the methods transform the model to cascade norm forms at home and abroad.Thirdly, transformed the underactuated overhead crane and Acrobot systems into cascade norm forms. Expanded the systems to common forms and adds disturbances, increased difficulty for the controller design. Presents a kind of sliding mode controller, to eliminate chattering, use the hyperbolic tangent function instead of sign function. The systems'asymptotically stable and robustness are proved by using Lyapunov theory and perturbation theory. This method can be applied to other underactuated systems. Using MATLAB simulation; simulation results demonstrate the efficacy on the anti-swing control of overhead crane systems and the Acrobot balance control system.Fourthly, for the underactuated ball and beam system which in cascade norm form, according to the state space expression, increasing the internal parameter uncertainties, and use backstepping adaptive controller to realize the control of the internal parameter uncertainty. Increased external interference terms, using dissipation theory to achieve the robustness to external disturbances. Using MATLAB simulation, simulation results demonstrate this method on the effectiveness of ball and beam system stability control and the boundedness of parameter estimation.Finally, the comparisons of several models transform methods and control methods are summarized and analyzed which describes the advantages and deficiencies. In this paper, every control method is given stability provability and simulation example as well results respectively, In summing up, obtained the main conclusions in this paper and the prospect of future research...